# Counterfactually Evaluating Explanations in Recommender Systems

Yuanshun Yao<EMAIL_ADDRESS>ByteDance AI LabUSA ,  Chong Wang
<EMAIL_ADDRESS>ByteDanceUSA and  Hang Li<EMAIL_ADDRESS>ByteDance AI LabChina

###### Abstract.

Modern recommender systems face an increasing need to explain their
recommendations. Despite considerable progress in this area, evaluating the
quality of explanations remains a significant challenge for researchers and
practitioners. Prior work mainly conducts human study to evaluate explanation
quality, which is usually expensive, time-consuming, and prone to human bias.
In this paper, we propose an offline evaluation method that can be computed
without human involvement. To evaluate an explanation, our method quantifies
its counterfactual impact on the recommendation. To validate the effectiveness
of our method, we carry out an online user study. We show that, compared to
conventional methods, our method can produce evaluation scores more correlated
with the real human judgments, and therefore can serve as a better proxy for
human evaluation. In addition, we show that explanations with high evaluation
scores are considered better by humans. Our findings highlight the promising
direction of using the counterfactual approach as one possible way to evaluate
recommendation explanations.

##  1\. Introduction

Today we expect more from recommender systems than merely making
recommendations. As a system that serves humans, a modern recommender system
needs to meet a range of advanced responsibility requirements, including
fairness, diversity, explainability, accountability, and safety etc. The
necessity of building responsible recommender systems comes from not only the
users’ natural requests which lead to product demands, but also an increasing
amount of moral pressure from the public opinions (you, 2020; fac, 2021; twi,
2021) as well as compliance requirement from the government guidelines and
regulations (dar, 2017; aiu, 2018; chi, 2017; cre, 2022). In short, for
today’s practitioners, building responsible recommender systems is
commercially, morally, and legally desirable.

Driven by the needs, researchers have made considerable progress in
constructing responsible recommender systems. In this paper, we focus on
explainability. This is an important part of a responsible system because it
offers several benefits to both users and systems. First, it gives users more
control over the system. If users know why a recommendation is made, they will
learn how to change their behaviors to receive different recommendations in
the future. Second, the system can gain users’ trust by showing that the
system is transparent. Third, explainability can also help practitioners to
debug the recommendation model.

For explainability of recommendation, a variety of approaches have been
proposed, and can be roughly categorized as collaborative filtering based
approach (Resnick et al., 1994; Herlocker et al., 2000; Sarwar et al., 2001)
(explain by relevant users or items), user opinion based approach (Zhang et
al., 2014; Wu and Ester, 2015; Costa et al., 2018) (explain by user reviews),
and social interaction based approach (Sharma and Cosley, 2013; Chaney et al.,
2015; Wang et al., 2014) (explain by user social information) etc. Another way
to classify existing approaches is by the type of models used to generate
explanations. For example, some work chooses factorization models (Zhang et
al., 2014; Zhang et al., 2015; Chen et al., 2016) or neural models (Seo et
al., 2017; Wu et al., 2019; Gao et al., 2019) while others select graph models
(Heckel et al., 2017; He et al., 2015; Wang et al., 2018a) or natural language
models (Chang et al., 2016; Wang et al., 2018b; Costa et al., 2018).

Prior work so far focuses on developing algorithms that generate explanations,
while little attention is paid to evaluating the quality of generated
explanations. Because eventually recommendation explanations are judged
subjectively by users, prior work relies largely on conducting human studies
to assess how well their proposed algorithms perform. However, for a
recommender system deployed in the real world, conducting user studies is a
costly and painful process. First, it is slow to collect users’ feedback and
therefore would become the bottleneck of the algorithm development. Second, it
is expensive since online human assessment costs more than offline algorithm
testing. Third, it is prone to numerous human biases, e.g. methodological
bias, familiarity bias, and culture bias etc. In summary, we believe the use
of suitable evaluation methods is vital to the development of explainability
in recommender systems, and it is currently missing in this research area.

To overcome the challenge, we propose an offline evaluation method that can be
computed without human involvement. It is fast, low-cost, scalable, unaffected
by human bias, and therefore more suitable for evaluating explanations in
real-world recommender systems. We design the evaluation method based on
counterfactual logic, following the insights from counterfactual psychology
(Kahneman and Tversky, 1981; Mandel et al., 2005; Carpenter, 1973; Fillenbaum,
1974) and counterfactual machine learning (Wachter et al., 2017; Mothilal et
al., 2020; Russell, 2019). Our method produces a score that measures the
quality of an explanation by quantifying the explanation’s counterfactual
impact on the recommendation. Through an intensive user study ($N=400$), we
show that the evaluation scores are closely correlated with the human
judgments, and therefore can serve as a good proxy for the evaluation of
explanations. In addition, we demonstrate that the explanations with high
scores are generally considered better by humans than those from the baseline
approaches. We summarize our contributions as follows:

  * •

We propose a new method that evaluates the quality of explanations in
recommender systems using counterfactual logic.

