# Causal Disentanglement with Network Information for Debiased Recommendations

Paras Sheth  Arizona State UniversityTempeAZUSA<EMAIL_ADDRESS>,  Ruocheng
Guo<EMAIL_ADDRESS>City University of Hong KongHong Kong ,  Lu
Cheng<EMAIL_ADDRESS>Arizona State UniversityTempeAZUSA ,  Huan Liu
<EMAIL_ADDRESS>Arizona State UniversityTempeAZUSA and  K. Selçuk Candan
<EMAIL_ADDRESS>Arizona State UniversityTempeAZUSA

(2018)

###### Abstract.

Recommender systems aim to recommend new items to users by learning user and
item representations. In practice, these representations are highly entangled
as they consist of information about multiple factors, including user’s
interests, item attributes along with confounding factors such as user
conformity, and item popularity. Considering these entangled representations
for inferring user preference may lead to biased recommendations (e.g., when
the recommender model recommends popular items even if they do not align with
the user’s interests). Recent research proposes to debias by modeling a
recommender system from a causal perspective. The exposure and the ratings are
analogous to the treatment and the outcome in the causal inference framework,
respectively. The critical challenge in this setting is accounting for the
hidden confounders. These confounders are unobserved, making it hard to
measure them. On the other hand, since these confounders affect both the
exposure and the ratings, it is essential to account for them in generating
debiased recommendations. To better approximate hidden confounders, we propose
to leverage network information (i.e., user-social and user-item networks),
which are shown to influence how users discover and interact with an item.
Aside from the user conformity, aspects of confounding such as item popularity
present in the network information is also captured in our method with the aid
of causal disentanglement which unravels the learned representations into
independent factors that are responsible for (a) modeling the exposure of an
item to the user, (b) predicting the ratings, and (c) controlling the hidden
confounders. Experiments on real-world datasets validate the effectiveness of
the proposed model for debiasing recommender systems.

causal learning, network data, deep learning, recommender systems,
confounders,

††copyright: acmcopyright††journalyear: 2018††doi:
10.1145/1122445.1122456††conference: Woodstock ’18: ACM Symposium on Neural
Gaze Detection; June 03–05, 2018; Woodstock, NY††booktitle: Woodstock ’18: ACM
Symposium on Neural Gaze Detection, June 03–05, 2018, Woodstock, NY††price:
15.00††isbn: 978-1-4503-XXXX-X/18/06

##  1\. Introduction

Recommender systems have become ubiquitous in our daily lives. These systems
recommend new items to the users based on their past interactions. However,
recent studies have shown that these systems suffer from multiple types of
biases, including conformity bias and popularity bias (Wang et al., 2020;
Schnabel et al., 2016; Chen et al., 2020). Due to these biases, the
performance of these systems deteriorates, and the recommender systems may not
recommend relevant items to the users. As a result, these biases hurt user
engagement which may harm the business in the long term (Abdollahpouri et al.,
2021; Zhu et al., 2021). Developing methods to mitigate these biases and
improve recommendation performance is a common approach to address this
problem (Borges and Stefanidis, 2021; Wei et al., 2021; Zhang et al., 2021;
Liang et al., 2016).

Recently, a series of work investigates how to pose the problem of recommender
systems from a causal perspective to mitigate the various types of bias. In
recommender systems, the users are first exposed to a set of items based on
the selection mechanisms of an existing recommender algorithm. Then, a user
interacts with a subset of these items generating the observed ratings from
the set of the exposed items. Under the causal lens, the exposure of an item
to the user is considered the treatment variable $T$, such that $T=0$ implies
the user was not exposed to an item and $T=1$ implies the user was exposed to
a particular item. At the same time, the actual ratings are considered to be
the outcomes (Wang et al., 2020; Liang et al., 2016). Traditional recommender
systems only utilize the observed user-item ratings to infer the user
preference and recommend new items. However, this strategy only provides
unbiased inference of user preference over items if users randomly interacted
with the items. This is because randomly assigned treatment eliminates the
bias induced by the confounders (Schulz, 1998). Since users do not interact
with items at random, inferring their preference from the observed ratings
data becomes challenging. Furthermore, in most cases, there exist some hidden
confounders – the variables that affect both the exposure (treatment) and the
ratings (outcomes). For instance, recommender systems may recommend popular
items to the user, and at the same time, due to herd mentality (Baddeley,
2010), users may rate these items similarly. Thus, the item’s popularity acts
as a confounder in this setting. Also, to make valid causal inference, it is
essential to adjust for all confounders (Rosenbaum and Rubin, 1983). Recent
works, including (Wang et al., 2020) and (Liang et al., 2016), learn to
estimate the true exposure using Poisson Factorization models and use the
estimated exposure as a substitute for hidden confounders.

Figure 1. The social recommender systems from a causal perspective. Exposure
of an item to a user denotes the treatment; the observed ratings denote the
outcomes. The disentangled factors from the user-social networks and item-user
networks correlate with the factors for modeling the exposure, factors
responsible for the hidden confounders, and factors for predicting the rating.

An important problem that has not been investigated is the confounding bias in
recommender systems with social network information. Social recommender
systems learn the user and item representations by leveraging both the user-
social networks and user-item networks (Fan et al., 2019; Yang et al., 2021b;
Zafarani et al., 2014). These representations consist of a variety of
information, and not all the information is helpful in terms of mitigating the
confounding bias. Under the causal setting, factors such as social relations
can act as noisy measures of confounders. For instance, in the physical world
a user is likely to seek suggestions from their friends before making any
purchases and the user’s friends may provide good recommendations (Sinha et
al., 2001). A user’s preferences are similar to or influenced by their social
relations. Analogous to the physical world, this can also be observed in the
digital world. This can be corroborated by social correlation theories such as
homophily (Ma et al., 2009) and social influence (Marsden and Friedkin, 1993).
Homophily indicates that users with similar preferences are more likely to be
connected, and social influence reveals that users who are connected are more
likely to have similar preferences. Unfortunately, current social
recommendation models cannot distinguish between confounding factors and other
factors. Hence, they learn highly entangled representations which lead to
biased recommendations. To alleviate this problem, we aim to causally
disentangle the learned representations when there exists social network
information. This is a challenging task due to the following reasons:

  * •

First, the learned representations consist of a variety of information. Each
component of the representation may be effective for either predicting the
exposure of an item to the user or acting as a confounder between the exposure
and rating, or useful in predicting the rating. For example, user
representations learned from complex user interactions might consist of latent
features that are highly entangled with each other, such as user preferences
and the confounding factor – user conformity (Zheng et al., 2021). Similarly,
item representations consist of entangled information about an item’s latent
features and confounding factors, including the item’s popularity. Thus, the
representations should be carefully disentangled such that each factor has its
distinct contribution.

