11institutetext: Yaochen Zhu 22institutetext: Department of Electrical and
Computer Engineering, University of Virginia, 22email<EMAIL_ADDRESS>33institutetext: Jing Ma 44institutetext: Department of Computer Science,
University of Virginia, 44email<EMAIL_ADDRESS>55institutetext: Jundong
Li 66institutetext: Department of Electrical and Computer Engineering,
Department of Computer Science, and School of Data Science, University of
Virginia, 66email<EMAIL_ADDRESS>
# Causal Inference in Recommender Systems: A Survey of Strategies for Bias
Mitigation, Explanation, and Generalization

Yaochen Zhu  Jing Ma  and Jundong Li

###### Abstract

In the era of information overload, recommender systems (RSs) have become an
indispensable part of online service platforms. Traditional RSs estimate user
interests and predict their future behaviors by utilizing correlations in the
observational user historical activities, user profiles, and the content of
interacted items. However, since the inherent causal reasons that lead to the
observed user behaviors are not considered, multiple types of biases could
exist in the generated recommendations. In addition, the causal motives that
drive user activities are usually entangled in these RSs, where the
explainability and generalization abilities of recommendations cannot be
guaranteed. To address these drawbacks, recent years have witnessed an upsurge
of interest in enhancing traditional RSs with causal inference techniques. In
this survey, we provide a systematic overview of causal RSs and help readers
gain a comprehensive understanding of this promising area. We start with the
basic concepts of traditional RSs and their limitations due to the lack of
causal reasoning ability. We then discuss how different causal inference
techniques can be introduced to address these challenges, with an emphasis on
debiasing, explainability promotion, and generalization improvement.
Furthermore, we thoroughly analyze various evaluation strategies for causal
RSs, focusing especially on how to reliably estimate their performance with
biased data if the causal effects of interests are unavailable. Finally, we
provide insights into potential directions for future causal RS research.

##  1 Introduction

With information growing exponentially on the web, recommender systems (RSs)
are playing an increasingly pivotal role in modern online services, due to
their ability to automatically deliver items111We use the term item in a broad
sense to refer to anything recommendable to users, such as news
liu2010personalized , jobs paparrizos2011machine , articles
wang2011collaborative , music yi2021cross , movies harper2015movielens ,
micro-videos xie2020multimodal , PoIs ye2011exploiting , hashtags
gong2016hashtag , etc. to users based on their personalized interests.
Traditional RSs can be mainly categorized into three classes
ricci2011introduction : Collaborative filtering-based methods
koren2022advances , content-based methods lops2011content , and hybrid methods
ccano2017hybrid . Collaborative filtering-based RSs estimate user interests
and predict their future behaviors by exploiting their past activities, such
as browsing, clicking, purchases, etc. Content-based methods, on the other
hand, predict new recommendations by matching user interests with item
content. Hybrid methods combine the advantages of both worlds, where
collaborative information and user/item feature information are
comprehensively considered to generate more accurate recommendations.

Although recent years have witnessed substantial achievements for all three
classes of RSs introduced above, a great limitation of these methods is that
they can only estimate user interests and predict future recommendations based
on correlations in the observational user historical behaviors and user/item
features, which guarantee no causal implications yao2021survey ; gao2022causal
. For example, a collaborative filtering-based RS may discover that several
drama shows from a certain genre tend to have high ratings from a group of
users, and conclude that we should keep recommending drama shows from the same
genre to these users. But there is an important question: Are the high ratings
caused by the fact that the users indeed like drama shows from this genre, or
they were limitedly exposed to drama shows from the same genre (i.e., exposure
bias), and if given a chance, they would prefer something new to watch? In
addition, a content-based RS may observe that micro-videos with certain
features are associated with more clicks and conclude that these features may
reflect the current trend of user interests. But are the clicks because these
micro-videos tend to have sensational titles as clickbait where users could be
easily deceived? Moreover, if the titles of these micro-videos are changed to
the ones that reflect their true content, would users still click them? The
above questions are causal in nature because they either ask about the effects
of an intervention (e.g., what the rating would be if a new drama show is made
exposed to the user) or a counterfactual outcome (e.g., would the user still
click a micro-video if its title had been changed to faithfully reflect the
content), rather than mere associations in the observational data. According
to Pearl pearl2018book , these questions lie on Rungs 2 and 3 of the Ladder of
Causality, i.e., interventional and counterfactual reasoning, and they cannot
be answered by traditional RSs that reason only with associations, which lie
on Rung 1 of the ladder.

Why are these causal questions important for RSs? The first reason is that
failing to address them may easily incur bias in recommendations, which can
get unnoticed for a long time. If the collaborative filtering-based RSs
mentioned above mistake exposure bias for user interests, they would amplify
the bias by continuously recommending users with similar items; eventually,
recommendations will lose serendipity, and users’ online experience can be
severely degraded. Similarly, for the content-based micro-video RSs, if they
cannot distinguish clicks due to user interests from the ones deceived by
clickbait, they may over-recommend micro-videos with sensational titles, which
is unfair to the uploaders of high-quality micro-videos who put much effort
into designing the content. In addition, understanding the cause of user
activities can help improve the explainability of recommendations. Consider
the causal question of whether a user purchases an item due to its quality or
its low price. Pursuing the causal explanations behind user behaviors can help
service providers to enhance the RS algorithm based on users’ personalized
preferences. Finally, causal inference allows us to identify and base
recommendations on causal relations that are stable and invariant, while
discarding other correlations that are undesirable or susceptible to change.
Take restaurant recommendations as an example. Users can choose a restaurant
because of its convenience (e.g., going to a nearby fast food shop to quickly
grab a bite, but they do not necessarily like it, a non-stable correlation) or
due to their personal interests (e.g., traveling far away for a hot-pot
restaurant, a stable causal relation). If an RS can properly disentangle
users’ intent that causally affects their previous restaurant visits, even if
the convenience levels of different restaurants may change due to various
internal or external reasons such as users’ moving to a new place, the system
can still adapt well to the new situation. From this aspect, the
generalization ability of the causal RSs can be substantially improved.

This survey provides a systematic overview of recent advances in causal RS
research. The organization is illustrated in Fig. 1. We start with the
fundamental concepts of traditional RSs and their limitation of correlational
reasoning in Section 2. Then Section 3 recaps two important causal inference
paradigms in machine learning and statistics, and shows their connections with
the recommendation task. Section 4 thoroughly discusses how different causal
inference techniques can be introduced to address the limitations of
traditional RSs, with an emphasis on debiasing, explainability promotion, and
generalization improvement. Section 5 summarizes the general evaluation
strategies for causal RSs. Finally, Sections 6 and 7 discuss prospective open
questions and future directions for causal RSs and conclude this survey.

Figure 1: An overview of the structure of this survey and connections between
different sections.

##  2 Recommender System Basics

To keep this survey compact, we confine our discussions to simple RSs with $I$
users and $J$ items. The main data for the RSs, i.e., users’ historical
behaviors, are represented by a user-item rating matrix
$\mathbf{R}\in\mathbb{R}^{I\times J}$, where a non-zero element $r_{ij}$
denotes user $i$’s rating to item $j$, and a zero element $r^{0}_{ik}$
indicates the rating is missing 222We use rating to refer to any user-item
interaction that can be represented by a numerical value. This includes both
explicit feedback such as likes/dislikes, and implicit feedback such as views
and clicks. When $r_{ij}$ represents implicit feedback, the missing elements
$r^{0}_{ik}$ in $\mathbf{R}$ may be used as weak negative feedback in the
training phase hu2008collaborative . This may complicate the causal problems.
Therefore, we assume RSs are trained on observed ratings to simplify the
discussion unless specified otherwise.. To make the discussions of RSs
compatible with causal inference, we take a probabilistic view of $\mathbf{R}$
mnih2007probabilistic , where $r_{ij}$ is assumed to be the realized value of
the random variable $R$ dependent on user $i$ and item $j$333However, we do
not distinguish random variables and their specific realizations if there is
no risk of confusion. For simplicity, we assume $R$ to be Gaussian unless
specified otherwise.. In addition to $\mathbf{R}$, an RS usually has access to
side information like user features
$\mathbf{f}^{u}_{i}\in\mathbb{R}^{K^{u}_{F}}$, such as her age, gender,
location, etc., or item features
$\mathbf{f}^{v}_{j}\in\mathbb{R}^{K^{v}_{F}}$, such as its content and textual
description. $K^{u}_{F}$ and $K^{v}_{F}$ are the dimensions of user and item
features, respectively. The main purpose of an RS is to predict users’ ratings
for previously uninteracted items (i.e., the missing values $r^{0}_{ik}$ in
$\mathbf{R}$) based on the observed ratings $r_{ij}$ in $\mathbf{R}$ and the
available user and item side information such as $\mathbf{f}^{u}_{i}$ and
$\mathbf{f}^{v}_{j}$, such that new relevant items can be properly recommended
based on users’ personalized interests.

###  2.1 Collaborative Filtering

Collaborative filtering-based RSs recommend new items by leveraging user
ratings in the past. They generally consider the ratings $r_{ij}$ as being
generated from a user latent variable $\mathbf{u}_{i}\in\mathbb{R}^{K}$ that
represents user interests and an item latent variable
$\mathbf{v}_{j}\in\mathbb{R}^{K}$ that encodes the item attributes (i.e., item
latent semantic information), where $K$ is the dimension of the latent space.
Here we list three widely-used collaborative filtering-based RSs, which will
be frequently used as examples in this survey:

  * •

Matrix Factorization (MF) koren2009matrix . MF models $r_{ij}$ with the inner
product between $\mathbf{u}_{i}$ and $\mathbf{v}_{j}$, where
$r_{ij}\sim\mathcal{N}(\mathbf{u}_{i}^{T}\cdot\mathbf{v}_{j},\sigma_{ij}^{2})$
and $\sigma_{ij}^{2}$ is the predetermined variance444For works that do not
explicitly treat $r_{ij}$ as a random variable, we assume it follows a
Gaussian distribution with zero variance. The generative process then becomes
as $r_{ij}=\mathbf{u}_{i}^{T}\cdot\mathbf{v}_{j}$. .

  * •

Deep Matrix Factorization (DMF) xue2017deep . DMF extends MF by applying deep
neural networks (DNNs) zhang2019deep , i.e.,
$f^{u}_{nn},f^{v}_{nn}:\mathbb{R}^{K}\rightarrow\mathbb{R}^{K^{\prime}}$, to
$\mathbf{u}_{i}$ and $\mathbf{v}_{j}$, where the ratings are assumed to be
generated as $r_{ij}\sim\mathcal{N}(f_{nn}^{u}(\mathbf{u}_{i})^{T}\cdot
f^{v}_{nn}(\mathbf{v}_{j}),\sigma_{ij}^{2})$.

  * •

Auto-encoder (AE)-based RSs wu2016collaborative ; liang2018variational  model
user $i$’s ratings to all $J$ items as
$\mathbf{r}_{i}\sim\mathcal{N}(f^{u}_{nn}(\mathbf{u}_{i}),\boldsymbol{\sigma}_{i}^{2}\cdot\mathbf{I}_{K})$,
where $f^{u}_{nn}:\mathbb{R}^{K}\rightarrow\mathbb{R}^{J}$ is a DNN and item
latent variables $\mathbf{v}_{j}$ for all items are implicit in last layer
weights of the decoder zhu2022mutually .

In the training phase, the models learn the latent variables $\mathbf{u}_{i}$,
$\mathbf{v}_{j}$ and the associated function $f_{nn}$ by fitting on the
observed ratings $r_{ij}$ (e.g., via maximum likelihood estimation, which
essentially estimates the conditional distribution
$p(r_{ij}|\mathbf{u}_{i},\mathbf{v}_{j})$ from the observational data
xu2021causal ). Afterward, we can use them to predict new ratings for
previously uninteracted items $k$, e.g.,
$\hat{r}^{\textrm{MF}}_{ik}=\mathbf{u}_{i}^{T}\cdot\mathbf{v}_{k}$ for MF,
$\hat{r}^{\textrm{DMF}}_{ik}=f_{nn}^{u}(\mathbf{u}_{i})^{T}\cdot
f^{v}_{nn}(\mathbf{v}_{k})$ for DMF, and
$\hat{r}^{\textrm{AE}}_{ik}=f^{u}_{nn}(\mathbf{u}_{i})_{k}$ for AE-based RSs,
where the top ones that best match users’ interests can be selected as
recommendations. Traditional collaborative filtering-based RSs reasons with
correlations. Ideally, we would expect $\mathbf{u}_{i}$, $\mathbf{v}_{j}$ and
$f_{nn}$ to capture the causal influence of user interests and item attributes
on ratings, i.e., what the rating would be if item $j$ is made exposed to user
$i$ xu2021causal . However, since the collected rating data are observational
rather than experimental, what actually learned by $\mathbf{u}_{i}$,
$\mathbf{v}_{j}$, and $f$ are the co-occurrence patterns in users’ past
behaviors, which guarantee no causal implications. Consequently, spurious
correlations and biases can be captured by the model, which will be amplified
in future recommendations wang2021deconfounded . Furthermore, the learned user
latent variable $\mathbf{u}_{i}$ generally entangles different factors that
causally determine user interests. From this perspective, the explainability
and generalization of these methods cannot be guaranteed.