  * •

Through an extensive user study, we validate the effectiveness of the
evaluative scores produced by our method by demonstrating its close
correlation to human judgments.

  * •

We show that humans consider the explanations with high evaluation scores
better.

We hope that our work can bring more attention to research on evaluation
methods for explainability in recommender systems. Our counterfactual design
is one possible way to approach the problem, and there might be other ways to
design evaluation metrics. Algorithm development requires a variety of
evaluation metrics, and the more the better. As we see from other areas, e.g.
BLEU score (Papineni et al., 2002) in natural language processing and NDCG
measure (Al-Maskari et al., 2007) in information retrieval, a good evaluation
method can greatly accelerate the advancement of a field.

##  2\. Background

In this section, we begin by providing some background information on
explainable recommender system and then counterfactual machine learning.

###  2.1. Explainable Recommender System

Why Explainable Recommender System? An explainable recommender system offers
several benefits to both users and the system. First, it provides users with
more control over the system. If a user is unhappy with the current
recommendation, the explanation can tell users what actions to take to change
future recommendations. Tran et al.  (Tran et al., 2021b) show that users are
more likely to want explanations when they dislike the current recommendation.
In this case, by choosing to interact with items different from those in the
explanation, users can stop receiving similar recommendations in the future.
Second, explainability might help the conventional goals of recommendation,
e.g. knowing why an item is recommended might increase the chance for users to
interact with the item. Third, the system can gain user trust by showing the
system is transparent through explanations. Forth, explainability can also
help practitioners debug the recommendation models. Finally, it fulfills the
potential legal requirements as explainability has been increasingly mentioned
in governmental AI proposals from various countries including US (dar, 2017;
cre, 2022), UK (aiu, 2018), and China (chi, 2017).

Current Approach. In the following, we briefly summarize the major categories
of existing approaches to explain recommendations in recommender systems. For
more details, refer to (Zhang and Chen, 2018) for a general survey.

  * •

Collaborative filtering based logic: The logic uses relevant users or items to
explain recommendations. In user-based collaborative filtering (Resnick et
al., 1994; Herlocker et al., 2000) logic, the recommender system finds a group
of users similar to the current user, and explains that the system recommends
the current item because some neighborhood users had some positive feedback on
it. On the other hand, item-based collaborative filtering (Sarwar et al.,
2001) logic explains the recommendation by finding a group of items from the
current user’s interaction history and then informing the user the
recommendation reason is that the user has interacted those similar items in
the past. For both logic, the relevance is usually obtained from user-item
interaction. But broadly speaking, it can also be defined by features of item
or user, e.g. user demographic information (Pazzani, 1999; Zhao et al., 2014,
2016) or item features (Vig et al., 2009; Cramer et al., 2008; Pazzani and
Billsus, 2007; Hou et al., 2019).

  * •

User opinion based logic: The logic explains the recommendation through user
opinions, mostly from user reviews. Most of the work is based on natural
language processing techniques. For example, some prior work uses topic
modeling to generate word clouds as explanations (Zhang et al., 2014; Wu and
Ester, 2015). In addition, using natural language generation, Costa et al.
(Costa et al., 2018) train language models on user review corpus, and generate
explanations in the form of natural language paragraphs based on the learned
language models. Chang et al.  (Chang et al., 2016) generate personalized
natural language explanations based on explanations collected from
crowdsourcing. Furthermore, Wang et al.  (Wang et al., 2018b) propose a multi-
task learning modeling framework that predicts how the user would appreciate a
particular item during training.

  * •

Social interaction based logic: The logic generates explanations based on the
users’ social information. Sharma and Cosley show users a number of friends
who also liked the item (Sharma and Cosley, 2013). Chaney et al.  (Chaney et
al., 2015) incorporate social influence information from social network into
the model, and provide explanations by indicating friends as the source of
influence. Wang et al.  (Wang et al., 2014) find a group of users who are the
most persuasive in terms of explaining, and provide explanations in the text
form “A and B also like the item.”

Note that different explaining logic would require different explaining user
interfaces. For example, collaborative filtering logic’s displaying user
interface shows the relevant users or items, user opinion logic’s is a text
block, and social interaction logic’s is usually dependent on the design,
ranging from a text sentence/paragraph to links to source influence. Because
of their difference in displaying forms, it is difficult to compare
explanations generated from different explaining logic in a controlled
experimental setting. In this work, we focus on item-based collaborative
filtering logic.