  * •

Second, to make valid causal inferences, it is essential that the learned
factors are independent of each other (Hassanpour and Greiner, 2019b). Hence,
it is critical to ensure independence among the disentangled factors in the
learned representations.

  * •

Third, the disentangled representations learned for the confounders still
exhibit some degree of bias, although less than the entangled representations.
This remaining bias exists because, the confounders contribute to predicting
both the treatment (exposure) and the outcomes (ratings) (Hassanpour and
Greiner, 2019a). Thus, the remaining bias should also be mitigated.

To deal with the above challenges, we propose a causal disentanglement model
for social recommender systems111We will release the code once the paper gets
accepted. We first formulate the social recommender system problem from a
causal perspective as illustrated by the causal graph in Fig. 1. To learn the
representations, we explicitly consider two common types of networks – user-
social networks and user-item interaction networks. We argue that if the
representations are disentangled into specific components as highlighted in
Fig. 1, it would facilitate capturing each component’s contribution for a
specific task and aid in generating debiased recommendations. In our causal
disentanglement model, the user and item latent representations are learned
using the user-social and user-item interaction networks. Then, the
representations are disentangled to account for three independent types of
variables: confounding variables, factors that model the exposure (treatment)
only, and those that are predictive of the ratings (outcome) only. Including
the hidden confounders in computing the rating predictions would allow us to
address the confounding bias. As a result, it would facilitate learning a
debiased recommender system. Also, to ensure that the learned factors are
independent of one another, we utilize Integral Probability Metric (Müller,
1997). To ensure the remaining bias from the confounders is eliminated, we
utilize context-aware importance sampling weights (Hassanpour and Greiner,
2019b). The significant contributions of this work are:

  * •

Investigating a novel setting of mitigating confounding bias in social
recommender systems,

  * •

Proposing to use a disentangling approach, D2Rec to identify and capture the
different factors with specific roles in the causal inference formulation of
recommender systems, and

  * •

Demonstrating the effectiveness of the proposed framework on various real-
world datasets with comparative analysis and ablation studies.

The remaining sections of the paper are categorized as follows. In Section 2,
we introduce the related work that has been developed in debiasing recommender
systems and how our method varies in comparison to them. In Section 3, we
present the technical preliminaries for the problem of posing a recommender
system from a causal perspective. In Section 4, we propose a causal
disentanglement model with technical details. In Section 5, we show the
results on two real-world datasets and discuss observations on different
baselines and the relevance of different components in our model. We conclude
this paper in Section 6.

##  2\. Related Work

Disentangling user and item representations for recommendation. This branch of
research focuses on disentangling user and item latent features for better and
explainable recommendations. To better understand user preferences and
identify system defects, the authors of (Liu et al., 2020) proposed to
generate explainable recommendations with the help of a framework that brings
transparency in the representation learning process. The authors propose to
discriminate information from different layers of graph convolutional
networks. Another line of work focuses on disentangling latent user
representations for news recommendations. The authors aim to disentangle and
learn latent factors that influence a user to share a news article by
leveraging a neighborhood routing algorithm (Hu et al., 2020). The authors of
(Qian et al., 2021) proposed a model to disentangling user and item latent
representations for better recommendations. The user representations are
disentangled into conformity influence and personal interest factors to
improve recommendations of long-tail items. The item representations are
disentangled the item attributes have a causal relation in the user
preferences (Nema et al., 2020), and disentangling user representations into
user interest and conformity in an implicit feedback scenario (Zheng et al.,
2021).

Debiasing Recommender Systems. Recommender systems suffer from various biases
(Chen et al., 2020). As a result, various methods have been developed to
facilitate debiasing the recommender systems to understand user preferences
better. For instance, to mitigate selection bias, recent efforts include
leveraging propensity score-based methods (Schnabel et al., 2016). Conformity
bias is mitigated by leveraging user social relations (Tang et al., 2012). To
deal with popularity bias, efforts leveraging disentanglement of latent
representations to represent interest and conformity factors are used (Zheng
et al., 2021). Methods leveraging re-weighting techniques for unobserved
samples with a uniform weight are developed to control exposure bias (Yu et
al., 2017). Similarly, regularization-based frameworks are used to enhance
long-tail coverage of items in a learning to rank algorithm (Abdollahpouri et
al., 2017).

Causal Recommender Systems. This branch of research aims to pose the
recommender systems from a causal perspective. The earliest work in this field
focuses on posing the recommendation problem as a causal inference problem
rather than a prediction problem. In this case, the exposure is considered as
treatment, and the ratings are considered as outcomes (Liang et al., 2016).
This work was later extended by modeling the exposure and using it as a
substitute for confounders (Wang et al., 2020). A recent work proposed in (Li
et al., 2021) utilized user’s social relations to estimate the exposure along
with propensity score and utilized this estimated exposure to mitigate
selection bias. Another line of work aims to learn an optimal recommendation
policy for each user. The authors aim to improve the recommender policy of the
system by considering logged feedback and predict recommendation outcomes
according to behavior under random exposure (Bonner and Vasile, 2018). Some
works, including (Zhang et al., 2021) proposed to leverage the good aspects of
popularity bias and deconfound the bad aspects for improving recommendations.
Moreover, to improve the personalized rankings of recommender systems (Yang et
al., 2021a) proposed to apply Pearl’s causal inference framework (Peters et
al., 2017).

Compared to earlier causal recommendation works, our work differs in two ways.
(1) Previous works utilize different estimation models to learn the substitute
of the hidden confounders (Liang et al., 2016; Wang et al., 2020), such as
estimating exposure using the Poisson Factorization model and utilizing the
estimated exposure as a substitute for the confounders. Although methods
leveraging user’s social relations to account for the confounders are proposed
in (Li et al., 2021) they do not consider any form of disentanglement. At the
same time, they learn the user and item representations from the user-item
networks. In contrast, our work aims to utilize disentanglement to learn a
representation for the hidden confounders in the latent space based on all the
observed information including the user’s social connections and an item’s
popularity. (2) Works such as DICE (Zheng et al., 2021) consider the causal
perspective of recommender systems with implicit feedback, which leads to a
different causal graph from the one considered in this work. For instance,
unlike explicit feedback, the observed data for implicit feedback consists of
a matrix of those items that the user viewed or clicked. Thus, DICE
disentangles the causes of clicks into two components, i.e., user interest and
item popularity. However, our work emphasizes the explicit feedback setting,
which is more descriptive about the user preference as they include a rating
score highlighting how much a user prefers an item. Moreover, we also include
the effect induced by the user’s social connections, which is not considered
in DICE. This work studies debiasing recommender systems with explicit
feedback from a causal perspective with network information.