###  2.2 Content-Based Recommender Systems

Personalized content-based RSs (CBRSs) estimate user interests based on the
features of the items they have interacted with. These models typically encode
user interests into user latent variables $\mathbf{u}_{i}\in\mathbb{R}^{K}$
and assume that the ratings are generated by matching user interests with item
content, i.e.,
$r_{ij}\sim\mathcal{N}(f(\mathbf{u}_{i},\mathbf{f}^{v}_{j}),\sigma_{ij})$,
where $f$ is a matching function. The training of personalized CBRSs follow
similar steps as collaborative filtering, where $\mathbf{u}_{i}$ and $f$ are
learned by fitting on the observed ratings (which essentially estimates the
conditional distribution $p(r_{ij}|\mathbf{u}_{i},\mathbf{f}^{v}_{j})$ from
the observational data), and new ratings can be predicted by
$\hat{r}_{ik}=f(\mathbf{u}_{i},\mathbf{f}^{v}_{k})$. The key step of building
a CBRS is to create item features $\mathbf{f}^{v}_{j}$ that can best reflect
user interests, which crucially depends on the item being recommended. For
example, for micro-videos, the visual, audio, and textual modalities are
comprehensively considered such that users’ interest in different aspects of a
micro-video can be well captured wei2019mmgcn .

Traditional content-based RSs cannot model the causal influence of user
interests $\mathbf{u}_{i}$ and item content $\mathbf{f}^{v}_{j}$ on user
rating $r_{ij}$. The reason is that, factors other than users’ interests in
the item content, such as users’ being deceived by clickbaits (e.g.,
sensational titles of micro-videos) wang2021clicks , etc., can create an
undesirable association between item content $\mathbf{f}^{v}_{j}$ and user
ratings $r_{ij}$ in the observed dataset, where the bias can be captured by
the user latent variables $\mathbf{u}_{i}$ and the matching function $f$, and
perpetuates into future recommendations.

###  2.3 Hybrid Recommendation

Hybrid RSs combine user/item side information with collaborative filtering to
enhance the recommendations. A commonly-used hybrid strategy is to augment
user and item latent variables $\mathbf{u}_{i}$ and $\mathbf{v}_{j}$ with
user/item side information $\mathbf{f}^{v}_{i}$ and $\mathbf{f}^{v}_{j}$ in
existing collaborative filtering methods by replacing $\mathbf{u}_{i}$ and
$\mathbf{v}_{j}$ with
$\mathbf{u}^{+}_{i}=[\mathbf{u}_{i}||\mathbf{f}^{u}_{i}]$ and
$\mathbf{v}^{+}_{j}=[\mathbf{v}_{j}||\mathbf{f}^{v}_{j}]$ in MF, DMF, and AE-
based RSs, where $[\cdot||\cdot]$ represents vector concatenation
koren2008factorization ; zhu2022variational . The dimensions of
$\mathbf{u}_{i}$ and $\mathbf{v}_{j}$ that encode the collaborative
information are adjusted accordingly to make $\mathbf{u}^{+}_{i}$ and
$\mathbf{v}^{+}_{j}$ compatible in the model. Another important class of
hybrid RS is the factorization machine (FM) rendle2010factorization  and its
extensions like he2017neuralf ; li2022causalfm , which can be viewed as
learning a bi-linear function $f_{fm}$ where the ratings are generated by
$r_{ij}\sim\mathcal{N}(f_{fm}(\mathbf{u}_{i},\mathbf{v}_{j},\mathbf{f}^{u}_{i},\mathbf{f}^{v}_{j}),\sigma_{ij}^{2})$.
Simple hybrid strategies cannot break the correlational reasoning limitation
of collaborative filtering and content-based RSs, because the objective of the
hybridization is still to improve the models’ fitting on the observational
user historical behaviors (i.e., estimating conditional distribution
$p(r_{ij}|\mathbf{u}_{i},\mathbf{v}_{j},\mathbf{f}^{u}_{i},\mathbf{f}^{v}_{j})$
from the data), where the causal reasons that lead to the observed user
behaviors are not considered. However, the idea of introducing extra user/item
side information is important for building causal RSs. The reason is that,
combined with the domain knowledge of human experts, the side information can
help form more comprehensive causal relations among the variables of
interests, such as user interests, item attributes, historical ratings, and
other important covariates that may lead to spurious correlations and biases,
which is usually a crucial step for causal reasoning in recommendations.

##  3 Causal Recommender Systems: Preliminaries

In the previous section, we discussed the recommendation strategies of the
traditional RSs and their limitations due to correlational reasoning on
observational user behaviors. In this section, we introduce two causal
inference frameworks, i.e., Rubin’s potential outcome framework (also known as
the Rubin causal model, RCM) imbens2015causal  and Pearl’s structural causal
model (SCM) pearl2009causality , in the context of RSs, aiming to provide a
theoretically rigorous basis for reasoning with correlation and causation in
recommendations. We show that both RCM and SCM are powerful frameworks to
build RSs with causal reasoning ability (i.e., causal RSs), but they are best
suited for different tasks and questions. The discussions in this section
serve as the foundation for more in-depth discussions of the state-of-the-art
causal RS models in Section 4.

###  3.1 Rubin’s Potential Outcome Framework

#### Motivation of Applications in RSs

To understand the correlational reasoning nature of traditional RSs, we note
that naively fitting models on the observed ratings can only answer the
question “what the rating would be if we observe an item was exposed to the
user”. Since item exposure is not randomized in the collected dataset 555which
can be attributed to multiple reasons such as users’ self-search
wang2021combating , the recommendations of previous models liu2020general ,
the position where the items are displayed wang2018position , item popularity
abdollahpouri2017controlling , etc. Generally, RCM-based causal RSs are
agnostic to the specific reason that causes the exposure bias., the predicate
“the item was exposed to the user” per se contains extra information about the
user-item pair (e.g., the item could be more popular than other non-exposed
items), which cannot be generalized to the rating predictions of arbitrary
user-item pairs. Therefore, what RS asks is essentially an interventional
question (and therefore a causal inference question), i.e., what the rating
would be if an item is made exposed to the user. To address this question,
RCM-based RSs draw inspiration from clinical trials, where exposing a user to
an item is compared to subjecting a patient to a treatment, and the user
ratings are analogous to the outcomes of the patients after the treatment
schnabel2016recommendations ; wu2022opportunity . Accordingly, RCM-based RSs
aim to estimate the causal effects of the treatments (exposing a user to an
item) on the outcomes (user ratings), despite the possible correlations
between the treatment assignment and the outcome observations
schnabel2016recommendations .

#### Definitions and Objectives

We first introduce necessary symbols and definitions to connect RCM with RSs.
We consider the unit as the user-item pair $(i,j)$ that can receive the
treatment “exposing user $i$ to item $j$”, and the population as all user-item
pairs $\mathcal{PO}=\\{(i,j),1\leq i,j\leq I,J\\}$ bonner2018causal . We start
by using a binary scalar $a_{ij}$ to denote the exposure status of item $j$
for user $i$, i.e., the assigned treatment. We further define the rating
potential outcome $r_{ij}(a_{ij}=1)$ as user $i$’s rating to item $j$ if the
item is made exposed to the user and $r_{ij}(a_{ij}=0)$ as the rating if the
item is not exposed wang2020causal . For user $i$, if she rated item $j$, we
observe $r_{ij}(a_{ij}=1)=r_{ij}$. Otherwise, we observe the baseline
potential outcome $r_{ij}(a_{ij}=0)=0$, which is usually ignored in debias-
oriented causal RS research schnabel2016recommendations ; steck2010training
666In the uplift evaluation of RSs that aims to estimate how recommendations
change user behaviors sharma2015estimating , $r_{ij}(a_{ij}=0)$ may be used to
represent user $i$’s rating to item $j$ through self-searching sato2019uplift
.. Similar to clinical trials, we can define the treatment group
$\mathcal{T}=\\{(i,j):a_{ij}=1\\}$ as the set of user-item pairs where user
$i$ is exposed to item $j$, and define the non-treatment group
$\mathcal{NT}=\\{(i,k):a_{ik}=0\\}$ accordingly. The purpose of RSs, under the
RCM framework, can be framed as utilizing the observed ratings from units in
the treatment group $\mathcal{T}$ to unbiasedly estimate the rating potential
outcomes for units from the population $\mathcal{PO}$, despite the possible
correlations between item exposures $a_{ij}$ and user ratings $r_{ij}$ in the
collected data.

#### Causal Analysis of Traditional RSs

Figure 2: A classical example of exposure bias in RSs steck2010training . The
example is composed of two horror lovers who always rate horror movies with
five while hating romance movies, and two romance lovers would who do exactly
the opposite. (a) shows the observed ratings $r_{ij}$. (b) shows the rating
potential outcomes $r_{ij}(a_{ij}=1)$. (c) shows the rating predictions of an
RS that maximizes the likelihood of the observed ratings in (a), but the RS is
bad because it predicts all ratings to five.

Traditional RSs naively train a rating prediction model that best fits the
ratings in the treatment group $\mathcal{T}$ (e.g., via maximum likelihood
introduced in Section 2) to estimate the unobserved rating potential outcomes
$r_{ij}(a_{ij}=1)$ for user-item pairs in $\mathcal{NT}$ chen2020bias , which
neglect the fact that exposure bias can lead to a systematic difference in the
distribution of $r_{ij}(a_{ij}=1)$ between $\mathcal{T}$ and $\mathcal{NT}$.
For example, users tend to rate items they like in reality, which could lead
to the following spurious correlation between item exposure $a_{ij}$ and
rating potential outcome $r_{ij}(a_{ij}=1)$:

$p(r_{ij}(a_{ij}=1)\mathrm{\ is\ high}|a_{ij}=1)>p(r_{ij}(a_{ij}=1)\mathrm{\
is\ high}|a_{ij}=0),$ (1)

i.e., users who have rated an item $j$ may have systematically higher ratings
than users who haven’t rated it yet. In this case, traditional RSs may have a
tendency to overestimate the ratings for units in $\mathcal{NT}$ (see Fig. 2
for an intuitive example). Theoretically, RCM attributes the exposure bias in
the collected dataset to the violation of the unconfoundedness assumption
imbens2015causal  defined as follows:

$r_{ij}(a_{ij}=1)\perp a_{ij}.$ (2)

The rationale is that, if Eq. (2) holds, the exposure of user $i$ to item $j$
(i.e., $a_{ij}$) is independent of the rating potential outcome
$r_{ij}(a_{ij}=1)$, which implies that $r_{ij}(a_{ij}=1)$ in $\mathcal{T}$ and
$\mathcal{NT}$ follows the same distribution. Therefore, the exposure of the
items is randomized, and exposure bias such as Eq. (1) will not exist
wang2020causal .

#### Potential Outcome Estimation with the RCM Framework

One classic solution from the RCM-based framework to address the exposure bias
is that we find user and item covariates $C$, such that in each data stratum
specified by $C=\mathbf{c}$, users’ exposure to items are randomized
imbens2015causal . The property of the covariates $C$ can be formulated as the
conditional unconfoundedness assumption as follows:

$r_{ij}(a_{ij}=1)\perp a_{ij}\mid\mathbf{c}.$ (3)

$C$ is sometimes non-rigorously referred to as confounder in the literature,
but we will see its formal definition in the next subsection. If Eq. (3)
holds, the item exposures are independent of the rating potential outcomes in
each data stratum specified by $C=\mathbf{c}$, and the exposure bias can be
attributed solely to the discrepancy in the distribution of the covariates
$C=\mathbf{c}$ between the treatment group $\mathcal{T}$ and the population
$\mathcal{PO}$, i.e., $p(\mathbf{c}|a_{ij}=1)$ and $p(\mathbf{c})$777! We can
gain an intuition of this claim from Fig. 2. Suppose covariates $C$ represent
the two-dimensional features (user type, movie type). Given $C=\mathbf{c}$,
$r_{ij}(a_{ij}=1)\perp a_{ij}\mid\mathbf{c}$ described in Eq. (3) is satisfied
because in each data stratum specified by $C=\mathbf{c}$ (i.e., the four
$2\times 2$ blocks in Fig. 2-(b)), $r_{ij}(a_{ij}=1)$ is constant. Fig. 2-(a)
shows that for the treatment group $\mathcal{T}$, $p(\mathbf{c}|a_{ij}=1)=1/2$
for $\mathbf{c}\in\mathcal{C}_{1}=\\{(\text{horror fan, horror
movie}),(\text{romance fan, romance movie})\\}$ and $p(\mathbf{c}|a_{ij}=1)=0$
for $\mathbf{c}\in\mathcal{C}_{2}=\\{(\text{horror fan, romance
movie}),(\text{romance fan, horror movie})\\}$. In contrast, for the
population $\mathcal{PO}$, $p(\mathbf{c})=1/4$ for
$\mathbf{c}\in\mathcal{C}_{1}\cup\mathcal{C}_{2}$. Therefore, in the treatment
group $\mathcal{T}$, user-item pairs with covariates in $\mathcal{C}_{1}$ are
over-represented, while those with covariates in $\mathcal{C}_{2}$ are under-
represented. However, we also note that this case is too extreme to be
addressed by RCM, as $p(\mathbf{c}|a_{ij}=1)=0$ for $C\in\mathcal{C}_{2}$
violates the positivity assumption mentioned in the above attention box.
Therefore, we can reweight the observed ratings in $\mathcal{T}$ based on the
covariates $C$ to address the bias, such that they can be viewed as pseudo
randomized samples. This leads to inverse propensity weighting (IPW), which
eliminates the exposure bias from the data’s perspective
schnabel2016recommendations . In addition, we can also adjust the influence of
$C$ in the RS model, where the exposure bias is addressed from the model side
wang2020causal . Both methods will be discussed in Section 4.1.