Evaluate Explanation Performance. To the best of our knowledge, most of the
prior work evaluates their explanation quality using online user study and
only a few works consider offline evaluation. For example, Abdollahi and
Nasraoui (Abdollahi and Nasraoui, 2017) propose evaluation metrics based on
the expected value of ratings given by similar users. The majority of prior
work relies on conducting human studies, which is slow to collect results and
expensive and therefore not suitable for rapid algorithm development and
testing needed in today’s recommender systems. In addition, user studies are
also prone to various human biases, e.g. methodological bias, familiarity
bias, and culture bias etc. Since reliable and low-cost evaluation metrics can
be beneficial by helping practitioners develop and test explaining algorithms,
we try to fill this gap in this paper.

###  2.2. Counterfactual Machine Learning

The term counterfactual refers to a way of thinking which assumes scenarios
that contradict the previous facts, i.e. “What-if” scenarios. Recently machine
learning researchers have been studying how to use counterfactual logic to
explain model predictions. A typical example is the loan application. Banks
develop models to predict if a user’s loan application is approved or rejected
based on the user’s features like income, age, credit card history etc.If a
user’s application is rejected by the model, a counterfactual explanation
would be given to the user by pointing out what changes on which features
would lead to an approval, e.g. “Had you earned $\$10,000$ dollars more
annually, we would approve your application.”

Compared to other explainable machine learning approaches, counterfactual
explanation has several advantages. First, it provides users actionable
advice, i.e. users would know how to change the model decisions, and can try
the advice if needed. Second, it might be more likely to be accepted by humans
because we naturally think counterfactually in everyday life (Kahneman and
Tversky, 1981; Mandel et al., 2005). Third, counterfactual explanations are
technically verifiable in the truthfulness. If we make a counterfactual claim,
we can test if this is true or not in our models. On the other hand, other
types of explanations are hard to validate their truthfulness of the claimed
reasons in reality.

Current Approach. Wachter et al.  (Wachter et al., 2017) propose one of the
first widely used approaches to counterfactually explain model predictions.
The idea is to use white-box optimization on models to find the smallest
change on an input’s features that can alter the model prediction on this
input. Mothilal et al.  (Mothilal et al., 2020) consider the need to generate
multiple explanations, and argue they should be different from each other. To
this end, they add a diversity loss into the optimization that maximizes the
diversity between explanations. Russell et al.  (Russell, 2019) propose a
mixed integer programming based approach to address the difficulty with
generating sensible explanations regarding categorical features. In addition
to generic models, counterfactual explanations are also designed in
applications like Computer Vision (Dhurandhar et al., 2018; Goyal et al.,
2019; Akula et al., 2020), Natural Language Processing (Wu et al., 2021; Yang
et al., 2020), and Graph Neural Networks (Ying et al., 2019; Yeh et al.,
2019).

Relatively fewer works consider applying the counterfactual approach to
generate recommendation explanations. Our work is close to this line of
research although our goal is evaluating explanations rather than generating
explanations. Ghazimatin et al.  (Ghazimatin et al., 2020) consider graph
recommender models that encode user-item interactions. The counterfactual
explanation is defined as a set of minimal actions performed by the user that,
if were removed, changes the recommendation to a different item. They propose
a Personal PageRank based approach that searches for the minimal change on the
graph. However, this approach is only applicable to PageRank-based recommender
models, and cannot be easily adapted to other model categories. In addition,
Tran et al.  (Tran et al., 2021a) propose a white-box explaining approach on
Neural-CF models. The approach is based on the influence function (Koh and
Liang, 2017) which estimates the influence of a training sample on the current
model prediction. They use the influence function to compute how the predicted
score on the explained item might change if some training items were removed.
Furthermore, Kaffes et al.  (Kaffes et al., 2021) propose a black-box solution
that performs Breadth First Search with heuristics that combine search length
and drop of the item rank if the candidate set were considered.

##  3\. Why Counterfactual Approach?

In this section, we explain why we think counterfactual logic can provide good
insights on how to evaluate recommendation explanations. Then we specify our
problem scope.

###  3.1. Goals and Challenges

The Goal of Explanation. Understanding causality is a notoriously hard problem
that has puzzled philosophers and scientists since the early days of human
civilizations (Pearl, 2000). If an explainable recommender system wants to
solve the same philosophical problem by finding the exact causes, then it
would be extremely challenging if not impossible. Rather, from the perspective
of utility in a recommender system, a more obtainable goal is to find
explanations that satisfy users. In other words, though it might sound
pragmatic, the goal of an explainable recommender system is to make users
think or feel that the shown explanations make sense.