Symbol | Description
---|---
$\bm{\theta_{u}}$ | Pre-trained user embedding from unsigned network
$\bm{\beta_{i}}$ | Pre-trained item embedding from unsigned network
$\bm{\alpha_{u}}$ | Disentangled user factor responsible for predicting exposure
$\bm{\alpha_{i}}$ | Disentangled item factor responsible for predicting exposure
$\bm{\gamma_{u}}$ | Disentangled user factor responsible for confounders
$\bm{\gamma_{i}}$ | Disentangled item factor responsible for confounders
$\bm{\Delta_{u}}$ | Disentangled user factor responsible for predicting rating
$\bm{\Delta_{i}}$ | Disentangled item factor responsible for predicting rating
$h_{i}$ | Feedforward neural networks
$\kappa$ | Coefficient that controls for discrepancy loss
$\sigma$ | Sigmoid activation function
ReLU | ReLU activation function
$y_{u,i}$ | Ground truth rating given to item $i$ by user $u$
$\hat{y}_{u,i}$ | Predicted rating that user $u$ would give to item $i$
$\exp_{u,i}$ | True exposure that user $u$ has interacted with item $i$
$\hat{\exp}_{u,i}$ | Predicted exposure that user $u$ would interact with item $i$

Table 1. Notations.

##  3\. Preliminaries

In this section, we first present the technical preliminaries. The notations
used in this work are summarized in Table 1 where the vectors are represented
in bold. Causal inference deals with the science of cause and effect. It helps
understand the impact of performing interventions on the data. Traditional
recommender systems (He et al., 2017; Mnih and Salakhutdinov, 2008) are
generally presented as a prediction problem, where, given the user and item
latent representations, the model utilizes techniques such as matrix
factorization to predict unseen ratings. However, these systems suffer from
the Missing Not At Random (MNAR) problem (Marlin and Zemel, 2009) which may
not lead to accurate predictions. Posing the recommender system problem from a
causal perspective can help in generating debiased recommendations. Earlier
works (Wang et al., 2020; Liang et al., 2016) considered exposure as
treatments and the observed ratings as the observed outcomes due to the
treatment. One difficulty with the causal approach is the presence of
confounders which are defined as the set of features that affect the treatment
and outcomes. For instance, the mechanism with which a user is either exposed
or not exposed to an item can influence the exposure value and the rating
value for that user-item pair. When the contribution due to the confounders is
not included while modeling the rating predictions, it may lead to biased
recommendations. A recent work, (Wang et al., 2020), proposed a deconfounded
recommender to explicitly control for confounding bias by accounting for the
effects induced by the confounders. A Poisson factorization model (Gopalan et
al., 2015) is used for modelling the exposure as:

(1) $\exp_{u,i}|\bm{\pi}_{u},\bm{\lambda}_{i}\sim
Poisson(\bm{\pi}_{u}^{T}\bm{\lambda}_{i}),$

where $\bm{\pi}_{u}$ and $\bm{\lambda}_{i}$ are the user and item embeddings
for modeling exposure. Then, the deconfounded recommender controls the
confounding bias by using the modelled exposure as a substitute for the hidden
confounders as follows:

(2)
$y_{u,i}=\bm{\theta}_{u}^{T}\bm{\beta}_{i}\cdot\exp_{u,i}+{\gamma}_{u}\hat{\exp}_{u,i}+\epsilon_{u,i},$

where $\epsilon_{u,i}\sim\mathcal{N}(0,\sigma^{2})$ is the noise term. The
term $\bm{\theta}_{u}^{T}\bm{\beta}_{i}\cdot\exp_{u,i}$ models the rating
prediction for which user $u$ was exposed to the item $i$.
${\gamma}_{u}\hat{\exp}_{u,i}$ models the effect of the substitute learned for
the hidden confounders, on the outcome, where ${\gamma}_{u}$ is a user-
specific coefficient that represents the sign and the magnitude of this effect
and $\hat{\exp}_{u,i}$ represents the substitute for the hidden confounders,
i.e., the inferred (probability of) exposure. When $\gamma_{u}$ is positive,
in Eq. (2), the product ${\gamma}_{u}\hat{\exp}_{u,i}$ models the positive
correlation between the confounder and rating.

##  4\. Causal Disentanglement for Debiased Recommender (D2Rec)

This work aims to debias the social recommender systems from a causal
perspective by leveraging auxiliary network information, including the user-
social network and user-item interaction network. The goal is to learn three
independent disentangled factors from the user and item’s latent
representations and control for the confounding bias. In the proposed Causal
Disentanglement for DeBiased Recommendations (D2Rec) model, the user
representation learned from the user-social network acts as a diverse source
of information that consists of factors for the user’s preferences and factors
for the hidden confounders (e.g., conformity). Similarly, item representations
consist of the factors for the item attributes and the factors for the hidden
confounders (e.g., item popularity). Thus, D2Rec aids in causally
disentangling these learned representations to account for the hidden
confounders, the factors for causing the exposure (treatment) and the factors
for causing the rating (outcome). Furthermore, to ensure each factor is
independent of the other factors, we utilize discrepancy loss (Gretton et al.,
2012; Müller, 1997) to maximize the distance between the distribution of the
learned disentangled factors, similar to (Zheng et al., 2021).

An overview of the proposed D2Rec can be found in Fig. 2. The approach
consists of three key components. First, it has a node embedding learning
module that takes (1) the user-social network as input to learn the user
embeddings; and (2) the user-item interaction network as input for learning
the item embeddings.

Figure 2. An overview of the architecture of the proposed D2Rec model. Here,
$f_{u}$ represents the function to learn user embeddings from the user-social
network, $f_{i}$ represents the function to learn item embeddings from the
user-item interactions network, $\bm{\theta_{u}}$ and $\bm{\beta_{i}}$
represents the user embeddings and item embeddings, Layer represents a
feedforward neural network used to learn the disentangled factors.
$\bm{\alpha_{u}}$,$\bm{\alpha_{i}}$,$\bm{\gamma_{u}}$,$\bm{\gamma_{i}}$,$\bm{\Delta_{u}}$,$\bm{\Delta_{i}}$
represent the learned disentangled user and item factors.

Second, we propose a novel module namely, causally disentangled representation
learning networks that disentangles the previously obtained user and item
embeddings into three factors that affect both the exposure (treatment) and
the ratings (outcomes). The third component of the proposed model is a neural
network that takes the factors mentioned above as the input and predicts the
rating and the exposure of a given user-item pair.