Attention: Extra Assumptions Required by Most RCM-based RSsIn addition to
unconfoundedness, most RCM-based RS need two extra assumptions to identify the
causal effects of item exposures on ratings: (1) The stable unit treatment
assumption (SUTVA), which states that items exposed to one user cannot affect
ratings of another user. (2) The positivity assumption, which states that
every user has a positive chance of being exposed to every item
imbens2015causal . For RCM-based causal RSs introduced in this survey, these
two assumptions are tacitly accepted.

###  3.2 Pearl’s Structural Causal Model

#### Motivation of Applications in RS

Different from RCM that uses rating potential outcomes to reason with
causality and attributes the biases in observed user behaviors to non-
randomized item exposures, Pearl’s structural causal model (SCM) delves deep
into the causal mechanism that generates the observed outcomes (and biases)
and represents it with a causal graph $G=(\mathcal{N},\mathcal{E})$. The nodes
$\mathcal{N}$ specify the variables of interests, which in the context of RS
could be user interests $U$, item attributes $V$, observed ratings $R$, and
other important covariates $C$, such as item popularity, user features,
etc888In causal graphs, the subscripts $i$, $j$ for each node are omitted for
simplicity.. The directed edges $\mathcal{E}$ between nodes represent their
causal relations determined by researchers’ domain knowledge. Each node
$X\in\mathcal{N}$ is associated with a structural equation
$p_{G}(X|Pa(X))$999We also omit the mutually independent exogenous variables
for each node and summarize their randomness into the structural equations
with probability distributions gao2022causal . Subscript $G$ is used to
distinguish structural equations from other conditional relationships that can
be inferred from $G$., which describes how the parent nodes $Pa(X)$ causally
influence $X$ (i.e., the response of $X$ when setting nodes in $Pa(X)$ to
specific values)

Although RCM and SCM are generally believed to be fundamentally equivalent
pearl2009causality , both have their unique advantages. Compared to RCM, the
key advantage of SCM is that causal graph offers an intuitive and
straightforward way to encode and communicate domain knowledge and substantive
assumptions of researchers, which is beneficial even for the RCM-based RSs
wang2020causal . Furthermore, SCM is more flexible as it can represent and
reason with the causal effects between any subset of nodes in the causal graph
(e.g., between two causes $U,V$ and one outcome $R$), as well as the causal
effects along specific paths (e.g., $U\rightarrow R$ and $U_{c}\rightarrow
R$). Therefore, SCMs are broadly applicable to multiple problems in RSs (not
limited to exposure bias), such as clickbait bias, unfairness, entanglement,
domain adaptation, etc gao2022causal .

Attention: Two Caveats of SCM-based Causal RSs.There are two caveats of SCM-
based causal RSs. (1) Causal graphs for RSs often involve user, item latent
variables $U$, $V$ that encode user interests and item attributes. Most works
infer them alongside the estimation of structural equations and treat them as
if they were observed when analyzing the causal relations. Alternatively, this
can be viewed as representing users and items with their IDs (i.e., $i$ and
$j$) in the causal graph and subsuming the embedding process into the
structural equations xu2022dynamic . (2) Generally, the causal graph should
describe the causal mechanism that generates the observed data, because it
allows us to distinguish invariant, causal relations from undesirable
correlations. For example, we may argue that item popularity $C$ should be
determined by item attributes $V$, i.e., $V\rightarrow C$. But to describe the
generation of the observed ratings, causal relation $C\rightarrow V$ is
usually assumed instead as item popularity causally influences the exposure
probability of each item zhang2021causal .

#### Atomic Structures of Causal Graphs

Figure 3: (a): A generic causal graph for RS that depicts the causal influence
of user interests $U$, user conformity to the popularity trend $U_{c}$, and
item attributes $V$ on the observed ratings $R$. Specifically, the causal
paths $U\rightarrow R$ and $V\rightarrow R$ are confounded by $C_{u}$ and
$C_{v}$, which represent user features and item popularity, respectively.
(b)(c)(d): Three atomic structures identified from (a).

The structure of causal graphs represents researchers’ domain knowledge
regarding the causal generation process of the observational data, which is
the key to distinguishing stable, causal relations from other undesirable
correlations between variables of interest. Here, we use a generic causal
graph applicable to RSs in Fig. 3-(a) as a running example to illustrate three
atomic graph structures:

  * •

Chain, e.g., $C_{u}\rightarrow U\rightarrow R$. In a chain, the successor node
is assumed to be causally influenced by the ancestor nodes. In the example,
$U$ is a direct cause of $R$, whereas $C_{u}$ indirectly influences $R$ via
$U$ as a mediator.

  * •

Fork, e.g., $U\leftarrow C_{u}\rightarrow R$. In the fork, $C_{u}$ is called a
confounder as it causally influences two children $U$ and $R$. From a
probabilistic perspective, $U$ and $R$ are not independent unless conditioned
on the confounder $C_{u}$ koller2009probabilistic . This leads to the tricky
part of a fork structure, i.e., confounding effect pearl2009causality , where
an unobserved $C_{u}$ can lead to spurious correlations between $U$ and $R$.

  * •

V-structure, e.g., $U\rightarrow R\leftarrow U_{c}$. In the V-structure, $R$
is called a collider because it is under the causal influence of two parents,
i.e., $U$ and $U_{c}$. An interesting property of the V-structure is the
colliding effects pearl2009causality , where observing $R$ creates a
dependence on $U$ and $U_{c}$, even if they are marginally independent.

Confounders can lead to non-causal dependencies among variables in the
observational dataset. This could introduce bias in traditional RSs, where the
confounding effects are mistaken as causal relations. Confounding bias is a
generic problem in RSs xu2021causal , which will be further analyzed in the
following subsections. In addition, abstracted V-structure usually leads to
the entanglement of causes, which could jeopardize the explainability of RSs.
For example, a user’s purchase of an item may be due to her interest, i.e.,
$U$, or her conformity to the popularity trend, i.e., $U_{c}$. Since most RSs
summarize both into a user latent variable $U$, the V-structure $U\rightarrow
R\leftarrow U_{c}$ is abstracted away, where the two causes of the purchase
cannot be distinguished.

#### Causal Analysis of Traditional RSs

Figure 4: (a): SCM assumed by non-causal collaborative filtering-based RS.
(b): The confounded SCM that depicts the true data generation process. (c):
SCM under intervention $do(V)$.

In this section, we investigate the susceptibility of traditional
collaborative filtering-based RSs to the confounding bias. As discussed in
Section 2.1, a commonality of these models is that they estimate conditional
distribution $p(r_{ij}|\mathbf{u}_{i},\mathbf{v}_{j})$ from observed ratings
and use it to predict new ratings. For
$p(r_{ij}|\mathbf{u}_{i},\mathbf{v}_{j})$ to represent the causal influence of
user interests $\mathbf{u}_{i}$ and item attributes $\mathbf{v}_{j}$ on
ratings $r_{ij}$ (which, in the context of collaborative filtering, means the
rating of any arbitrary item $j$ that is made exposed to user $i$ xu2021causal
), the causal graph $G_{1}$ of Fig. 4-(a) is tacitly assumed, i.e., no
unobserved confounders for causal paths $U\rightarrow R$ and $V\rightarrow
R$101010This corresponds to the case where item exposures are randomized (see
the discussions in Section 3.1), as the user-item pair $(U,V)$ is not
determined by other factors associated with $R$ richardson2013single ..

However, in reality, both $U\rightarrow R$ wang2021deconfounded ; wei2021model
and $V\rightarrow R$ agarwal2019general ; chen2021autodebias  can be
confounded, where the confounding effects can be implicitly captured by
$p(r_{ij}|\mathbf{u}_{i},\mathbf{v}_{j})$ that bias future recommendations. To
reveal the bias, we consider the scenario where the causal path $V\rightarrow
R$ is confounded by $C_{v}$ (e.g., item popularity). We assume the causal path
$C_{v}\rightarrow V$ denotes the causal influence of $C_{v}$ on the exposure
probability of item $V$ zhang2021causal . In this case, the observed ratings
are generated according to the causal graph $G_{2}$ in Fig. 4-(b). Utilizing
the law of total probability, the conditional distribution
$p(r_{ij}|\mathbf{u}_{i},\mathbf{v}_{j})$ estimated from the confounded data
can be calculated as:

$p(r_{ij}|\mathbf{u}_{i},\mathbf{v}_{j})=\sum_{\mathbf{c}}p(\mathbf{c}|\mathbf{v}_{j})\cdot
p_{G_{2}}(r_{ij}|\mathbf{u}_{i},\mathbf{v}_{j},\mathbf{c})=\mathbb{E}_{p(C_{v}|\mathbf{v}_{j})}[p_{G_{2}}(r_{ij}|\mathbf{u}_{i},\mathbf{v}_{j},C_{v})].$
(4)

The issue of Eq. (4) is that, the $p(\mathbf{c}|\mathbf{v}_{j})$ term is not
causal (as we only have an edge $C_{v}\rightarrow V$ in the causal graph but
not $V\rightarrow C_{v}$). In fact, $p(\mathbf{c}|\mathbf{v}_{j})$ represents
abductive reasoning because it infers the cause $\mathbf{c}$ (e.g., item
popularity) from the effect $\mathbf{v}_{j}$ (i.e., item $j$ is exposed to
user $i$) and uses the inferred $\mathbf{c}$ to support the prediction of the
rating $r_{ij}$. However, such reasoning cannot be generalized to the rating
prediction of an arbitrary item $\mathbf{v}_{j}$, i.e., an item that is made
exposed to the user. In other words, uncontrolled confounder $C_{v}$ leaves
open a backdoor path (i.e., non-causal path) between $V$ and $R$, such that
non-causal dependence of $R$ on $V$ exists in the data, which can be captured
by traditional RSs and bias future recommendations. 111111The similarity
between this section and Section 3.1 shows us the connection between RCM-based
and SCM-based causal RSs, where the claim that when item exposure is not
randomized, “observing that an item was exposed to the user per se contains
extra information about the user-item pair” is mathematically transformed into
the abductive inference of $\mathbf{c}$ from $\mathbf{v}_{j}$ by
$p(\mathbf{c}|\mathbf{v}_{j})$.

#### Causal Reasoning with SCM

To calculate the causal effect of $\mathbf{u}_{i}$ and $\mathbf{v}_{j}$ on
$r_{ij}$, we should conduct intervention on $U$ and $V$. This means that we
set $U$, $V$ to $\mathbf{u}_{i}$, $\mathbf{v}_{j}$ regardless of the values of
their parent nodes in the causal graph, including the confounder $C_{v}$
(because these nodes determine the exposure of item $j$ to user $i$ in the
observed data). SCM denotes the intervention with do-operator as
$p(r_{ij}|do(\mathbf{u}_{i},\mathbf{v}_{j}))$ to distinguish it from the
conditional distribution $p(r_{ij}|\mathbf{u}_{i},\mathbf{v}_{j})$ that
reasons with correlations in the observational data. Consider again the causal
graph $G_{2}$ illustrated in Fig. 4-(b). The intervention on node $V$ can be
realized by removing all the incoming edges for node $V$ and setting the
structural equation $p_{G_{2}}(V|C_{v})$ deterministically as
$V=\mathbf{v}_{j}$, while other structural equations remain intact (Fig.
4-(c)). If the confounder $C_{v}$ can be determined and measured for each
item, the interventional distribution
$p(r_{ij}|do(\mathbf{u}_{i},\mathbf{v}_{j}))$ can be directly calculated from
the confounded data via backdoor adjustment pearl2009causality  as:

$p(r_{ij}|do(\mathbf{u}_{i},\mathbf{v}_{j}))=\sum_{\mathbf{c}}p_{G_{2}}(\mathbf{c})\cdot
p_{G_{2}}(r_{ij}|\mathbf{u}_{i},\mathbf{v}_{j},\mathbf{c})=\mathbb{E}_{p_{G_{2}}(C_{v})}[p_{G_{2}}(r_{ij}|\mathbf{u}_{i},\mathbf{v}_{j},C_{v})],$
(5)

which, compared with Eq. (4), blocks the abductive inference of $\mathbf{c}$
from $\mathbf{v}_{j}$, such that the causal influence of $\mathbf{u}_{i}$,
$\mathbf{v}_{j}$ on $r_{ij}$ can be properly identified.