Challenges. To this end, we need to find explanations that can satisfy users
psychologically. The main reason why it is difficult is that we lack the
computational models that can describe the human psychology of causal
reasoning. In other words, we do not know what makes a human consider an
explanation reasonable or not, therefore we cannot model it computationally
and have to conduct slow and expensive user studies instead.

###  3.2. How Counterfactual Logic Can Help

Counterfactual thinking involves “What-if” reasoning that is contrary to prior
facts, e.g. “What if I did that instead?”. Psychological research has found
counterfactual thinking is a frequent pattern of human reasoning in everyday
activities (Kahneman and Tversky, 1981; Mandel et al., 2005). Therefore not
only it provides a possible way to model human reasoning, but also this
frequently used thinking pattern is already familiar to humans and therefore
is likely to be understood and accepted by users. It naturally represents a
common pattern of human reasoning in everyday life, and can serve as a proxy
of human judgments. If an explanation is close to being counterfactual, then
it is more likely to fit the pattern of human counterfactual thinking, and
satisfy users psychologically.

Under the explainable recommender system setting, the term counterfactual
means “Had you not interacted with those items, you would not receive this
recommendation.” Compared to the conventional explaining logic, it offers some
unique perspectives. Consider the following conventional recommendation
explanation: “You have interacted with those items in the past that are
similar to the recommended item, therefore we recommend it to you.” This
explanation has two disadvantages. First, the claim misses the causal link
between the past interactions and the current recommendation, i.e. how did the
past interactions lead to this recommendation? Without answering it, users
might not be satisfied. On the other hand, the counterfactual version provides
the logical connection (i.e. had the interactions not happened, we would not
recommend it) and therefore more psychologically convincing because humans
respect reasoning. Second, if the traditional explanation defines “similar” as
the distance between items, then unless the recommendation model’s decisions
are solely based on item distance, which is unlikely in today’s complex
recommender systems, this claim is not entirely solid technically and might be
questionable in terms of public trust and legal liability. On the contrary,
the claim from the counterfactual version is technically correct and
verifiable.

###  3.3. Problem Scope

We focus on the recommendation explanation based on item-based collaborative
filtering logic, which is to explain the current recommendation by its
relevant items, i.e. the model recommends the item because the item is similar
to some other items that the user has liked or interacted with previously. The
explanation user interface shows a set of similar items in the user’s history
with an explanation text like “You have interacted with those similar items
before.” or “You have rated high on those similar items before.” We focus on
this explanation logic for two reasons. First, it is simple and therefore easy
to implement within the existing recommender systems. It does not require
extra models and can be implemented with a small engineering module. Second,
it can be applied to any recommendation models because we can always find
relevant items based on criterion or distance metrics defined independently of
the recommendation model (e.g. item raw features). Note that the explanations
generated based on other logic, e.g. user-based collaborative filtering, user
opinion, or social interaction, are not comparable in our setting because they
would require different algorithm designs and explaining user interfaces, and
therefore cannot be applied to our scenario under a controlled experimental
setting.

##  4\. Methodology

In this section, we first introduce our problem setup, followed by the
demonstration of our key design insights. We then present the details of our
explanation evaluation method.

###  4.1. Problem Setup

In a recommender system, let $\mathcal{U}=\\{u_{1},\dots,u_{m}\\}$ be the set
of all users, $\mathcal{I}=\\{i_{1},\dots,i_{n}\\}$ be the set of all items,
and $\mathcal{S}\subseteq\mathcal{U}\times\mathcal{I}$ be the history of all
user-item interactions. For a given user $u$ who has interacted with the item
set $\mathcal{I}_{u}^{+}=\\{i\in\mathcal{I}:(u,i)\in\mathcal{S}\\}$ in the
past, if the recommendation model $\theta$ recommends an item $i$ to the user
$u$, then the goal of the explaining component of the system is to generate
explanations of why the item $i$ was recommended to the user $u$. This is
done, in an item-based collaborative filter logic, by showing user $u$ a
subset of his interaction history $E_{i,u}\subseteq\mathcal{I}_{u}^{+}$ as the
explanation.

Given an explanation $E_{i,u}$, the goal of an offline explanation evaluation
task that we target is to evaluate $E_{i,u}$’s quality by computing a
numerical score on $E_{i,u}$ which is correlated with human judgments if a
human were to see $E_{i,u}$.

Figure 1. The key insight of how to compute Counterfactual Proximity. Suppose
we remove $E_{i,u}$ from the model’s training data and retrain the model to
generate a new item ranking list, i.e. counterfactual ranking list. In the
counterfactual ranking list, the less likely for the recommended item $i$ to
stay on the top-1 position, the more confident we can say that removing
$E_{i,u}$ would have a large impact on the recommendation of item $i$, and we
should assign a higher counterfactual score to $E_{i,u}$.