###  4.1. Representation Learning Networks for Causal Disentanglement

Recent efforts, such as (Hassanpour and Greiner, 2019b), provide evidence that
observational data can be disentangled into its corresponding underlying
factors, which can improve performance against the downstream tasks. The
disentangled factors facilitate in a better understanding of the information
present in the latent space. As the user representations and item
representations are collective representations of multiple factors, the
proposed disentangling component can better capture different factors of the
user and item representations. Since we aim to look at recommender systems
from a causal perspective, we propose to disentangle the user and item latent
representations $(\bm{\theta_{u}}$ and $\bm{\beta_{i}})$ into three underlying
factors $\alpha$, $\gamma$, $\Delta$. Among them, $\alpha$ is partially
responsible for modeling the exposure (treatment), the factor $\Delta$ is
partially responsible for predicting the ratings (outcomes), and $\gamma$ is
the factor responsible for the confounding factors that causally affect both
the exposure and the ratings. We use the user-social network to learn the
embedding for each user, and we use the user-item interaction network to learn
the embedding for each item. Note that we only use the user-social network to
learn the user embeddings. It is possible to learn user embeddings by
leveraging both user-social networks and user-item interaction networks (Fan
et al., 2019), which we leave for future work. The user and item embeddings
are defined as:

(3) $\displaystyle\bm{\theta_{u}}=\max_{f}\sum_{u\in
V}\log\operatorname{Pr}\left(N_{S}(u)\mid
f(u)\right),\quad\bm{\beta_{i}}=\max_{f}\sum_{i\in
V}\log\operatorname{Pr}\left(N_{S}(i)\mid f(i)\right).$

The representation networks consist of six independent layers that facilitate
the learning of the disentangled factors from the obtained user
representations and item representations $\bm{\theta_{u}}$ and
$\bm{\beta_{i}}$. They are $\bm{\alpha_{u}}$, $\bm{\alpha_{i}}$,
$\bm{\gamma_{u}}$, $\bm{\gamma_{i}}$, $\bm{\Delta_{u}}$, and
$\bm{\Delta_{i}}$, denoting the underlying factors for exposure prediction
($\alpha$), confounders ($\gamma$), and rating prediction ($\Delta$).
Formally,

(4)
$\displaystyle\bm{\alpha_{u}}=\text{ReLU}(h_{1}(\bm{\theta_{u}}));\quad\bm{\alpha_{i}}=\text{ReLU}(h_{4}(\bm{\beta_{i}}));$
$\displaystyle\bm{\gamma_{u}}=\text{ReLU}(h_{2}(\bm{\theta_{u}}));\quad\bm{\gamma_{i}}=\text{ReLU}(h_{5}(\bm{\beta_{i}}));$
$\displaystyle\bm{\Delta_{u}}=\text{ReLU}(h_{3}(\bm{\theta_{u}}));\quad\bm{\Delta_{i}}=\text{ReLU}(h_{6}(\bm{\beta_{i}})).$

where ReLU represents the nonlinear ReLU activation function,
$h_{k},k=1,...,6$ denote feedforward neural networks.

###  4.2. Rating and Exposure Prediction

We leverage the disentangled factors for users and items obtained from Eq. (4)
for rating prediction and exposure modeling for user-item pairs; each factor
plays a pivotal role in either computing the rating or the exposure. To ensure
the learned representations are independent of one another, we use an Integral
Probability Metric – Maximum Mean Discrepancy ($\operatorname{MMD}$) (Gretton
et al., 2012), which aims to measure how close two distributions are. The
discrepancy loss (Hassanpour and Greiner, 2019b) is given by,

(5)
$\displaystyle\mathcal{L}_{disc}=\operatorname{MMD}(\bm{\alpha_{u}},\bm{\gamma_{u}})+\operatorname{MMD}(\bm{\alpha_{u}},\bm{\Delta_{u}})+\operatorname{MMD}(\bm{\gamma_{u}},\bm{\Delta_{u}})+\operatorname{MMD}(\bm{\alpha_{i}},\bm{\gamma_{i}})+\operatorname{MMD}(\bm{\gamma_{i}},\bm{\Delta_{i}})+\operatorname{MMD}(\bm{\alpha_{i}},\bm{\Delta_{i}}),$

in which MMD refers to,

(6)
$\operatorname{MMD}(\mathbb{P},\mathbb{Q};\mathcal{F}):=\sup_{f\in\mathcal{F}}|\mathbb{E}[f(X)]-\mathbb{E}[f(Y)]|.$

Here, $\mathbb{P}$ and $\mathbb{Q}$ are probability distributions, and
$\mathcal{F}$ is a set containing all continuous functions. We take each
disentangled user factor and perform a Hadamard product ($\odot$) to its
counterpart in the item factors to generate a joint user-item representation
for the particular disentangled factor. We obtain the combined factors,
$\alpha_{u,i}$, $\gamma_{u,i}$, and $\Delta_{u,i}$ as follows:

(7)
$\displaystyle\alpha_{u,i}=\bm{\alpha_{u}}\odot\bm{\alpha_{i}};\quad\gamma_{u,i}=\bm{\gamma_{u}}\odot\bm{\gamma_{i}};\quad\Delta_{u,i}=\bm{\Delta_{u}}\odot\bm{\Delta_{i}}.$

Looking from a causal perspective, the factor $\alpha_{u,i}$ is used for
modeling the treatment (exposure), the factor $\gamma_{u,i}$ is used for
modeling the confounders that affect both the treatment (exposure) and the
outcome (ratings), and the factor $\Delta_{u,i}$ is used for modeling the
outcomes (ratings). We then group $\alpha_{u,i}$, $\gamma_{u,i}$, and
$\Delta_{u,i}$ into the following categories: the factors $\alpha_{u,i}$ and
$\gamma_{u,i}$ are collectively used for modelling the exposure, and factors
$\gamma_{u,i}$ and $\Delta_{u,i}$ are collectively used for modelling the
ratings. Traditional recommenders utilize the entangled user and item
representations to minimize the errors on the observed ratings. However, based
on Fig. 1 we argue that not all components of the representations are helpful
for rating prediction. Thus, with the aid of disentanglement, we learn factors
from the user and item latent representations that only affect the ratings and
are independent of the exposure mechanism and vice versa (since $\Delta_{u,i}$
and $\alpha_{u,i}$ are independent of each other) which helps the rating
prediction model to generate debiased recommendations. Given the
disentanglement, we proceed to compute the exposure as

(8) $\hat{\exp}_{u,i}=\sigma(\alpha_{u,i}\cdot\gamma_{u,i}),$

where $\cdot$ represents the dot product, $\sigma$ is the sigmoid activation
function. Similarly, the rating can be computed as

(9)
$\hat{y}_{u,i}=\omega(\exp_{u,i},\hat{\exp}_{u,i},\gamma_{u,i})\cdot\text{ReLU}(\gamma_{u,i}\cdot\Delta_{u,i}),$

where $\exp_{u,i}$ denotes the true exposure for user $u$ and item $i$,
$\hat{\exp}_{u,i}$ represents the predicted exposure learned from Eq. (8) and
$\omega(\exp_{u,i},\hat{\exp}_{u,i},\gamma_{u,i})$ is the re-weighting
function. By taking the confounding factors as an input to the rating
prediction function we mitigate the confounding bias. As mentioned earlier,
the factor $\gamma$ is likely to exhibit some degree of bias, as it consists
of the information affecting both the exposure and ratings. To counter this,
we rely on context-aware importance sampling weights that could mitigate the
remainder bias (Hassanpour and Greiner, 2019b):