Backdoor adjustment requires all confounders to be determined and measured in
advance, but there are other SCM-based causal inference methods that can
estimate causal effects with unknown confounders, and we refer readers to
xu2021deconfounded ; zhu2022mitigating  for details. Moreover, causal graphs
allow us to conduct other types of causal reasoning based on the encoded
causal knowledge, such as debiasing for non-confounder-induced biases (e.g.,
clickbait bias and unfairness), causal disentanglement, and causal
generalization zheng2021disentangling . These will be thoroughly discussed in
the next section.

##  4 Causal Recommender Systems: The State-of-the-Art

Based on the preliminary knowledge of RSs and causal inference discussed in
previous sections, we are ready to introduce the state-of-the-art causal RSs.
Specifically, we focus on three important topics, i.e., bias mitigation,
explainability promotion, and generalization improvement, as well as their
inter-connections, where various limitations of traditional RSs due to
correlational reasoning can be well addressed.

###  4.1 Causal Debiasing for Recommendations

The correlational reasoning of traditional RSs can inherit multiple types of
biases in the observational user behaviors and amplify them in future
recommendations chen2020bias . The biases may result in various consequences,
such as the discrepancy between offline evaluation and online metrics, loss of
diversity, reduced recommendation quality, offensive recommendations, etc.
Causal inference can distinguish stable causal relations from spurious
correlations and biases that could negatively influence the recommendations,
such that the robustness of recommendations can be improved.

#### Exposure Bias

Exposure bias in RSs broadly refers to the bias in observed ratings due to
non-randomized item exposures. From the RCM’s perspective, exposure bias can
be defined as the bias where users are favorably exposed to items depending on
their expected ratings for them (i.e., rating potential outcomes)
steck2010training . Exposure bias occurs due to various reasons, such as
users’ self-search or the recommendation of the previous RSs liu2020general ,
which leads to the down-weighting of items less likely to be exposed to users.
Since item exposures can be naturally compared with treatments in clinical
trials, we discuss the debiasing strategies with the RCM framework.

Inverse Propensity Weighting (IPW). IPW-based causal RSs aim to reweight the
biased observed ratings $r_{ij}$ for user-item pairs in the treatment group,
i.e., $\mathcal{T}=\\{(i,j):a_{ij}=1\\}$, to create pseudo randomized samples
sato2020unbiased  for unbiased training of RS models that aim to predict the
rating potential outcomes $r_{ij}(a_{ij}=1)$ for the population
$\mathcal{PO}=\\{(i,j),1\leq i,j\leq I,J\\}$. Intuitively, we can set the
weight of $r_{ij}$ for units in $\mathcal{T}$ to be the inverse of item $j$’s
exposure probability to user $i$, such that under-exposed items can be up-
weighted and vice versa. If for each user-item pair, the covariates
$\mathbf{c}$ that satisfy the conditional unconfoundedness assumption in Eq.
(3) are available, the exposure probability $e_{ij}$ can be unbiasedly
estimated from $\mathbf{c}$ via

$e_{ij}=p(a_{ij}=1|\mathbf{c})=\mathbb{E}[a_{ij}|\mathbf{c}],$ (6)

which is formally known as propensity score in causal inference literature
rosenbaum1983central .

Background: The Balancing Property of Propensity Scores.Propensity scores have
the following property called balancing imbens2015causal ; WinNT , which is
the key to proving the unbiasedness of IPW-based RSs:

$\displaystyle\mathbb{E}\Big{[}\frac{r_{ij}}{e_{ij}}\Big{|}a_{ij}=1\Big{]}=\mathbb{E}\Big{[}\frac{r_{ij}\cdot
a_{ij}}{e_{ij}}\Big{]}=\mathbb{E}\Big{[}\mathbb{E}\Big{[}\frac{r_{ij}\cdot
a_{ij}}{e_{ij}}\Big{|}\mathbf{c}\Big{]}\Big{]}$ (7) $\displaystyle=$
$\displaystyle\mathbb{E}\Big{[}\mathbb{E}\Big{[}\frac{r_{ij}(a_{ij}=1)\cdot
a_{ij}}{e_{ij}}\Big{|}\mathbf{c}\Big{]}\Big{]}\overset{(a)}{=}\mathbb{E}\Big{[}\frac{\mathbb{E}[r_{ij}(a_{ij}=1)\mid\mathbf{c}]\cdot\mathbb{E}[a_{ij}\mid\mathbf{c}]}{e_{ij}}\Big{]}$
$\displaystyle=$
$\displaystyle\mathbb{E}\Big{[}\frac{\mathbb{E}[r_{ij}(a_{ij}=1)\mid\mathbf{c}]\cdot
e_{ij}}{e_{ij}}\Big{]}=\mathbb{E}[r_{ij}(a_{ij}=1)],$

where the step $(a)$ follows the conditional unconfoundedness assumption in
Eq. (3). We first discuss the implementation of IPW-based RS and its
unbiasedness if user and item covariates $\mathbf{c}$ that satisfy Eq. (3) are
available and the propensity scores $e_{ij}$ can be calculated exactly as Eq.
(6). We denote the rating predictor of an RS that aims to predict the rating
potential outcome $r_{ij}(a_{ij}=1)$ as $\hat{r}_{ij}$ and assume
$r_{ij}(a_{ij}=1)$ follows the unit-variance Gaussian distribution. Ideally,
we would like $\hat{r}_{ij}$ to maximize the log-likelihood on the rating
potential outcomes $r_{ij}(a_{ij}=1)$ for all user-item pairs in
$\mathcal{PO}$, which is equivalent to the minimization of the mean squared
error (MSE) loss between $\hat{r}_{ij}$ and $r_{ij}(a_{ij}=1)$ as follows:

$\mathcal{L}^{\text{True}}=\frac{1}{I\times
J}\sum_{i,j}(\hat{r}_{ij}-r_{ij}(a_{ij}=1))^{2}.$ (8)

However, since $r_{ij}(a_{ij}=1)$ is unobservable for user-item pairs in the
non-treatment group $\mathcal{NT}$, $\mathcal{L}^{\text{True}}$ is impossible
to calculate. Therefore, traditional RSs only maximize the log-likelihood of
the observed ratings for user-item pairs in the treatment group $\mathcal{T}$,
which leads to the empirical MSE loss as follows:

$\mathcal{L}^{\text{Obs}}=\frac{1}{|(i,j):a_{ij}=1|}\sum_{(i,j):a_{ij}=1}(\hat{r}_{ij}-r_{ij})^{2},$
(9)

where $|(i,j):a_{ij}=1|$ is the number of observed ratings. When exposure bias
exists, item exposure $a_{ij}$ depends on the rating potential outcome
$r_{ij}(a_{ij}=1)$. Therefore, $\mathcal{L}^{\text{Obs}}$ is a biased
estimator for $\mathcal{L}^{\text{True}}$, because the observed ratings for
user-item pairs in the treatment group $\mathcal{T}$ are biased samples from
the rating potential outcomes of the population $\mathcal{PO}$ (see Fig. 5-(a)
and Fig. 5-(b) for an example). To remedy the bias, IPW-based causal RSs
reweight the observed ratings $r_{ij}$ in $\mathcal{T}$ by the inverse of the
propensity scores, i.e., $\frac{1}{e_{ij}}$, which leads to the following new
training objective:

$\mathcal{L}^{\text{IPW}}=\frac{1}{I\times
J}\sum_{(i,j):a_{ij}=1}\frac{1}{e_{ij}}\cdot(\hat{r}_{ij}-r_{ij})^{2}.$ (10)

The proof for the unbiasedness of $\mathcal{L}^{\text{IPW}}$ for
$\mathcal{L}^{\text{True}}$ can be achieved by utilizing the balancing
property of propensity scores in Eq. (7), where we substitute
$(\hat{r}_{ij}-r_{ij})^{2}$ for $r_{ij}$ in the LHS of Eq. (7) and treat the
rating predictor $\hat{r}_{ij}$ as constant schnabel2016recommendations . We
also provide a toy example in Fig. 5 to intuitively show the calculation of
$e_{ij}$, the biasedness of $\mathcal{L}^{\text{Obs}}$ and the unbiasedness of
$\mathcal{L}^{\text{IPW}}$. The objective for IPW-based RSs defined in Eq.
(10) is model-agnostic. Therefore, it is applicable to all traditional RSs we
introduced in Section 2. For example, for MF-based RSs, we can plug in
$\hat{r}^{\textrm{MF}}_{ij}=\mathbf{u}_{i}^{T}\cdot\mathbf{v}_{j}$, for DMF-
based RSs, we plug in
$\hat{r}^{\textrm{DMF}}_{ij}=f^{u}_{nn}(\mathbf{u}_{i})^{T}\cdot
f^{v}_{nn}(\mathbf{v}_{j})$, etc.

Figure 5: An example adapted from Fig. (2) where the positivity assumption
holds. Suppose again covariates $C$ represent the two-dimensional features
(user type, movie type). (a) shows the observed ratings; (b) shows rating
potential outcomes; (d) shows the predicted rating potential outcome of an RS
model. The propensity scores
$e_{ij}=p(a_{ij}|\mathbf{c})=\mathbb{E}[a_{ij}|\mathbf{c}]$ are shown in (c).
Based on (a)(d) and Eq. (9), $\mathcal{L}^{\text{Obs}}=(5-1)^{2}\times 2/8=4$.
Based on (b)(d) and Eq. (8), $L^{\text{True}}=(5-1)^{2}\times 8/16=8$. Based
on (a)(c)(d) and Eq. (10),
$\mathcal{L}^{\text{IPW}}=\frac{1}{1/4}(5-1)^{2}\times 2/16=8$, which is
unbiased for $L^{\text{True}}$.

In practice, since the conditional unconfoundedness assumption in Eq. (3) is
untestable, it is usually infeasible to calculate the exact value of $e_{ij}$
based on user/item covariates that satisfy Eq. (3). Nevertheless, we can still
calculate approximate propensity scores $\tilde{e}_{ij}$ and reweight the
observed ratings by $1/\tilde{e}_{ij}$, but the unbiasedness of Eq. (10) after
the reweighting cannot be guaranteed. Here we introduce two strategies for the
approximate estimation. If user/item features $\mathbf{f}^{u}_{i}$ and
$\mathbf{f}^{v}_{j}$ are available, $\tilde{e}_{ij}$ can be estimated with
logistic regression schnabel2016recommendations  as follows:

$\tilde{e}^{\text{LR}}_{ij}=\text{Sigmoid}\Big{(}\Big{(}\sum_{k}w^{u}_{k}f^{u}_{ik}\Big{)}+\Big{(}\sum_{k}w^{v}_{k}f^{v}_{jk}\Big{)}+b_{i}+b_{j}\Big{)},$
(11)

where $\text{Sigmoid}(x)={(1+\mathrm{exp}(-x))}^{-1}$, $w^{u}_{k}$ and
$w^{v}_{k}$ are the regression coefficients, and $b_{i}$, $b_{j}$ are the user
and item-specific offsets, respectively. If user/item features
$\mathbf{f}^{u}_{i}$ and $\mathbf{f}^{v}_{j}$ are not available, we can
crudely approximate $e_{ij}$ based on the exposure data alone. For example, we
can estimate $\tilde{e}_{ij}$ with Poisson factorization liang2016causal  as:

$\tilde{e}^{\text{PF}}_{ij}\approx
1-\mathrm{exp}\left(-\boldsymbol{\pi}_{i}^{T}\cdot\boldsymbol{\gamma}_{j}\right),$
(12)

where $\boldsymbol{\pi_{i}}$ and $\boldsymbol{\gamma_{j}}$ are trainable user
and item embeddings with Gamma prior, and they can be inferred from the
exposure data as discussed in gopalan2015scalable . Additional strategies to
calculate the propensity scores can be found in ai2018unbiased ;
zhang2020large ; wang2022unbiased ; zhou2021contrastive .

The advantage of IPW is that the unbiasedness of Eq. (10) for rating potential
outcome estimation can be guaranteed if the propensity scores $e_{ij}$ are
correctly estimated. However, the accuracy of the propensity score estimation
models relies heavily on the domain knowledge and expertise of human experts,
which is untestable by experiments. In addition, IPW suffers from a large
variance and numerical instability issues, especially when the estimated
propensity scores $e_{ij}$ are very small. Therefore, variance reduction
techniques such as clipping and multi-task learning are usually applied to
improve the stability of the training dynamics bottou2013counterfactual ;
saito2020unbiased ; zhu2020unbiased .