###  4.2. Design Insights

We now describe the key design insights of our counterfactual evaluation
method.

Qualitative Definition. We define an explanation $E_{i,u}$ to be
counterfactual if $E_{i,u}$ were removed from user $u$’s interaction history
$\mathcal{I}_{u}^{+}$, and the model were trained on the removed training set
$\mathcal{S}\setminus\\{u\times E_{i,u}\\}$ instead, then the counterfactually
trained model $\theta^{cf}$ would no longer recommend item $i$ to user $u$.

Mathematically, a counterfactually trained model $\theta^{cf}$ w.r.t $E_{i,u}$
is defined as:

(1) $\theta^{cf}=\operatorname*{arg\,min}_{\theta\in\Theta}{\sum_{(x,y)\in
S\setminus\\{u\times E_{u,i}\\}}{\ell(x,y;\theta)}}$

where $\Theta$ is the model parameter space and $\ell(x,y;\theta)$ is the loss
of model $\theta$ on the user $x$ and the item $y$.

To simply the notations, define
$\mathcal{I}_{u}^{-}=\mathcal{I}\setminus\mathcal{I}_{u}^{+}$, i.e. items
without interaction or feedback from user $u$ and therefore are available for
the current recommendation, and $\mathcal{I}_{u}^{-cf}=\mathcal{I}_{u}^{-}\cup
E_{i,u}$, i.e. items available to be recommended to user $u$ in the
counterfactual case. Let $f(u,i;\theta)$ be the predicted score of item $i$
for user $u$ by the model $\theta$, then an explanation $E_{i,u}$ is
qualitatively counterfactual if

(2)
$\bigg{[}\operatorname*{arg\,max}_{j\in\mathcal{I}_{u}^{-cf}}{f(u,j;\theta^{cf})\bigg{]}\neq
i}.$

Quantitative Measure. Note that definition (2) is either satisfied or
unsatisfied. However, in practice it is better to have a quantitative metric
which is a continuous score that measures the closeness of an explanation to
its counterfactual state. In other words, we would like to have a continuous
spectrum that captures the degree of how counterfactual it is. It is because a
continuous metric is easier for practitioners to compare. Considering two
explanations that both satisfy the qualitative definition of being
counterfactual, we would like to know which one is more counterfactual, i.e.
which one, if were removed, would have a larger impact on the current
recommendation. A continuous degree of counterfactuality would capture if an
explanation fits with the counterfactual state on a finer granularity. We name
this quantitative metric as Counterfactual Proximity.

Figure 1 shows the key insight of how to compute Counterfactual Proximity.
Suppose we remove $E_{i,u}$ from the model’s training data and retrain the
model to generate a new item ranking list (to the user $u$), i.e.
counterfactual ranking list. In the counterfactual ranking list, the less
likely for the recommended item $i$ (which was on the top-1 position in the
original model) to stay on the top-1 position, the more confident we can say
that removing $E_{i,u}$ would have a large impact on the recommendation of
item $i$ (by pulling the item $i$ away from the top-1 position and therefore
changing the recommendation to something else), and we should assign a higher
counterfactual score to $E_{i,u}$.

###  4.3. Evaluation Score: Counterfactual Proximity

With the above insights in mind, there are two different cases dependent on
the position of item $i$ in the counterfactual ranking list:

  * •

Qualitatively Counterfactual Case: If item $i$ falls off from the top-1
position, i.e. $E_{i,u}$ is qualitatively counterfactual that is able to
change the prediction if $E_{i,u}$ were removed, then we can quantify how
counterfactual $E_{i,u}$ is by observing the distance between item $i$ and the
item ranked at the current top-1 position (i.e. top-1 item). The further item
$i$ is from the top-1 position, the more counterfactual $E_{i,u}$ is. The
distance can be specified by the predicted score difference between top-1 item
and item $i$:

(3)
$\bigg{[}\max_{j\in\mathcal{I}_{u}^{-cf}}{f(u,j;\theta^{cf})}\bigg{]}-f(u,i;\theta^{cf})$

The score is positive, and the larger means the more counterfactual $E_{i,u}$
is.