(10) $\begin{aligned}
\omega&(\exp_{u,i},\hat{\exp_{u,i}},\gamma_{u,i})&=1+\frac{\operatorname{Pr}\left(\exp_{u,i}=1\right)}{1-\operatorname{Pr}\left(\exp_{u,i}=1\right)}\times\frac{1-\operatorname{Pr}\left(\hat{\exp}_{u,i}=1\mid\gamma_{u,i}\right)}{\operatorname{Pr}\left(\hat{\exp}_{u,i}=1\mid\gamma_{u,i}\right)},\end{aligned}\
$

where $\exp_{u,i}$ represents the true exposure, i.e. whether the user was
exposed to the item and $\hat{\exp}_{u,i}$ represents the predicted exposure
learned from Eq. (8). The reweighting function is effective as no confounders
are discarded, and only the legitimate confounders are used to derive the
weights. Once we obtain the predicted exposure from Eq. (8) and predicted
ratings from Eq. (9), we compute the overall objective function as

(11) $\displaystyle
J(\hat{y}_{u,i},\hat{\exp}_{u,i})=\kappa\cdot\mathcal{L}_{disc}+\mathcal{L}(y_{u,i},\hat{y}_{u,i})+\mathcal{L}_{\exp}(\exp_{u,i},\hat{\exp}_{u,i}),$

where we aim to minimize $\mathcal{L}(y_{u,i},\hat{y}_{u,i})$, which
represents the mean squared error in predicting the ratings:

(12) $\mathcal{L}=\sum_{u,i}(y_{u,i}-\hat{y}_{u,i})^{2}.$

We also aim to minimize $\mathcal{L}_{\exp}(\exp_{u,i},\hat{\exp}_{u,i})$,
which represents the binary cross-entropy loss formulated as

(13)
$\begin{split}\mathcal{L}_{\exp}=-\sum_{u,i}(\exp_{u,i}\cdot\log(\hat{\exp}_{u,i})+(1-\exp_{u,i})\cdot\log(1-\hat{\exp}_{u,i})).\end{split}$

To ensure that the learned disentangled representations are independent of one
another, we use the discrepancy loss in Eq. (5) that measures how close two
distributions are. Therefore, the goal is to maximize this discrepancy loss.
Furthermore, since the discrepancy loss directly influences the distribution
of the learned embeddings, we use $\kappa$ to control the effect of
discrepancy loss on the overall objective function.

##  5\. Experiments

The node embedding module of D2Rec learns the user and item embeddings from
social network information. We leverage the Node2vec (Grover and Leskovec,
2016) framework to obtain the user and item embeddings. More advanced node
embedding methods, as well as GNN based methods to directly incorporate
network information while learning the user and item representations can also
be used with D2Rec and, will be explored in future work.

We conducted a series of experiments to understand whether disentangling the
user and item latent features learned from auxiliary network information can
help adjust for confounding bias in debiased social recommendations. Ideally,
a causal method is evaluated based on how well an algorithm mitigates
confounding bias with a test set where treatments are randomly assigned
(Shadish et al., 2008).

Since the existing real-world social recommender system datasets do not have
unbiased test sets, we need to first create pseudo unbiased test sets through
sampling from observational data. We follow the standard protocol introduced
by (Liang et al., 2016; Bonner and Vasile, 2018) to create such pseudo
unbiased test sets. In a pseudo unbiased test set, items are uniformly
exposed, i.e., each item has precisely the same number of appearances in the
test set. In particular, we split each dataset into training and test sets as
follows. First, the training samples are randomly sampled from the original
data (thus biased). Then, from the rest of the dataset, we create subsets as
the unbiased test sets by conditioning on item popularity to make each pseudo
unbiased test set have an equal number of ratings for items. In this way, we
ensure that the pseudo unbiased test set has different exposure distribution
from its corresponding training set. Thus, we can verify whether D2Rec
effectively adjusts for the confounding bias by computing its generalization
performance on the pseudo unbiased test sets (Bühlmann, 2020). We conduct
experiments to answer the following research questions.

  * •

RQ.1 Can disentangling the user and item embeddings with network information
help debias recommendations?

  * •

RQ.2 What are the roles played by the network information and by the
disentanglement module concerning the performance of D2Rec, respectively?

###  5.1. Experiment Setup

This section introduces the datasets, evaluation metrics, parameter settings,
and the baselines used for the experiments. To simulate the causal evaluation
settings as mentioned earlier, we generate test sets ranging from 2 through 10
ratings per item. Finally, we report the performance comparison across the
different baselines and perform an ablation study on various components of
D2Rec to comment on their significance.

####  5.1.1. Datasets

For our experiments, we use two representative real-world datasets
Ciao222https://www.cse.msu.edu/~tangjili/Ciao.rar and
Epinions333https://www.cse.msu.edu/~tangjili/Epinions.rar. Both these datasets
are derived from popular social networking websites
Ciao444http://www.ciao.co.uk and Epinions555www.epinions.com. These websites
allow users to rate multiple items, browse/write reviews, and formulate
trust/distrust relations among users. They can provide a vast amount of rating
information and social information. The social interactions denote the trust
relationships between users. We created self-loops for users who did not have
any social interactions denoting that they trusted themselves. The ratings are
in the range of 1 to 5. A summary of the datasets can be found in Table 2.

Dataset | No. of Users | No. of Items | No. of Ratings | Rating Density | No. of Social Connections | Social Connections Density
---|---|---|---|---|---|---
Ciao | 7,375 | 105,114 | 284,086 | 0.0366 | 112,384 | 0.2060
Epinions | 40,163 | 139,738 | 664,824 | 0.0118 | 455,751 | 0.0282

Table 2. Statistics of the Datasets.

####  5.1.2. Evaluation Metrics

For evaluation of D2Rec and baselines, we rely on rating prediction and
ranking metrics.

Rating Prediction Metrics. To evaluate rating performance, we use two popular
metrics, Mean Squared Error (MSE) and Mean Absolute Error (MAE):

(14) $\displaystyle MAE$ $\displaystyle=$
$\displaystyle\frac{1}{N_{ts}}\sum_{(u,i)}|y_{u,i}-\hat{y}_{u,i}|,\quad MSE$
$\displaystyle=$
$\displaystyle\frac{1}{N_{ts}}\sum_{(u,i)}(y_{u,i}-\hat{y}_{u,i})^{2}.$

Here $N_{ts}$ denotes the total number of ratings in the test set, $y_{u,i}$
denotes the true observed rating for the entry of the user-item pair $(u,i)$,
and $\hat{y}_{u,i}$ denotes the predicted rating for the corresponding user-
item pair.