Substitute Confounder Adjustment. IPW-based RSs address exposure bias from the
data’s perspective: They reweight the biased observational dataset to create a
pseudo randomized dataset that allows unbiased training of RSs. Confounder
adjustment-based methods, in contrast, estimate confounders $C$ that cause the
exposure bias and adjust their effects in the rating prediction model (A
simple adjustment strategy is to control $C$ as extra covariates121212Consider
again the toy example in Fig. 5. If we know exactly the user type and item
type $\mathbf{c}$ for each user-item pair, the predictions can be unbiased
even if the item exposures are non-randomized. ). For the adjustment to be
unbiased, classical causal inference requires the conditional unconfoundedess
assumption in Eq. (3) hold, i.e., no unobserved confounders imbens2015causal ,
which is generally infeasible in practice. Fortunately, recent advances in
multi-cause causal inference wang2019blessings  have shown that we can control
substitute confounders estimated from item co-exposure data instead, where
exposure bias can be mitigated with weaker assumptions.

We use $\mathbf{a}_{i}=[a_{i1},\cdots,a_{iJ}]$ to denote the exposure status
of all $J$ items to user $i$, which can be viewed as a bundle treatment in
clinical trials zou2020counterfactual . Wang et al. wang2020causal  showed
that if we can estimate user-specific latent variables $\boldsymbol{\pi}_{i}$,
such that conditional on $\boldsymbol{\pi}_{i}$, the exposures of different
items to the user are mutually independent, controlling $\boldsymbol{\pi}_{i}$
can eliminate the influence of multi-cause confounders $\mathbf{c}_{i}^{m}$
(i.e., confounders that simultaneously affect the exposure of multiple items
and ratings). A simple proof of the claim is that, if $\mathbf{c}_{i}^{m}$ can
still influence $\mathbf{a}_{i}$ and $\mathbf{r}_{i}$ after conditioning on
$\boldsymbol{\pi}_{i}$, since $\mathbf{c}_{i}^{m}$ is an unobserved common
cause for the exposure of different items, $a_{ij}$ cannot be conditionally
independent (see the discussion of the fork structure in section 3.2), which
renders a contradiction. The rigorous proof can be found in wang2019blessings
. Wang et al. further assumed that
$p(\mathbf{a}_{i}|\boldsymbol{\pi}_{i})=\Pi_{j}p(a_{ij}|\boldsymbol{\pi}_{i})=\Pi_{j}\text{Poission}(\boldsymbol{\pi}_{i}^{T}\cdot\boldsymbol{\gamma_{j}})$
and used the Poisson factorization to infer $\boldsymbol{\pi}_{i}$ and
$\boldsymbol{\gamma_{j}}$. Afterward, exposure bias can be mitigated by
controlling $\boldsymbol{\pi}_{i}$ as extra covariates in the RS model
imbens2015causal . For example, controlling $\boldsymbol{\pi}_{i}$ in MF-based
RSs leads to the following adjustment:

$r^{\text{adj}}_{ij}(a_{ij}=1)\sim\mathcal{N}\Big{(}\underbrace{\vphantom{\sum_{k}w_{k}\pi_{ik}}\mathbf{u}_{i}^{T}\cdot\mathbf{v}_{j}}_{\mathrm{user\
interests}}+\underbrace{\sum_{k}w_{k}\pi_{ik}}_{\mathrm{adj.\ for\\\ \ expo.\
bias}},\sigma_{ij}^{2}\Big{)}.$ (13)

The property of propensity scores can be utilized to further simplify Eq.
(13): If unconfoundedness in Eq. (3) holds for $C=\boldsymbol{\pi}_{i}$, it
will also hold for $C=\tilde{e}_{ij}=p(a_{ij}|\boldsymbol{\pi}_{i})$
rosenbaum1983central . Therefore, we can control the approximate propensity
scores estimated by $\boldsymbol{\pi}_{i}$, i.e.,
$\tilde{e}_{ij}=\boldsymbol{\pi}_{i}^{T}\cdot\boldsymbol{\gamma_{j}}$, which
leads to the simplified adjustment formula:

$r^{\text{adj}}_{ij}(a_{ij}=1)\sim\mathcal{N}\left(\mathbf{u}_{i}^{T}\cdot\mathbf{v}_{j}+w_{i}\cdot\tilde{e}_{ij},\sigma_{ij}^{2}\right),$
(14)

where $w_{i}$ is a user-specific coefficient that captures the influence of
$\tilde{e}_{ij}$ on ratings.

Despite the success in addressing exposure bias with weaker assumptions, one
limitation of the above method is that, since Poisson factorization is a
shallow model, it may fail to capture the complex influences of multi-cause
confounders on item co-exposures. To address this problem, recent works have
introduced deep neural networks (DNNs) to infer the user-specific substitute
confounders $\boldsymbol{\pi}_{i}$ from bundle treatment $\mathbf{a}_{i}$
zhu2022deep ; ma2021multi . These methods generally assume that
$\mathbf{a}_{i}$ are generated from $\boldsymbol{\pi}_{i}$ via
$p(\mathbf{a}_{i}|\boldsymbol{\pi}_{i})$ parameterized by a deep generative
network $f^{\text{exp}}_{nn}$ as:

$p(\mathbf{a}_{i}|\boldsymbol{\pi}_{i})=\Pi_{j}\text{Bernoulli}(\text{Sigmoid}(f^{\text{exp}}_{nn}(\boldsymbol{\pi}_{i})_{j})),$
(15)

where the intractable posterior of $\boldsymbol{\pi}_{i}$ is then approximated
with a Gaussian distribution parameterized by DNNs via the variational auto-
encoding Bayes algorithm kingmaauto , i.e.,
$q(\boldsymbol{\boldsymbol{\pi}_{i}}|\mathbf{a}_{i})=\mathcal{N}(f^{\boldsymbol{\mu}}_{nn}(\mathbf{a}_{i}),\text{diag}(f^{\sigma^{2}}_{nn}(\mathbf{a}_{i})))$,
where $f^{\boldsymbol{\mu}}_{nn}$ and $f^{\boldsymbol{\sigma}^{2}}_{nn}$ are
two DNNs that calculate the posterior mean and variance (before
diagonalization) of $\boldsymbol{\pi}_{i}$. With deep generative models
introduced to estimate the substitute confounders $\boldsymbol{\pi}_{i}$, non-
linear influences of multi-cause confounders on item exposures can be adjusted
in the RS models, where exposure bias can be further mitigated in
recommendations.

The key advantage of substitute confounder estimation-based causal RSs is that
controlling confounders in the potential outcome prediction model generally
leads to lower variance than IPW-based methods wang2020causal . However, these
models need to estimate substitute confounders $\boldsymbol{\pi}_{i}$ from the
item co-exposures and introduce extra parameters in the RS models to adjust
their influences, which may incur extra bias if the confounders and the
parameters are not correctly estimated. In addition, exposure bias due to
single-cause confounders cannot be addressed by these methods.

#### Popularity Bias

Popularity bias can be viewed as a special kind of exposure bias where users
are overly exposed to popular items steck2011item ;
abdollahpouri2019unfairness . Therefore, it can be addressed with techniques
introduced in the previous section, especially the IPW-based methods
zhu2021popularity . The reason is that, if we define the popularity of an item
as its exposure rate:

$m_{j}=\frac{\sum_{i}a_{ij}}{\sum_{j}\sum_{i}a_{ij}},$ (16)

we can view $m_{j}$ as pseudo propensity scores and use IPW to reweight the
observed ratings. Alternatively, we can also analyze and address popularity
bias with the structural causal model (SCM), where the causal mechanism that
generates the observed ratings under the influence of item popularity is
deeply investigated.

Figure 6: (a): SCM that explicitly models item popularity. (b): SCM under
intervention $do(V)$.

The discussion is mainly based on the popularity-bias deconfounding (PD)
algorithm proposed in zhang2021causal . PD assumes that the relations among
user interests $\mathbf{u}_{i}$, item latent attributes $\mathbf{v}_{j}$, item
popularity $m_{j}$, and observed ratings $r_{ij}$ can be represented by the
causal graph illustrated in Fig. 6, where item popularity can be clearly
identified as a confounder that spuriously correlates the item attributes and
the user ratings. PD aims to eliminate such spurious correlations with
backdoor adjustment, such that the causal influences of $\mathbf{u}_{i}$ and
$\mathbf{v}_{j}$ on $r_{ij}$ (which represents users’ interests on intrinsic
item properties) can be properly identified. Recall that backdoor adjustment
with SCM involves two stages: (1) During the training phase, the relevant
structural equations in the causal graph are estimated from the collected
dataset. (2) Afterward, we adjust the influence of confounders according to
Eq. (5) to remove the spurious correlations. Therefore, we need to estimate
$p_{G}(r_{ij}|\mathbf{u}_{i},\mathbf{v}_{j},m_{j})$ with the observed ratings
$r_{ij}$ and item popularty $m_{j}$ and infer the latent variables
$\mathbf{u}_{i}$ and $\mathbf{v}_{j}$. In PD,
$p_{G}(r_{ij}|\mathbf{u}_{i},\mathbf{v}_{j},m_{j})$ is modeled as a variant of
MF as follows:

$p_{G}(r_{ij}|\mathbf{u}_{i},\mathbf{v}_{j},m_{j})\propto\underbrace{\text{Elu}(\mathbf{u}^{T}_{i}\cdot\mathbf{v}_{j})\vphantom{m_{j}^{\lambda}}}_{\mathrm{user\
interests}}\ \ \times\underbrace{m_{j}^{\lambda}}_{\mathrm{pop.\ bias}},$ (17)

where $\lambda$ is a hyper-parameter that denotes our belief toward the
strength of influence of item popularity on ratings, and the function Elu
(defined as $\text{Elu}(x)=e(x)$ if $x<0$ else $x+1$) makes the RHS of Eq.
(17) a proper unnormalized probability density function. After
$\mathbf{u}_{i}$, $\mathbf{v}_{j}$ are estimated from the datasets with Eq.
(17), we conduct an intervention on the item node $V$ in the causal graph (see
Eq. (5)), where the spurious correlation due to item popularity can be
eliminated with backdoor adjustment:

$p(r_{ij}|do(\mathbf{u}_{i},\mathbf{v}_{j}))\propto\mathbb{E}_{p(m_{j})}[\text{Elu}(\mathbf{u}^{T}_{i}\cdot\mathbf{v}_{j})\times
m_{j}^{\lambda}]=\text{Elu}(\mathbf{u}^{T}_{i}\cdot\mathbf{v}_{j})\times\mathbb{E}_{p(m_{j})}[m_{j}^{\lambda}].$
(18)

Since the second term $\mathbb{E}_{p(m_{j})}[m_{j}^{\lambda}]$ in Eq. (18) is
a constant and Elu is a monotonically increasing function, they have no
influence on the ranking of the uninteracted items in the prediction phase.
Therefore, we can drop them and use
$\hat{r}_{ij}=\mathbf{u}^{T}_{i}\cdot\mathbf{v}_{j}$ as the unbiased rating
predictor to generate future recommendations.

Generally, the debiasing mechanism of PD is very intuitive and universal among
backdoor adjustment-based causal RSs wang2021deconfounded ; xu2021causal :
When fitting the RS model on the biased training set, we explicitly introduce
the item popularity $m_{j}$ (i.e., the confounder) in Eq. (17) to explain away
the spurious correlation between item attributes and the observed user
ratings. Therefore, the user/item latent variables $\mathbf{u}_{i}$ and
$\mathbf{v}_{j}$ used to generate future recommendations, i.e.,
$\hat{r}_{ij}=\mathbf{u}^{T}_{i}\cdot\mathbf{v}_{j}$, can focus exclusively on
estimating users’ true interests on intrinsic item properties. Is popularity
bias always bad? Recently, more researchers have begun to believe that
popularity bias is not necessarily bad for RSs, because some items are popular
because they per se have better quality than other items or they catch the
current trends of user interests, where more recommendations for these items
can be well-justified zhao2022popularity ; chen2022co . Therefore, rather than
setting the interventional distribution of item popularity to $p(m_{j})$, PD
introduced above as well as some other methods zhang2021causal  further
propose to make it correspond to item qualities or reflect the future
popularity predictions. We will introduce these strategies in Section 4.3
regarding causal generalizations of RSs.

#### Clickbait Bias

Different from previous subsections that mainly focus on causal debiasing
strategies for collaborative filtering-based RSs, this section discusses
content-based recommendations. Specifically, we discuss the clickbait bias,
which is defined as the bias of overly recommending items with attractive
exposure features such as sensational titles but with low content qualities.
The discussion is mainly based on wang2021clicks . We assume that item
features $\mathbf{f}^{v}_{j}$ can be further decomposed into the item content
feature $\mathbf{f}_{j}^{c}$ that captures item content information and the
item exposure feature $\mathbf{f}_{j}^{b}$ whose main purpose is to attract
users’ attention. Taking micro-video as an example, item content feature
$\mathbf{f}_{j}^{c}$ can be the audiovisual content of the video, whereas item
exposure feature $\mathbf{f}_{j}^{b}$ can be its title, which is not obliged
to describe its content faithfully.