  * •

Qualitatively Non-counterfactual Case: If item $i$ stays on the top-1
position, i.e. $E_{i,u}$ is not qualitatively counterfactual, then we can
quantify how counterfactual $E_{i,u}$ is by observing the distance between
item $i$ and the item ranked at the current top-2 position (i.e. top-2 item).
The closer item $i$ is from the top-2 item, the more likely item $i$ would be
replaced by the top-2 item, and therefore more counterfactual item $i$ is. The
distance can be specified by the predicted score difference between top-2 item
and item $i$:

(4)
$\bigg{[}\max_{j\in\mathcal{I}_{u}^{-cf}\setminus\\{i\\}}{f(u,j;\theta^{cf})}\bigg{]}-f(u,i;\theta^{cf})$

The score is non-positive, and the larger (i.e. closer to 0) means the more
counterfactual $E_{i,u}$ is.

Combine Both Cases. We can combine both cases together. Define benchmark item
to be the item other than item $i$ that is ranked highest in the
counterfactual ranking list. In the counterfactual case, the benchmark item is
the new top-1 item; in the non-counterfactual case, it is the top-2 item below
item $i$. When $E_{i,u}$ is more counterfactual, it implies that item $i$ is
closer to being ranked lower than any other items (i.e. closer to being
replaced by an item), which is equivalent to being ranked lower than the
benchmark item. Therefore the counterfactual score can be quantified by
comparing the distance between the benchmark item and item $i$. To sum up, we
compute Counterfactual Proximity ($\mathcal{CF}$ in short) by the following:

(5)
$\displaystyle\mathcal{CF}(u,i,E_{i,u},S)=\bigg{[}\max_{j\in\mathcal{I}_{u}^{-cf}\setminus\\{i\\}}{f(u,j;\theta^{cf})}\bigg{]}-f(u,i;\theta^{cf})$
$\displaystyle\text{where
}\theta^{cf}=\operatorname*{arg\,min}_{\theta\in\Theta}{\sum_{(x,y)\in
S\setminus\\{u\times E_{u,i}\\}}{\ell(x,y;\theta)}}$

Properties of Counterfactual Proximity. Assume each predicted score is
normalized between 0 and 1 (this can be done by simple score post-processing
like min-max normalization), then $\mathcal{CF}\in[-1,1]$. The sign of
$\mathcal{CF}$ has meaning: if it is positive, then it implies that $E_{i,u}$
satisfies the qualitative counterfactual definition; otherwise, it does not
satisfy. The higher $\mathcal{CF}$ is, the more counterfactual $E_{i,u}$ is,
and therefore is considered to be a better explanation by the counterfactual
logic.

Note that the above definition focuses on how the top-1 recommended item would
change counterfactually because we assume the recommender system only shows
the top-1 recommended item to users. One can easily extend it to top-K
recommended items if one is interested in the scenario in which users are
shown multiple recommended items from the ranking list simultaneously.

###  4.4. Approximate Counterfactual Proximity

Counterfactual Proximity can be expensive to compute because it requires
retraining the model. In practice, it might be too costly for large models. To
speed up, we can approximate it by not fully retraining the model. To this
end, we can perform warm-start with the previous model weights, and finetune
the model on the counterfactual training dataset. Since the previous model has
already converged, this usually requires much fewer iterations to reach a good
state. After we have this approximated version of the counterfactual model, we
can compute the score by the same Eq (5). We refer to the resulting score as
Approximate Counterfactual Proximity or $\mathcal{CF^{A}}$ in short. It can be
viewed as a faster but less accurate version of Counterfactual Proximity.

###  4.5. Comment on Computational Cost

We admit that, in some large-scale settings, even finetuning in Approximate
Counterfactual Proximity might be expensive to perform. This is the major
limitation of our approach. As the first paper that demonstrates the
possibility of using the counterfactual approach as evaluation, our main focus
is its effectiveness of serving as a proxy of human judgments (which will be
shown in the next sections) rather than efficiency optimization. We believe if
the direction seems promising, then in the future the community can work
towards algorithmic speedup. In fact, the problem of how to obtain the
counterfactual models efficiently without full retraining is the exact topic
of machine unlearning (Cao and Yang, 2015; Bourtoule et al., 2021; Gupta et
al., 2021; Guo et al., 2020). It is an ongoing research area that studies,
after removing samples from the training set, how to efficiently approximate
the resulting models without retraining the models from scratch. We believe as
machine unlearning algorithms advance, our evaluation method will become more
and more efficient. In addition, compared to the current approach of
conducting online user studies, our method is still relatively fast.

##  5\. User Study: Design

To understand the evaluative power of our proposed score, we ask the following
research questions:

  * •

RQ1: Is the proposed score correlated with real human judgment?

  * •

RQ2: Can the proposed score be used to predict human judgment?

  * •

RQ3: Is an explanation with a high proposed score considered good by humans?