Ranking Metrics. To evaluate personalized ranking performance, we use two
popular metrics, Hit-Ratio@K and Normalized Discounted Cumulative Gain
(NDCG@K):

  * •

Hit-Ratio@K refers to the proportion of users for which the model can
correctly include the items a user has interacted within the list of top-K
recommended items

(15) $HR=\frac{|U_{\text{hit }}^{K}|}{|U_{\text{all}}|},$

where $|U_{\text{hit }}^{K}|$ is the number of users for which the recommender
systems was able to include the items user has interacted with in the top-K
recommended items list and $|U_{\text{all}}|$ denotes the total number of
users in the test set.

  * •

For user-item interactions, gain for an item refers to the relevance score. To
take order of the ranking into consideration, Discounted Cumulative Gain (DCG)
is formulated as

(16) $DCG_{K}^{i}=\sum_{r=1}^{K}\frac{2^{{y}_{u,r}}-1}{\log_{2}(1+r)},$

where ${y}_{u,r}$ refers to the ground truth rating for user $u$ and $r^{th}$
ranked item. The normalized discounted gain (nDCG) is then defined as

(17) $nDCG_{K}=\frac{1}{|U|}\sum_{u\in U}\frac{DCG_{K}^{u}}{IDCG_{K}^{u}},$

where $|U|$ refer to the total number of users in the test set and
$IDCG_{K}^{u}$ refers to the best possible value of $DCG_{K}^{u}$.

####  5.1.3. Parameter Settings

We implemented all baseline models on a Linux server with Tesla K-80 25GB GPU.
We implemented D2Rec in Pytorch. To verify if D2Rec is helping with debiasing
recommender systems, we first perform a train/test split of 60/40; we further
split the test set into subgroups conditioned in terms of popularity to obtain
subsets of items with 2 through 10 ratings per item. The embedding size, $d$,
was varied from {32,64,128,256}. We varied the batch size from
{64,128,512,1000} and the learning rate was varied from {0.0001,0.001,0.01}.
Moreover, we set the activation function as ReLU. We employed six different
neural networks for calculating $\bm{\alpha_{i}}$, $\bm{\alpha_{u}}$,
$\bm{\gamma_{i}}$, $\bm{\gamma_{u}}$, $\bm{\Delta_{i}}$, and
$\bm{\Delta_{u}}$. The maximum number of epochs was set to 200, and an early
stopping strategy was performed, where we stopped training if the MSE on the
train set did not decrease for ten successive epochs. The parameters were
initialized with the corresponding papers’ values and then tuned to achieve
the best empirical performance for all baselines. We optimized all models with
the Adam optimizer. $\kappa$ is set to 0.5 to denote the contribution of
discrepancy loss to the objective functions.

Model | Popularity Debiased Test Sets
---|---
Popularity=2 | Popularity=3 | Popularity=5 | Popularity=10
NDCG@10 | HR@10 | NDCG@10 | HR@10 | NDCG@10 | HR@10 | NDCG@10 | HR@10
SocialMF (Jamali and Ester, 2010) | 0.32 | 0.64 | 0.34 | 0.67 | 0.35 | 0.70 | 0.37 | 0.73
GraphRec (Fan et al., 2019) | 0.24 | 0.56 | 0.23 | 0.55 | 0.20 | 0.52 | 0.20 | 0.51
ConsisRec (Yang et al., 2021b) | 0.36 | 0.70 | 0.38 | 0.74 | 0.41 | 0.77 | 0.43 | 0.79
NeuMF (He et al., 2017) | 0.31 | 0.65 | 0.31 | 0.66 | 0.32 | 0.67 | 0.33 | 0.69
PMF (Mnih and Salakhutdinov, 2008) | 0.33 | 0.69 | 0.34 | 0.71 | 0.36 | 0.72 | 0.38 | 0.74
IPS-MF (Liang et al., 2016) | 0.31 | 0.65 | 0.32 | 0.68 | 0.38 | 0.73 | 0.40 | 0.78
CIRS (Wang et al., 2020) | 0.37 | 0.70 | 0.39 | 0.74 | 0.39 | 0.75 | 0.42 | 0.80
DICE (Zheng et al., 2021) | 0.34 | 0.68 | 0.36 | 0.70 | 0.38 | 0.74 | 0.42 | 0.81
D2Rec | 0.38 | 0.73 | 0.38 | 0.76 | 0.41 | 0.80 | 0.44 | 0.83

Table 3. Comparing the ranking performance of different recommender system
models with D2Rec for Epinions.

Model | Popularity Debiased Test Sets
---|---
Popularity=2 | Popularity=3 | Popularity=5 | Popularity=10
NDCG@10 | HR@10 | NDCG@10 | HR@10 | NDCG@10 | HR@10 | NDCG@10 | HR@10
SocialMF (Jamali and Ester, 2010) | 0.31 | 0.60 | 0.36 | 0.70 | 0.40 | 0.77 | 0.44 | 0.82
GraphRec (Fan et al., 2019) | 0.16 | 0.37 | 0.14 | 0.35 | 0.15 | 0.38 | 0.18 | 0.44
ConsisRec (Yang et al., 2021b) | 0.29 | 0.59 | 0.32 | 0.63 | 0.35 | 0.68 | 0.37 | 0.72
NeuMF (He et al., 2017) | 0.26 | 0.54 | 0.28 | 0.58 | 0.30 | 0.61 | 0.32 | 0.68
PMF (Mnih and Salakhutdinov, 2008) | 0.29 | 0.60 | 0.32 | 0.66 | 0.36 | 0.70 | 0.43 | 0.82
IPS-MF (Liang et al., 2016) | 0.27 | 0.55 | 0.30 | 0.60 | 0.39 | 0.74 | 0.44 | 0.83
CIRS (Wang et al., 2020) | 0.34 | 0.62 | 0.36 | 0.68 | 0.38 | 0.73 | 0.43 | 0.81
DICE (Zheng et al., 2021) | 0.29 | 0.58 | 0.34 | 0.66 | 0.37 | 0.70 | 0.46 | 0.80
D2Rec | 0.30 | 0.60 | 0.36 | 0.70 | 0.41 | 0.79 | 0.49 | 0.89

Table 4. Comparing the ranking performance of different recommender system
models with D2Rec for Ciao.

####  5.1.4. Baselines

Given that our framework focuses on mitigating confounding bias in an explicit
feedback setting by leveraging auxiliary network information, we consider the
following three types of baselines that represent the benchmark works in the
respective categories:

Social Recommender Systems. D2Rec leverages auxiliary network information to
account for confounders and better capture the user and item latent features.
We, therefore, compare D2Rec with benchmarks for social recommendations.