The relations among user interests $\mathbf{u}_{i}$, item exposure feature
$\mathbf{f}_{j}^{b}$, item content feature $\mathbf{f}_{j}^{c}$, item fused
features $\mathbf{v}_{j}$, and the observed ratings $r_{ij}$ are depicted in
the causal graph in Fig. 7-(a). We note that clickbait bias occurs when a
user’s recorded click on an item because she was cheated by the item exposure
feature $\mathbf{f}_{j}^{b}$ before viewing the item content
$\mathbf{f}_{j}^{c}$. Therefore, the bias can be defined as the direct
influence of $\mathbf{f}_{j}^{b}$ on ratings $r_{ij}$ represented by the
causal path $F^{b}\rightarrow R$. To eliminate the clickbait bias, we need to
block the direct influence of $F^{b}$ on rating predictions, such that the
item content quality can be comprehensively considered in recommendations.

Figure 7: (a): The SCM that considers both the causal influences of item
content feature $F^{c}$ and item exposure feature $F^{b}$ on item latent
variable $V$. (b): The counterfactual SCM where $V^{*}$ is determined by
baseline value $F^{b*}$ and $F^{c*}$ to model the undesirable direct effects
of $F^{b}$.

As with SCM-based causal RSs, we first estimate structural equations of
interest in the causal graph, i.e.,
$p_{G}(\mathbf{v}_{j}|\mathbf{f}^{b}_{j},\mathbf{f}^{c}_{j})$ and
$p_{G}(r_{ij}|\mathbf{u}_{i},\mathbf{v}_{j},\mathbf{f}^{b}_{j})$. Since
distributions in wang2021clicks  are reasoned in a deterministic manner (i.e.,
Gaussian distributions with infinite precision), we keep the discussion
consistent with them. Specifically, we use
$\mathbf{v}_{j}(\mathbf{f}^{b}_{j},\mathbf{f}^{c}_{j})=f^{ff}(\mathbf{f}^{b}_{j},\mathbf{f}^{c}_{j})$
to represent the structural equation
$p_{G}(\mathbf{v}_{j}|\mathbf{f}^{b}_{j},\mathbf{f}^{c}_{j})$, where $f^{ff}$
is the feature fusion function that aggregates
$\mathbf{f}^{b}_{j},\mathbf{f}^{c}_{j}$ into $\mathbf{v}_{j}$, and use
$r_{ij}(\mathbf{u}_{i},\mathbf{v}_{j},\mathbf{f}^{b}_{j})$ to represent the
structural equation
$p_{G}(r_{ij}|\mathbf{u}_{i},\mathbf{v}_{j},\mathbf{f}^{b}_{j})$,
respectively. To explicitly disentangle the influence of item exposure feature
$\mathbf{f}^{b}_{j}$ and item latent variable $\mathbf{v}_{j}$ on the observed
ratings, $r_{ij}(\mathbf{u}_{i},\mathbf{v}_{j},\mathbf{f}^{b}_{j})$ is assumed
to factorize as follows:

$r_{ij}(\mathbf{u}_{i},\mathbf{v}_{j},\mathbf{f}^{b}_{j})=\underbrace{f^{uv}_{nn}(\mathbf{u}_{i},\mathbf{v}_{j}\vphantom{\text{Sigmoid}\left(f^{uf}_{nn}(\mathbf{u}_{i},\mathbf{f}^{c}_{j})\right)})}_{\mathrm{user\
interests}}\cdot\underbrace{\text{Sigmoid}\left(f^{uf}_{nn}(\mathbf{u}_{i},\mathbf{f}^{b}_{j})\right)}_{\mathrm{potential\
clickbait\ bias}},$ (19)

where the Sigmoid function provides necessary non-linearity in the fusion
process. Essentially, Eq. (19) represents the causal mechanism that generates
the observed ratings, which entangles both user interests in item content and
clickbait bias.

However, after learning the latent variables $\mathbf{u}_{i},\mathbf{v}_{j}$
and functions $f^{uf}_{nn},f^{uv}_{nn}$ via Eq. (19), removing clickbait bias
from the rating predictions is not as straightforward as the PD algorithm,
because we should eliminate only the direct influence of item exposure feature
$\mathbf{f}^{b}_{j}$ on ratings $r_{ij}$, while preserving its indirect
influence mediated by item latent variable $\mathbf{v}_{j}$, such that all
available item features can be comprehensively considered in recommendations.
To achieve this purpose, we first calculate the natural direct effect (NDE)
pearl2001direct  of item exposure feature $\mathbf{f}_{j}^{b}$ on ratings
$r_{ij}$ as follows:

$\text{NDE}(\mathbf{u}_{i},\mathbf{v}^{*}_{j},\mathbf{f}^{b}_{j})=r_{ij}(\mathbf{u}_{i},\mathbf{v}^{*}_{j},\mathbf{f}^{b}_{j})-r_{ij}(\mathbf{u}_{i},\mathbf{v}^{*}_{j},\mathbf{f}^{b*}_{j}),$
(20)

where
$\mathbf{v}^{*}_{j}=f^{ff}_{nn}(\mathbf{f}^{b*}_{j},\mathbf{f}^{c*}_{j})$, and
the baseline values $\mathbf{f}^{b*}_{j}$, $\mathbf{f}^{c*}_{j}$ are treated
as if the corresponding features are missing from the item wang2021clicks .
Since the second term
$r_{ij}(\mathbf{u}_{i},\mathbf{v}^{*}_{j},\mathbf{f}^{b*}_{j})$ in Eq. (20)
denotes the user’s rating to a “void” item and can be viewed as a constant, it
will not affect the rank of the items. So we only adjust the first term of Eq.
(20), which reasons with user $i$’s rating to item $j$ in a counterfactual
world where item $j$ has only the exposure feature $\mathbf{f}^{b}_{j}$ but no
content and fused features $\mathbf{f}^{c*}_{j}$ and $\mathbf{v}^{*}_{j}$, in
Eq. (19) (Fig. 7-(b)). The adjustment leads to the following estimator,

$\hat{r}_{ij}=r_{ij}(\mathbf{u}_{i},\mathbf{v}_{j},\mathbf{f}^{b}_{j})-r_{ij}(\mathbf{u}_{i},\mathbf{v}^{*}_{j},\mathbf{f}^{b}_{j})\triangleq\underbrace{r_{ij}(\mathbf{u}_{i},\mathbf{v}_{j},\mathbf{f}^{b}_{j})}_{\text{user
interests + clickbait}}-\ \
\underbrace{r_{ij}(\mathbf{u}_{i},\mathbf{v}^{*}_{j},\mathbf{f}^{b}_{j})}_{\text{clickbait
bias}}.$ (21)

Eq. (21) removes the direct influence of $\mathbf{f}^{b}_{j}$ on rating
predictions, such that item content quality can be comprehensively considered
in future recommendations.

#### Unfairness

Recently, with the growing concern of algorithmic fairness, RSs are expected
to show no discrimination against users from certain demographic groups
li2021user ; dong2022fairness ; li2022fairness . However, traditional RSs may
capture the undesirable associations between users’ sensitive information and
their historical activities, which leads to potentially offensive
recommendations to the users. Causal inference can help identify and address
such unfair associations, where fairness can be promoted in future
recommendations. This section focuses on the user-oriented fairness discussed
in li2021towards , which is defined as the bias where RS discriminately treats
users with certain sensitive attributes.

Figure 8: The SCM that reasons with the causal decision mechanism of
traditional RSs. Observed user ratings $R$ can be causally driven by user
features $F$, including sensitive features $S$, which can then unfairly
influence the inference of user latent variables $U$ and new rating
predictions $\hat{R}$.

When considering the user-oriented fairness for RSs, a subset of user features
$\mathbf{f}_{i}$, which we denote as $\mathbf{s}_{i}$, is assumed to contain
the sensitive information of users, such as gender, race, and age. Features
$\mathbf{s}_{i}$ are sensitive because recommendations that improperly rely on
these features may be offensive to users, which degrade both their online
experiences and their trust in the system. The causal graph that depicts the
causal decision mechanism of most traditional RSs is illustrated in Fig. 8
li2021towards . From Fig. 8 we can find that the user historical behaviors,
i.e., the observed ratings $r_{ij}$, are causally driven by user features
$\mathbf{f}_{i}$, including user sensitive features $\mathbf{s}_{i}$.
Therefore, the user latent variables $\mathbf{u}_{i}$ inferred from $r_{ij}$
could capture sensitive user information in $\mathbf{s}_{i}$, which unfairly
influences the rating predictions $\hat{r}_{ij}$ in the future.

To address this problem, Li et al. li2021towards  proposed to disentangle the
user sensitive features $\mathbf{s}_{i}$ from the user latent variable
$\mathbf{u}_{i}$, such that the unfair influence of $\mathbf{s}_{i}$ on
$\mathbf{u}_{i}$ represented by the causal chain $S\rightarrow R\rightarrow U$
can be maximally suppressed in the future recommendations. A common strategy
to achieve the disentanglement is adversarial training
goodfellow2020generative , where we train a discriminator
$f^{\text{cls}}_{nn}(\mathbf{u}_{i})\rightarrow\mathbf{s}_{i}$ that predicts
the sensitive features $\mathbf{s}_{i}$ from user latent variables
$\mathbf{u}_{i}$ alongside the RS. While fitting the RS on the observe ratings
$r_{ij}$, we constrain the inferred $\mathbf{u}_{i}$ to fool the discriminator
$f^{\text{cls}}_{nn}$ by making wrong predictions about $\mathbf{s}_{i}$,
which discourages $\mathbf{u}_{i}$ from capturing sensitive information in
$r_{ij}$ due to its unfair correlations with $\mathbf{s}_{i}$. Here we take
the MF-based RS as an example to show the details. We use
$\mathcal{L}^{\text{Rec}}$ to denote the original training objective of the
MF-based RS that maximizes the log-likelihood on observed ratings $r_{ij}$ and
use $\mathcal{L}^{\text{cls}}$ to denote the loss function of the
discriminator $f^{\text{cls}}_{nn}$. The adjusted training objective
$\mathcal{L}^{\text{Fair}}$ with fairness constraint becomes the following:

$\mathcal{L}^{\text{Fair}}=\underbrace{\mathcal{L}^{\text{Rec}}(\mathbf{u}^{T}_{i}\cdot\mathbf{v}_{j},r_{ij})}_{\mathrm{user\
interests}}-\lambda\cdot\underbrace{\mathcal{L}^{\text{cls}}(f^{\text{cls}}_{nn}\left(\mathbf{u}_{i}),\mathbf{s}_{i}\right)}_{\mathrm{fairness\
constraint}},$ (22)

where $\lambda$ is a hyper-parameter that balances the recommendation
performance and the fairness objective. Generally, a higher $\lambda$ leads to
better fairness, but it also restricts the capacity of the user latent
variables $\mathbf{u}_{i}$, which could negatively impact the recommendation
performance. Although here we use the MF-based RS as an example, it is
straightforward to generalize Eq. (22) to DMF or AE-based RS by replacing the
$\mathbf{u}^{T}_{i}\cdot\mathbf{v}_{j}$ term with the corresponding rating
estimators.

###  4.2 Causal Explanation in Recommendations

In previous sections, we have introduced causality to address various types of
bias and spurious correlation issues for traditional RSs. In this section, we
use causality to explain the user decision process. Specifically, we discuss
an interesting question aiming to disentangle users’ intent that causally
explains their past behaviors, i.e., did a user purchase an item because she
conformed to the current trend or because she really liked it? The tricky part
of this question is that: in reality, we only observe the effects, i.e., the
purchases, which can be explained by both causes.

#### Disentangling Interest and Conformity with Causal Embedding

Figure 9: Causal Graphs for DICE (a) and its generalization to PoI
recommendations (b).

The discussion is based on DICE proposed in zheng2021disentangling . To
simplify the discussion, we consider $r_{ij}$ as implicit feedback and define
the set of user, positive item ($j:r_{ij}=1$), negative item ($k:r_{ik}=0$)
triplets as $\mathcal{R}_{pn}=\\{(i,j,k)|r_{ij}=1\land r_{ik}=0\\}$. The
popularity of each item $j$, i.e., $m_{j}$, which reflects the current trend,
can be calculated with Eq. (16). Observing that the causal relation between
user interests $U$, user conformity $U_{c}$ and observed ratings $R$ can be
represented as a V-structure in Fig. 9-(a), DICE exploits the colliding effect
to achieve the disentanglement, i.e., outcomes that cannot be explained by one
cause are more likely caused by another (see discussions in Section 3.2).
Therefore, although users’ interests cannot be directly estimated from their
ratings $r_{ij}$ due to entanglement, their conformity to the trend can be
estimated by the popularity level of item $j$, and positive feedback not
likely caused by conformity has a higher chance of reflecting users’ true
interests.