To understand the above questions, we design and conduct a survey-based user
study to collect user ratings on explanations that serve as the ground truth
to assess our evaluation method. In this section, we first introduce our
overall design, followed by how we generate the survey data, how we ask users
to rate explanations, and how we collect responses.

###  5.1. Overall Design

We choose movie recommendation to be our user study scenario because it is one
of the most widely used cases that study recommendation explanation in the
literature (Tran et al., 2021b; Resnick et al., 1994; Herlocker et al., 2000).
In our survey, we first ask users to imagine that they are browsing a movie
recommendation website. Then we show them a list of questions. In each
question, we display a group of movies as the hypothetical history that users
imagine having watched in the past. Next, we present them with the
corresponding recommended movie based on the history (generated from the
recommendation model). Then we provide the recommendation explanation based on
the item-based collaborative filtering logic, i.e. “We recommend this movie to
you because you watched the following movies in the past.” And we show users a
set of movies from the history as the explanation. We will explain how we
choose the explanation in Section 5.2. Finally, we ask the users to rate the
explanation based on various assessing dimensions introduced in Section 5.3.
We repeat the above process and include 12 questions totally in the survey.

###  5.2. Survey Data Generation

We now introduce how we generate data used in the survey question.

Dataset and Model. We use MovieLens (ml-latest-
small)111https://files.grouplens.org/datasets/movielens/ml-latest-small-
README.html as our dataset because it is one of the most popular datasets for
the movie recommendation scenario. It contains $\sim$600 users, $\sim$9.7K
items, and $\sim$101K ratings. We use Matrix Factorization (MF) model as our
recommendation model since it is a naturally suitable choice for collaborative
filtering based explanations (Resnick et al., 1994; Herlocker et al., 2000).

User History Generation. To ensure the movies are likely to be familiar to
participants, we choose movies in the watching history from popular movies.
Specifically, we first compute the distribution of each movie’s popularity
(number of users who watched/rated the movie) in MovieLens, then we take
$90\%$ quantile of that distribution, and use it as the minimum popularity
threshold to select movies in history.222We admit that the popularity
filtering might cause bias because the resulting history only represents the
scenario in which users watched popular movies in the past. But we think the
benefit that participants would be familiar with the movies and therefore
provide impartial feedback outweighs the potential risk of bias. In addition,
the scenario is likely to hold in practice for the majority of users. We leave
considering long-tailed users as future work. After the filtering, we randomly
choose 9 movies as watching history in each question.333We admit that assuming
a fixed-size history might cause bias in our design. However, it is difficult
to include all possible scenarios that one might encounter when using a
recommender system while maintaining a statistical significance given a
limited amount of resources.

Recommendation Generation. We train the MF model on the MovieLens dataset for
20 iterations with embedding size 40. Then we generate the recommended movie
by feeding the hypothetical user watching history into the trained MF model,
and choose the movie with the highest predicted score as the recommended movie
shown in the survey question.

Compare Evaluation Scores. To measure how well our proposed evaluation scores
perform when evaluating explanation quality, we include two baseline scores to
compare with: item similarity and movie genre overlap. Those two scores are
relatively simple because, to the best of our knowledge, few prior works have
considered proposing offline evaluation scores and we cannot find more
developed evaluation methods that fit into our scenario. In the following, we
explain how we compute each score in the survey. Note that we assume an
explanation $E_{i,u}$ is given as the input to the evaluation method, and we
will explain how we choose those explanations shortly after.

  * •

Counterfactual Proximity: Given an explanation $E_{i,u}$ for user $u$ to
explain the recommended item $i$, we compute the evaluation score based on Eq
(5). We follow the same configurations as the original training to retrain the
model on the counterfactual dataset (i.e. rating matrix after removing
interactions between user $u$ and explaining item set $E_{i,u}$) and obtain
the counterfactually trained model $\theta^{cf}$.

  * •

Approximate Counterfactual Proximity: Instead of fully retraining the MF
model, we finetune the model by Alternating Least Square (ALS) (Koren et al.,
2009). ALS trains an MF model by alternating between 1) fixing the item factor
while updating the user factor, and 2) fixing the user factor while updating
the item factor. In our case, we only run the first half of ALS, i.e. we fix
the item factor, and only update the user factor on the counterfactual
training set. (The reason is item embeddings should be relatively unaffected
by removing a few interactions from one user’s history while user embeddings
which include the particular user $u$ should be impacted more.) We run this
update for 5 iterations.

  * •

Item Similarity (baseline): The goal is to quantify how close the explanation
$E_{i,u}$ is to the recommended item $i$ in the item embedding space. To this
end, we compute the cosine similarity between the item embedding of each
explaining item in $E_{i,u}$ and the recommended item $i$, then we average the
similarities over all items in $E_{i,u}$. The larger is better. We name this
score as Item-Sim for short.