Social Matrix Factorization - SocialMF (Jamali and Ester, 2010) leverages
users’ social networks to model their preferences. This work considers social
relations among users by adding propagation of each relation into the matrix
factorization model.

Graphrec: Graph Neural Networks for Social Recommendation - Graphrec (Fan et
al., 2019) models social information with a Graph Neural Network. It leverages
user-user social networks to model user latent features. It also uses the
opinions associated with the user-item interactions network to model item
latent features.

ConsisRec: Enhancing GNN for Social Recommendation via Consistent Neighbor
Aggregation (Yang et al., 2021b) It is the state-of-the-art method in social
recommendation. This model introduces the social inconsistency problem in
social recommender systems and proposes to solve this problem by sampling-
based attention mechanism.

Traditional Recommender Systems. The second set of baselines are traditional
recommender systems.

Neural Collaborative Filtering - NeuMF (He et al., 2017) is a state-of-the-art
collaborative filtering model with neural network architecture. The authors
model the user and item features through embedding layers and leverage a
multi-layer perceptron to learn the user-item interactions for predicting
ratings.

Probabilistic Matrix Factorization - PMF (Mnih and Salakhutdinov, 2008) models
the user preference matrix as a product of two low-rank user and item matrices
generated from Gaussian distributions. The approach also uses adaptive priors
over the user and item latent features for model complexity.

Causal Recommender Systems. We compare D2Rec with the baselines that leverage
causal inference for debiasing recommender systems with explicit feedback and
DICE (Zheng et al., 2021) which is a causal disentanglement framework proposed
under an implicit feedback setting.

Inverse Propensity Score Matrix Factorization - IPS-MF (Liang et al., 2016)
makes use of inverse propensity scores to alleviate the selection bias
generated from the exposure data. The authors assign a probability to each
possible user-item pair to ensure that each user-item interaction can be
observed. Then, poisson factorization is used to compute propensity scores
from the observed exposure matrix, and weighted matrix factorization is
leveraged to correct for bias.

Causal Inference for Recommender Systems - CIRS (Wang et al., 2020) models the
item exposure to a user as the treatment and the observed ratings as the
outcomes. To measure the hidden confounders, this work uses a substitute by
generating predicted exposure with the help of Poisson Factorization. It is
used to compute the ratings by including the contribution of confounders for
each user. This approach is integrated into a standard matrix factorization
model.

Disentangling User Interest and Conformity for Recommendation with Causal
Embedding (Zheng et al., 2021) considers the implicit recommender system
setting. It considers the user interest and the conformity as the causes for
the observed clicks and proposes a disentanglement framework for debiased
recommendations. We only compare this baseline against the ranking prediction
since the MAE and MSE metrics are not valid for implicit recommender systems.

Model | Popularity Debiased Test Sets
---|---
Popularity=2 | Popularity=3 | Popularity=5 | Popularity=10
MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE
SocialMF (Jamali and Ester, 2010) | 1.36 | 3.89 | 1.05 | 2.32 | 0.91 | 1.61 | 0.87 | 1.47
GraphRec (Fan et al., 2019) | 0.64 | 0.88 | 0.68 | 0.90 | 0.72 | 0.97 | 0.75 | 1.05
ConsisRec (Yang et al., 2021b) | 0.63 | 0.85 | 0.60 | 0.84 | 0.56 | 0.78 | 0.52 | 0.70
NeuMF (He et al., 2017) | 1.31 | 2.75 | 1.27 | 2.61 | 1.25 | 2.51 | 1.23 | 2.48
PMF (Mnih and Salakhutdinov, 2008) | 1.25 | 2.92 | 1.03 | 2.01 | 0.93 | 1.60 | 0.92 | 1.56
IPS-MF (Liang et al., 2016) | 1.01 | 1.68 | 0.98 | 1.59 | 0.97 | 1.57 | 0.95 | 1.53
CIRS (Wang et al., 2020) | 1.08 | 3.36 | 0.74 | 1.90 | 0.49 | 0.94 | 0.35 | 0.55
D2Rec | 0.72 | 1.49 | 0.49 | 0.82 | 0.34 | 0.44 | 0.22 | 0.25

Table 5. Comparing the prediction performance of different recommender system
models with D2Rec for Epinions.

Model | Popularity Debiased Test Sets
---|---
Popularity=2 | Popularity=3 | Popularity=5 | Popularity=10
MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE
SocialMF (Jamali and Ester, 2010) | 1.40 | 4.20 | 1.00 | 2.20 | 0.78 | 1.10 | 0.72 | 0.95
GraphRec (Fan et al., 2019) | 0.62 | 0.72 | 0.67 | 0.80 | 0.71 | 0.84 | 0.74 | 0.92
ConsisRec (Yang et al., 2021b) | 0.59 | 0.60 | 0.54 | 0.58 | 0.50 | 0.46 | 0.43 | 0.32
NeuMF (He et al., 2017) | 1.23 | 2.43 | 1.20 | 2.31 | 1.16 | 2.15 | 1.13 | 2.09
PMF (Mnih and Salakhutdinov, 2008) | 1.21 | 2.75 | 0.94 | 1.72 | 0.80 | 1.15 | 0.78 | 1.08
IPS-MF (Liang et al., 2016) | 1.12 | 2.02 | 1.09 | 1.94 | 1.05 | 1.80 | 1.03 | 1.73
CIRS (Wang et al., 2020) | 0.92 | 3.10 | 0.52 | 1.44 | 0.28 | 0.56 | 0.17 | 0.24
D2Rec | 0.40 | 0.72 | 0.21 | 0.29 | 0.10 | 0.07 | 0.04 | 0.02

Table 6. Comparing the prediction performance of different recommender system
models with D2Rec for Ciao.

###  5.2. Performance Comparison (RQ.1)

We compare the different baseline models with D2Rec on two real-world
datasets, Epinions and Ciao. We split the test set into multiple test sets
such that in each set, we ensure the number of ratings per item is the same
for all items. Table 5 (for Epinions) and Table 6 (for Ciao) demonstrates the
performance comparison across test sets with the number of ratings per item
ranging from 2 through 10 for the different prediction performance metrics
(MSE and MAE), and Table 3 (for Epinions) and Table 4 (for Ciao) shows the
performance against different ranking performance metrics (Hit-Ratio@10 and
NDCG@10). We have the following observations regarding RQ.1:

  * •

Overall, D2Rec consistently yields the best performance among all datasets.
For instance, it leads to more accurate rating prediction over the best
baseline w.r.t. MSE/MAE. The results indicate that disentangling the factors
with the help of social network information facilitates in debiasing
recommendations. D2Rec also outperforms the other baselines in ranking
performance, achieving the highest NDCG@K and Hit-Ratio@K scores across
different test sets.