In implementation, DICE assumes that the observed ratings $r_{ij}$ can be
decomposed into the sum of a conformity part
$r^{c}_{ij}=f^{c}(\mathbf{u}^{c}_{i},\mathbf{v}^{c}_{j})$ and a user interests
part $r^{i}_{ij}=f^{i}(\mathbf{u}^{i}_{i},\mathbf{v}^{i}_{j})$, where
$\mathbf{u}^{c,i}_{i},\mathbf{v}^{c,i}_{j}$ are learnable user, item
embeddings that reflect user $i$’s interests in (i.e., superscript $i$) and
conformity to (i.e., superscript $c$) item $j$, respectively. According to the
colliding effect of causal graphs, we can split the triplets in
$\mathcal{R}_{pn}$ into two parts: In the first part $\mathcal{R}^{(1)}_{pn}$,
positive item $a$ in the triplet has a higher popularity level than the
negative item $b$, i.e., $m_{a}>m_{b}$. In this case, we can draw two general
conclusions from this triplet: (1) Overall, the user prefers item $a$ over
$b$; (2) She is more likely to conform to item $a$ than item $b$ due to $a$’s
higher popularity. These conclusions lead to the two inequalities as follows:

$\forall(i,a,b)\in\mathcal{R}^{(1)}_{pn}\mathrm{,we\ have}\begin{cases}\
r_{ia}^{c}>r_{ib}^{c}\ (\mathrm{conformity})\\\ \
r_{ia}^{i}+r_{ia}^{c}>r_{ib}^{i}+r_{ib}^{c}\ (\mathrm{overall\
preference}),\end{cases}$ (23)

where the dependency of $r^{c,i}_{i\\{a,b\\}}$ on latent variables
$\mathbf{u}^{c,i}_{i},\mathbf{v}^{c,i}_{\\{a,b\\}}$ are omitted for
simplicity. The second part, i.e., $\mathcal{R}^{(2)}_{pn}$, is the key to
achieving disentanglement, because for every triplet $(i,c,d)$ in
$\mathcal{R}^{(2)}_{pn}$, the negative item $d$ is more popular than the
positive item $c$. In this case, user $i$ could have simply conformed to the
trend and chosen item $d$ to consume, but instead, she actively chose the less
popular item $c$. Therefore, we can draw one more specific conclusion that
leads to the disentanglement between user interests and conformity: The choice
of item $c$ over $d$ is more likely due to user interests. Therefore, we can
form three inequalities as:

$\forall(i,c,d)\in\mathcal{R}^{(2)}_{pn}\mathrm{,we\ have}\begin{cases}\
r_{ic}^{i}>r_{id}^{i}\ (\mathrm{interests}),r_{ic}^{c}<r_{id}^{c}\
(\mathrm{conformity}),\\\ \ r_{ic}^{i}+r_{ic}^{c}>r_{id}^{i}+r_{id}^{c}\
(\mathrm{overall\ preference}).\end{cases}$ (24)

The inequalities in Eqs. (23) and (24) can be solved by ranking-based loss in
RSs, such as Bayesian personalized ranking (BPR) rendle2009bpr , where the
disentangled embeddings $\mathbf{u}^{c,i}_{i},\mathbf{v}^{c,i}_{j}$ and the
match functions $f^{c,i}(\cdot,\cdot)$ can be learned from
$\mathcal{R}^{(1)}_{pn}$ and $\mathcal{R}^{(2)}_{pn}$. Finally, we form a
rating predictor
$\hat{r}_{ij}=f^{i}(\mathbf{u}^{i}_{i},\mathbf{v}^{i}_{j})+f^{c}(\mathbf{u}^{c}_{i},\mathbf{v}^{c}_{j})$
for future recommendations.

#### Generalizations of DICE

DICE disentangles the user intent and promotes the explainability of RSs from
the data’s perspective: It partitions the triplets $(i,j,k)$ in
$\mathcal{R}_{pn}$ into two disjoint subsets $\mathcal{R}^{(1)}_{pn}$ and
$\mathcal{R}^{(2)}_{pn}$ based on the relative popularity of the positive and
negative items, and shows that the triplets in $\mathcal{R}^{(2)}_{pn}$ are
informative to distinguish the user interests from their conformity to the
popularity trend. The basic idea of DICE is generalizable to promote
explainability for other types of recommendation tasks, if we can find
alternative causal explanations to challenge the assumption that the observed
positive feedback in these tasks can be attributed solely to user interests.

For example, in point-of-interests (PoI) recommendations, the target items are
specific point locations that users may find useful or interesting to visit,
such as restaurants, grocery stores, and malls ye2011exploiting . In this
task, the location of a PoI is an important alternative explanation for users’
visits to the PoI other than user interests, because nearby POIs are more
convenient to visit than the remote ones wang2018exploiting . Therefore, to
disentangle user interests from potential geographical factors that could
causally influence users’ choices, we can take a similar strategy as DICE and
partition the user historical visit records according to the distance of
positive and negative PoIs to users. Then, the disentangled user interest
embeddings can be estimated based on the partitioned dataset with the same
ranking-based approach.

#### Other Works on Explainable RSs

Explanable recommendation is a broad topic zhang2020explainable , where
disentangling user’s intent based on data partitioning is a small part. There
are also plenty of works that focus on improving the explainability of RSs
from the model’s side, where specific disentanglement modules, such as
prototype learning ma2019learning , context modeling wang2022causal , and
aspect modeling tan2021counterfactual , are designed and integrated with
traditional RS models to further enhance their transparency and
explainability. We refer interested readers to the corresponding papers as
well as xu2021learning ; sheth2022causal  for further investigation.

###  4.3 Causal Generalization of Recommendations

After estimating the causal relations from potentially biased and entangled
observational datasets, the generalization ability of RSs can be substantially
enhanced, because even if the context (or environment) in which we make
recommendations changes (e.g., item popularity, user conformity, etc.), we can
still basing the recommendations on causal relations that are stable and
invariant, while discarding or correcting other undesirable correlations that
are transient and susceptible to change zheng2021disentangling ;
arjovsky2019invariant . In this section, we use the PD algorithm for
popularity bias and the DICE algorithm for causal explainability as two
examples to show how the generalization of RSs can be improved with causal
intervention and disentanglement.

#### Generalization Based on Intervention

First, we take the PD algorithm as an example to show how causal intervention
can improve the generalization of RSs within a dynamic environment. In RS, it
is generally assumed that user interests can remain unchanged for a certain
period of time, i.e., the causal structure $U\rightarrow R\leftarrow V$ in
Fig. (6) represents the stable user interests on intrinsic item properties.
However, the popularity of different items, i.e., the context in which we make
recommendations, can shift rapidly during the same period chen2022co . Recall
that PD disentangles the causal influences of user interests and item
popularity on ratings via the product of two terms, i.e.,
$\text{Elu}(\mathbf{u}^{T}_{i}\cdot\mathbf{v}_{j})$ and $m_{j}^{\lambda}$, as
Eq. (17). Suppose $m_{j}$ represents the current popularity level of item $j$.
If we predict that the popularity of item $j$ will change to $m^{\prime}_{j}$
in the future xie2020multimodal , we can conduct an intervention that sets $M$
to the predicted value $m_{j}^{\prime}$ in the structural equation
$p_{G}(R|U,V,M)$ and predict future ratings $r^{\prime}_{ij}$ via the
following formula:

$p_{G}(r^{\prime}_{ij}|\mathbf{u}_{i},\mathbf{v}_{j},do(m^{\prime}_{j}))\propto\underbrace{\vphantom{(m^{\prime}_{j})^{\lambda}}\text{Elu}(\mathbf{u}^{T}_{i}\cdot\mathbf{v}_{j})}_{\mathrm{stable\
user\
interests}}\times\underbrace{(m^{\prime}_{j})^{\lambda}}_{\mathrm{future\
popularity}},$ (25)

where the user, item latent variables $\mathbf{u}_{i}$ and $\mathbf{v}_{j}$
learned from the current time step remain unaltered. With the influence of
future changes in item popularity on ratings considered in the predictions,
service providers can make strategic decisions to allocate resources for items
with different popularity potentials. In contrast, traditional RSs could
mistakenly capture the influence of the current popularity level of items on
ratings as user interests. Therefore, they will not generalize well when the
item popularity $m_{j}$ changes to a different level $m^{\prime}_{j}$ due to
time evolution.

#### Generalization Based on Disentanglement

In addition, causal disentanglement can promote the generalization of RSs by
identifying and basing recommendations on causes that are more robust to
potential changes in the environments suter2019robustly ; yang2021causalvae .
For example, if users’ conformity and interest are disentangled based on their
historical behaviors, if a user’s conformity reduces to a low level due to
certain reasons, since user interests are assumed to be stable within a
certain period of time, we can still use the learned user/item interest
variables $\mathbf{u}^{i}_{i}$, $\mathbf{v}^{i}_{j}$ to make recommendations
based on their interests, where the previously estimated unreliable user
conformity information can be discarded or down-weighted. In contrast, for
traditional RSs, different factors that causally influence their historical
behaviors are entangled as a single user latent variable $\mathbf{u}_{i}$.
Therefore, even if some less stable causes of user behaviors are known to
change (e.g., in the PoI RS introduced above, a user could move to a new place
where the convenience levels of different PoIs change for the user), these
models will still utilize the outdated causes to make recommendations, which
could fail to generalize to the new environment.

##  5 Evaluation Strategies for Causal RSs

In the previous sections, we have discussed various causal inference
techniques that are promising to address multiple types of biases,
entanglement, and generalization problems in traditional RSs. However, without
a well-designed model evaluation strategy, it is difficult to tell whether the
proposed causal RS model is indeed effective, nor can we guarantee that the
model will perform reliably after deploying in a real-world environment. The
evaluation of causal models is particularly difficult, because the
groundtruths, i.e., the causal effects of interest, are usually infeasible.
Despite the challenges, there are several strategies that can reliably
evaluate causal RSs with biased real-world data, and we will thoroughly
discuss them in this section. In addition, we also compile the available real-
world datasets that conduct randomized experiments to eliminate exposure bias
to facilitate future causal RS research.

###  5.1 Evaluation Strategies for Traditional RSs

The assessment of traditional RSs generally follows three steps: First, the
observed ratings $r_{ij}$ in the rating matrix $\mathbf{R}$ are split into the
non-overlapping training set $\mathbf{R}_{tr}$ and test set $\mathbf{R}_{te}$,
usually by randomly holding out a certain percentage of the observed ratings
from each user. Then, the proposed RS is trained on ratings in
$\mathbf{R}_{tr}$ to learn the latent variables and the associated functional
models (see Section 2). Finally, the trained RS predicts the missing ratings
in $\mathbf{R}_{tr}$ for each user, where the results are compared with the
held-out ratings in $\mathbf{R}_{te}$ to evaluate the model performance. The
quality of rating predictions can be measured by accuracy-based metrics such
as mean squared error (MSE) and mean absolute error (MAE), and ranking-based
metrics such as recall, precision, normalized discounted cumulative gain
(NDCG), etc. More information on these evaluation metrics can be found in
shani2011evaluating .

###  5.2 Challenges for the Evaluation of Causal RSs

The above evaluation strategy, however, is not directly applicable to causal
RSs, because ratings in $\mathbf{R}_{te}$ may have the same spurious
correlation and bias as ratings in $\mathbf{R}_{tr}$, which makes the
evaluation on $\mathbf{R}_{te}$ a biased measure of the true model
performance. Therefore, to unbiasedly evaluate the effectiveness of causal
RSs, it is ideal that we have a biased/entangled training set
$\mathbf{R}^{b}_{tr}$ to learn the model, and an unbiased/disentangled test
set $\mathbf{R}^{ub}_{te}$ for model evaluation, such that the effectiveness
of the causal debiasing/disentangling algorithm can be directly verified from
experiments. However, such unbiased/disentangled test set
$\mathbf{R}^{ub}_{te}$ can be difficult to acquire and expansive to establish.
Therefore, we first introduce common data simulation strategies for causal RS
evaluation. We then discuss how real-world datasets can be directly utilized
to further promote the credibility of causal RS research.

###  5.3 Evaluation Based on Simulated Datasets

A good dataset simulation strategy to evaluate causal RSs should have the
following properties: (1) The generation mechanisms of the bias and
entanglement to be studied are clearly identified, credibly designed, and can
be adjusted in a flexible manner; (2) The available real-world information is
utilized as much as possible.

#### Simulation Based on Generative Models

One promising dataset simulation strategy that satisfies the above criteria is
to use deep generative models. Here we take exposure bias as an example to
demonstrate how it can be simulated from real-world datasets zhu2022deep . The
simulation is composed of two phases. In the training phase, two variational
auto-encoders (VAEs) liang2018variational ; kingmaauto  are trained on the
exposure and rating data in a real-world dataset (e.g., the MovieLens dataset
harper2015movielens ), which results in two decoder networks $f^{a}_{nn}$ and
$f^{r}_{nn}$ that generate item exposures $\mathbf{a}_{i}\in\\{0,1\\}^{J}$ and
user ratings $\mathbf{r}_{i}\in\mathbb{R}^{J}$ from $K$-dimensional Gaussian
user latent variables
$\mathbf{u}^{a}_{i}\sim\mathcal{N}(\mathbf{0},\mathbf{I}_{K})$ and
$\mathbf{u}^{r}_{i}\sim\mathcal{N}(\mathbf{0},\mathbf{I}_{K})$, respectively.
The decoders capture the generative distributions of item exposures and user
ratings based on the data of real users, where the available real-world
information is effectively utilized. In the generation phase, for each
hypothetical user $i^{\prime}$, we draw a confounder
$\mathbf{c}_{i^{\prime}}\sim\mathcal{N}(\mathbf{0},\mathbf{I}_{K})$ that
simultaneously affects $\mathbf{u}^{a}_{i^{\prime}}$ and
$\mathbf{u}^{r}_{i^{\prime}}$. Then, to simulate the exposure bias, we set
$\mathbf{u}^{a}_{i^{\prime}}=\mathbf{c}_{i^{\prime}}$ and
$\mathbf{u}^{r}_{i^{\prime}}=\lambda\cdot\mathbf{c}_{i^{\prime}}+(1-\lambda)\boldsymbol{\epsilon}_{i^{\prime}}$
and use $f^{a}_{nn}$, $f^{r}_{nn}$ to generate the simulated item exposures
$\mathbf{a}_{i^{\prime}}$ and ratings $\mathbf{r}_{i^{\prime}}$, where
$\boldsymbol{\epsilon}_{i^{\prime}}\sim\mathcal{N}(\mathbf{0},\mathbf{I}_{K})$
and hyper-parameter $\lambda$ controls the strength of the confounding bias.
Finally, we mask $\mathbf{r}_{i^{\prime}}$ with $\mathbf{a}_{i^{\prime}}$ to
form the biased training set $\mathbf{R}^{b}_{tr}$, and keep the generated
ratings $\mathbf{r}_{i^{\prime}}$ unmasked in the test set
$\mathbf{R}^{ub}_{te}$ for an unbiased evaluation of model performance.

The advantage of dataset simulation strategies based on generative models is
that the true causal mechanisms of interest, such as the rating potential
outcomes, are available in the evaluation stage, which is generally impossible
for real-world datasets. Therefore, the effectiveness of causal RSs can be
easily verified based on the simulated groundtruths. In addition, the
simulations are flexible as the strength of biases and entanglements can be
set into different levels (e.g., $\lambda$ in the example), where the
sensitivity and robustness of causal RSs can be thoroughly investigated.

#### Test Set Intervention

Another reliable dataset simulation strategy is test set intervention, where
an intervened test set is created from the original test set, such that it has
a different bias/entanglement distribution from the training set
zheng2021disentangling ; liang2016causal ; zhu2022deeptag . For example, to
study the popularity bias, we can first select observed ratings from
$\mathbf{R}$ such that 90% of the interacted items are popular and 10% are
unpopular to form the training set $\mathbf{R}_{tr}$ yi2022debiased . We then
select from the remaining ratings, i.e., the original test set
$\mathbf{R}_{te}$, a subset with a different ratio of popular and unpopular
items (e.g., 10% popular and 90% unpopular) to form the intervened test set
$\mathbf{R}^{int}_{te}$. If the causal RSs trained on $\mathbf{R}_{tr}$ can
still perform well on the intervened test set $\mathbf{R}^{int}_{te}$, the
model’s invariance to the popularity bias can be supported. A similar test set
intervention strategies can be used to evaluate the disentanglement of user
interests and conformity for DICE zheng2021disentangling .

The advantage of the test set intervention-based causal RS evaluation strategy
is that extra assumptions that cannot be justified by real-world information
are minimally introduced, because the intervention is usually achieved by
selecting samples from the original test set to change the data distribution,
which does not introduce extra assumptions of the generative mechanisms or
hypothetical users, items, and ratings. From this perspective, the evaluation
results based on test set intervention may be more credible compared with the
generative model-based strategies.

###  5.4 Evaluation Based on Real-world Datasets

#### Randomized Experiments

For the study of exposure bias, it is feasible to establish-bias free real-
world datasets, where ratings for either every item or randomly selected items
are collected from a subset of users. This can be extremely expansive and
user-unfriendly, but recent years have witnessed a growing interest in causal
RS research from the industry, where more such randomized datasets are
established and released to facilitate causal RS research. The available real-
world datasets are compiled as follows:

  * •

Coat datasets131313https://www.cs.cornell.edu/~schnabts/mnar/
schnabel2016recommendations  (2016). The Coat dataset is a small-scale dataset
crowdsourced from the Amazon Mechanical Turkers platform with 300 users and
290 items. Specifically, each Turker is first asked to self-select 24 coats to
rate, where the ratings form the biased training set $\mathbf{R}^{b}_{tr}$.
Then each Turker is asked to rate 16 random coats, and these ratings form the
unbiased test set $\mathbf{R}^{ub}_{te}$.

  * •

Yahoo! R3
dataset141414https://webscope.sandbox.yahoo.com/catalog.php?datatype=r&did=3
marlin2007collaborative ; marlin2009collaborative  (2009). The Yahoo! R3
dataset is collected from the Yahoo! Music platform. The biased training set
$\mathbf{R}^{b}_{tr}$ is composed of 300,000 self-supplied ratings from 15,400
users to 1,000 items. In addition, a subset of 5,400 users is presented with
ten randomly selected items to rate, and the ratings are used to create the
unbiased test set $\mathbf{R}^{ub}_{te}$.

  * •

KuaiRec dataset151515https://github.com/chongminggao/KuaiRec gao2022kuairec
(2022). The KuaiRec dataset is established based on a popular micro-video
sharing platform, KuaiShou, in China (known as Kwai internationally). The
dataset records self-supplied ratings from 7,176 users to 10,728 items as the
biased training set $\mathbf{R}^{b}_{tr}$. The unbiased test set
$\mathbf{R}^{ub}_{te}$ is composed of a subset of 1,411 users and 3,327 items,
where the ratings between these users and items are almost fully observed
(with 99.6% density).

The statistics of the datasets are summarized in Table 1 for reference. There
are also randomized datasets for some related topics such as click-through
rate prediction zhou2018deep , i.e., Criteo Ads
datasets161616http://cail.criteo.com/criteo-uplift-prediction-dataset/
diemert2018large , and bandit-based RS bouneffouf2012contextual , i.e., Open
Bandit dataset171717https://research.zozo.com/data.html saito2020large , where
the sources are also provided in case the readers are interested.

Dataset | # Users | # Items | Item Type | Training Sets | Test Sets
---|---|---|---|---|---
Coat | 300 | 290 | Coat | 24 i/u (self-supplied) | 16 i/u (random)
Yahoo! R3 | 15,400 | 1,000 | Music | 300,000 r (self-supplied) | 10 i/u (random) for 5,400 u
KuaiRec | 7,176 | 10,728 | Video | 16.3% r (self-supplied) | 99.6% r for 1,411 u and 3,327 i
Table 1: Characteristics of the currently available real-world causal
recommendation datasets, where the test sets are devoid of exposure bias
either due to randomized item exposures or fully observed ratings. In the
table, terms like 24 i/u mean that every user rates 24 items, the term 300,000
r denotes the number of observed ratings, and terms like 16.3% r represent the
density of interactions.

From Table 1 we can find that, the Coat dataset is small in scale. While for
the Yahoo! R3 dataset, the training set is comparatively large (15,400 users
and 1,000 items), the randomized experiment conducted to establish the
unbiased test set is small-scale in comparison (16 and 10 randomly exposed
items per user, respectively). Therefore, although these ratings are unbiased
due to randomization, they may not capture well-rounded user interests and
therefore induce a high evaluation variance. For the recently released KuaiRec
datasets, large-scale experiments are conducted on users to establish the
bias-free test set, where the 1,411 users’ ratings for 3,327 items are almost
fully collected. Therefore, it may be a promising new benchmark that allows
the evaluation of more complex causal RS models with a lower variance.

#### Qualitative Evaluation and Case Study

For other types of biases in RSs that cannot be attributed to non-randomized
item exposures (e.g., clickbait bias and unfairness), the establishment of
bias-free test sets is more challenging. For example, when studying the
clickbait bias, it is difficult to determine whether a user clicked an item
due to interests or clickbait. Similarly, when examining the user-oriented
fairness of RSs, we cannot know if the generated items are offensive to the
users. Under such circumstances, we can still conduct case studies for
qualitative model evaluations, where we manually select some representative
samples from the original test set and observe whether the trained causal RS
model would respond as expected to these samples wang2022causalRep .

Consider the evaluation of the robustness of a causal RS to clickbait bias. We
can select some representative items with low-quality content but highly-
attractive exposure features and other items with high-quality content but
normal exposure features from the original test set. Then, we obtain rating
predictions for items from these two groups and draw comparisons. If the
studied causal RS indeed ranks items in the second group higher than those in
the first group, we can likely conclude that the model is robust to clickbait
bias because the quality of the item content, not its exposure features, is
prioritized in recommendations. In addition, to evaluate the user-oriented
fairness of a causal RS, we can analyze the generated recommendation for users
from certain demographic groups. If the recommended items tend to capture the
social stereotypes that are negatively associated with user sensitive
features, we can conclude that the model is still discriminatory against
users.

##  6 Future Directions

Despite the recent achievements in marrying causal inference with traditional
RSs to address their various limitations of correlational reasoning on
observational user data, causal RS research is still in its emerging stage.
Several promising directions could be pursued to further advance this field.
In this section, we identify four interesting and important open problems
worthy of exploration in the future.

First, the assumptions required by existing causal RSs could be too strong,
which may not hold in reality. For example, most RCM-based causal RSs rely on
SUTVA to exclude the interference of item exposures for different users.
However, if users are connected by a social network, they may interact closely
with each other or be heavily affected by the influencers in the network
ma2022learning2 . Consequently, SUTVA can be violated because the
recommendations made to one user may causally affect the ratings of others
(i.e., the spill-over effects li2022causal ; ma2022learning ). In addition,
the positivity assumptions may also be violated if some users never click
certain types of items (i.e., non-compliance and defiers imbens2015causal ).
Therefore, it is crucial to further weaken the assumptions of causal RSs to
make them more practical for real-world applications.

In addition, there currently lacks a universal causal model for RSs that can
be applied for different causal reasoning purposes. Most SCM-based causal RSs
are designed to address one specific type of bias or entanglement problem,
where other issues are tacitly assumed to be absent and omitted from the
causal graph. Moreover, even for causal RSs that address the same problem,
several varieties of causal graphs that include different sets of variables
and relationships can be assumed, which leads to inconsistency between
different works. Therefore, it would be promising and beneficial to have a
generic and widely-accepted causal model that is able to comprehensively
address multiple types of causal problems in recommendations.

Furthermore, certain types of biases in RSs are double-blade swords, where the
positive side is seldom investigated. Consider the item exposure bias
discussed in Section 4.1. We should note that some items are more likely to be
exposed because they have higher quality than other items. Therefore, the
higher exposure rate of these items can be well justified and may be utilized
to further enhance the recommendation performance. In addition, recent
research also found that confounders that spuriously correlate item exposures
and user ratings may also help explain the co-occurrence patterns of different
items zhu2022deep . Therefore, how to properly identify and utilize the
positive side of biases while maximally suppressing their negative effects is
of great importance and deserves more in-depth investigations in the future.

Finally, although recent years have witnessed the establishment and release of
more real-world datasets for causal RS research from the industry, many causal
RS models still rely heavily on simulated datasets for evaluation. The
simulation can lead to the over-simplification of the problem and is often
designed to correspond exactly with the debiasing/disentanglement mechanism of
the proposed model. Therefore, the effectiveness of these methods in more
complicated real-world scenarios is still uncertain due to the lack of model
deployment and online tests. As such, to more convincingly demonstrate the
practical utility of causal RSs, more collaborations with the industry are
highly expected.

##  7 Summary

In this survey, we provide a comprehensive overview of recent advances in
causal inference for RSs. We start by pointing out issues of traditional RSs
that rely on correlations in observed user behaviors and user/item features.
We then introduce two mainstream causal inference frameworks, i.e., Rubin’s
RCM and Pearl’s SCM, which provide deeper insights into these issues and the
foundation for moving traditional RSs to the upper rungs of the Ladder of
Causality. Specifically, we thoroughly discuss several state-of-the-art causal
RS models that lead to enhanced robustness to various biases and improved
explainability. In addition, since causal RSs can base recommendations on
causal relationships that are stable and invariant, we also demonstrate that
their generalization abilities can be significantly improved. Finally, we
introduce evaluation strategies for causal RSs, with an emphasis on how to
reliably estimate the model performance based on biased real-world data. We
further compile real-world datasets where expensive randomized experiments are
conducted on users, which reflects growing attention to causal RSs from the
industry.

Overall, causal RS is still a relatively new and under-explored research
topic. More efforts are urgently demanded to systematize the existing works
and conduct deeper investigations for further improvements. Accordingly, we
point out four interesting and practically important open problems in causal
RSs. We hope that this survey can help readers gain a comprehensive
understanding of the main idea of applying causality in RSs and encourage
further progress in this promising area.

Acknowledgements. This work is supported by the National Science Foundation
under grants IIS-2006844, IIS-2144209, IIS-2223769, CNS-2154962, and
BCS-2228534, the JP Morgan Chase Faculty Research Award, and the Cisco Faculty
Research Award.

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