  * •

Among the three types of baselines, the causal recommender systems serve as
the strongest baselines in most cases, justifying that accounting for the
underlying causal model is effective for debiasing recommender systems with
explicit feedback. Causal recommender system models outperform traditional
baselines in both rating prediction and ranking. D2Rec further outperforms the
causal baselines because (1) it leverages social network information as a
substitute for the unobserved confounders and (2) D2Rec disentangles the user
and item representations into independent factors (exposure factors, rating
factors, or confounders) as shown in the causal graph (see Fig. 1). We also
observe that DICE (Zheng et al., 2021) outperforms other baselines showing
that causal disentanglement is beneficial for producing debiased
recommendations. However, D2Rec outperforms DICE due to two reasons. First,
D2Rec uses network information to learn a better substitute for the hidden
confounders, which DICE does not. Second, the performance discrepancy can
result from different design purposes of DICE and D2Rec. DICE is designed
specifically for the implicit feedback setting where the resulting causal
graph is different from D2Rec’s explicit feedback setting.

  * •

It is observed that the performance of the traditional recommender baselines
PMF and NeuMF, can drop significantly when items with extremely low popularity
dominate the test sets (e.g., when the number of ratings per item is 2). This
occurs because these models assume that ratings are missing at random, leading
to learn biased embeddings. As a result, their prediction performance
deteriorates on debiased test sets. Thus, these baselines are outperformed by
D2Rec and the causal baselines in most of the cases.

  * •

The error rate for the GraphRec baseline increases as the number of ratings
per item increases. We believe this occurs because of a problem prominent to
Graph Neural Networks (GNNs) – over-smoothing (Cai and Wang, 2020). GNNs
aggregate feature vectors from the neighbors of a node and combine them with
the node’s features to compute its representations. In addition, item
popularity follows a long-tailed distribution (Yang et al., 2018). Over-
smoothing can make GraphRec overfit the unpopular items as they dominate the
population. Although popular items have more ratings in the training set, the
computation of their representations considers their k-hop neighbors where
there are enormous unpopular items. We follow (Fan et al., 2019) to use three-
layer GNNs in the GraphRec implementation. This explains why GraphRec performs
well when unpopular items dominate the test set while its performance drops
when the number of ratings per item increases in the debiased test sets. Since
ConsisRec utilizes a more restrictive sampling strategy based on consistency
scores between users and utilizes an attention mechanism to select consistent
relations, it overcomes the over-smoothing problem. SocialMF does well as it
does not use a GNN to learn embeddings but learns user features by only
incorporating the information of 1-hop neighbors in both user-social and user-
item networks.

###  5.3. Ablation Study (RQ.2)

Model | Popularity Debiased Test Sets
---|---
Popularity=2 | Popularity=3 | Popularity=5 | Popularity=10
MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE
D2Rec | 0.72 | 1.49 | 0.49 | 0.82 | 0.34 | 0.44 | 0.22 | 0.25
D2Rec w/o network embeddings | 0.70 | 1.30 | 0.53 | 0.83 | 0.41 | 0.49 | 0.30 | 0.34
D2Rec w/o disentanglement | 0.72 | 1.67 | 0.58 | 1.03 | 0.45 | 0.50 | 0.31 | 0.33

Table 7. Analyzing (1) the effect of removing the disentanglement from D2Rec
and (2) the effect of removing network embedding across different metrics for
Epinions.

Model | Popularity Debiased Test Sets
---|---
Popularity=2 | Popularity=3 | Popularity=5 | Popularity=10
MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE
D2Rec | 0.40 | 0.72 | 0.21 | 0.29 | 0.10 | 0.07 | 0.04 | 0.02
D2Rec w/o network embeddings | 0.40 | 0.60 | 0.26 | 0.32 | 0.16 | 0.12 | 0.10 | 0.04
D2Rec w/o disentanglement | 0.43 | 0.80 | 0.30 | 0.54 | 0.20 | 0.18 | 0.14 | 0.10

Table 8. Analyzing (1) the effect of removing the disentanglement from D2Rec
and (2) the effect of removing network embedding across different metrics for
Ciao.

To assess the contribution of the different components of D2Rec concerning the
performance, we conduct the following experiments. We consider two variants of
D2Rec, one which is trained on non-network embeddings removing the effect
induced by the network information namely, D2Rec w/o network embeddings. The
second variant of D2Rec is utilizes the network information but doesn’t
undergo any form of disentanglement. We denote this variant by D2Rec w/o
disentanglement. We conduct the same experiments across popularity debiased
test sets where the item popularity ranges from 2-10. The results obtained can
be seen in Table 7 for Epinions and Table 8 for Ciao. As observed, D2Rec
performs the best when both the network information and the disentanglement
are considered. Among the two variants, it is observed that D2Rec benefits
more from the disentanglement module when compared to the network information.
We believe such a pattern is observed because the network information aids in
accounting for a specific type of confounders, i.e., the user conformity. In
contrast, the disentanglement module acts as the base of learning specific
components of the user and item representations that helps debias the
recommender system by introducing the contribution of confounders in rating
prediction.

##  6\. Conclusion and Future work

This work aims to leverage network information to debias social
recommendations with the aid of causal disentanglement. Recommender systems
suffer from a range of biases which hurt their performance. A common approach
to generate debiased recommendations is to pose the recommender system problem
from a causal perspective. However, this setting has not been adapted for the
social recommender systems. We first formulate the social recommender systems
problem from a causal perspective. In this setting, the exposure of an item to
the user is analogous to the treatment, and the rating of an item is analogous
to the outcome. A user’s preferences are similar to or influenced by their
social relations. Thus, the social relations can aid in mitigating confounding
bias as they act as noisy measures of hidden confounders. Aside from the user
conformity, aspects of confounding such as item popularity present in the
network information is also captured in our method with the aid of causal
disentanglement which unravels the learned representations into three
independent factors. Each factor contributes to either predicting the exposure
(treatment) or the rating (outcome) or accounts for the hidden confounders.
Empirical evaluations on two real-world datasets corroborate the effectiveness
of D2Rec. By leveraging network information and causal disentanglement, D2Rec
consistently outperforms state-of-the-art algorithms with remarkable
improvements. The analysis of the different components of D2Rec reveals that
the causal disentanglement is more important than the network information in
debiasing the recommendation performance.

D2Rec considers a unified representation for the confounders. A meaningful
direction for future work is extending D2Rec to include more fine-grained
confounders, such as user conformity and item popularity factors. Another
possible direction would be to explore how D2Rec would perform with distrust
networks. Overall, we believe causal disentanglement of the user and item
latent representations opens new doors for understanding user-item
interactions of recommender systems.

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