  * •

Movie Genre Overlap (Vig et al., 2009) (baseline): The goal is to quantify how
close the explanation $E_{i,u}$ is to the recommended item $i$ in terms of
movie genre’s overlap. To this end, we compute the Jaccard index between the
movie tags of each explaining item in $E_{i,u}$ and the recommended item $i$,
then we average the Jaccard similarity over all items in $E_{i,u}$. The larger
is better. We name this score as Genre-Jacc for short.

Choose Explanations. We now explain how we choose explanations shown in our
survey. To answer RQ1 and RQ2 which are about the relationship between
evaluation score and human rating on the explanations, we do not need to
consider what kind of explanations are used. This is because what we want to
assess is the quality of the score that serves as an evaluative function
rather than the quality of the explanations. Hence explanations produced by
any method are usable. However, to answer RQ3, we would need to have
explanations with different ranges of evaluation scores so that we can compare
the rating difference between explanations with different score levels. In
summary, RQ1 and RQ2 are indifferent to which explanations are chosen while
answering RQ3 needs to have explanations that cover a range of different score
levels. Therefore we choose to use explanations with different levels of
evaluation scores.

With the above insights in mind, we select explanations with three different
ranges for each score. We fix the explanation size to be 3 items. For
$\mathcal{CF}$ and $\mathcal{CF^{A}}$, we enumerate 3-item subsets of the
history as the explanation candidates. Then we compute $\mathcal{CF}$ or
$\mathcal{CF^{A}}$ on each candidate and pick three candidates with the
highest, the lowest, and (closest to) the average score respectively as the
final explanations. For Item-Sim and Genre-Jacc, we compute the score on all
items in the history, and select 3 items with the highest, the lowest, and
(closest to) the average score. In total, for each of the four evaluation
scores, we have three explanations chosen at different score levels. Hence we
have 12 explanations in total; one for each question. For each chosen
explanation, we also compute the other three scores so that we can compare
them together.

###  5.3. Explanation Rating Question

To gather human judgments on explanations with multiple assessing dimensions,
we follow the prior work (Tintarev and Masthoff, 2007; Zhang and Chen, 2018;
Tran et al., 2021b; Wang et al., 2018b), and design questions from seven
dimensions:

  1. (1)

Explainability: Given a scale from 1 to 5, does the explanation help you
understand why we recommend this movie to you? (1 is the least helpful, 5 is
the most helpful)

  2. (2)

Informativeness: Given a scale from 1 to 5, does the explanation help you know
more about the recommended movie? (1 is the least helpful, 5 is the most
helpful)

  3. (3)

Effectiveness: Given a scale from 1 to 5, does the explanation help you decide
whether you want to watch this recommended movie? (1 is the least helpful, 5
is the most helpful)

  4. (4)

Persuasiveness: Given a scale from 1 to 5, does the explanation convince you
to watch the recommended movie? (1 is the least convincing, 5 is the most
convincing)

  5. (5)

Transparency: Given a scale from 1 to 5, does the explanation help you
understand how the system works? (1 is the least helpful, 5 is the most
helpful)

  6. (6)

Trustworthiness: Given a scale from 1 to 5, does the explanation increase your
trust in the system? (1 is increasing the least, 5 is increasing the most)

  7. (7)

Satisfaction: Given a scale from 1 to 5 does the explanation make you happier
about the system? (1 is the least satisfactory, 5 is the most satisfactory)

In addition to those rating questions, we also ask users, in some of the
questions, to write down the reason why they give such ratings so that we can
analyze the reasons in our study.

###  5.4. Response Collection

Quality Control. To ensure response quality, we use five mechanisms to filter
out low-quality responses. First, we select workers with at least $80\%$
approval rate in participating history (HIT rate on Amazon MTurk) and with at
least $50$ tasks approved in the past. Second, to make sure participants are
reasonably familiar with movies, we declare, in the advertisements, the
requirement of movie familiarity to the participants. Third, in the middle of
our survey, we insert a quality control question (“Please choose both A and
D.”). Participants who fail to respond properly to this simple question are
excluded from the results. Fourth, at the end of the survey, we ask
participants how many movies they usually watch in a month, and we remove any
participants who answer less than one movie per month. Finally, when
participants finish the survey, we ask them to disclose their familiarity with
the movies that they have seen in the survey (“What percentage of movies shown
in this survey are familiar to you?”), and we exclude participants who claim
more than $40\%$ of movies they saw are unfamiliar.

We recruit survey respondents from Amazon Mechanical Turk (MTurk). We send out
the survey to $400$ participants. After applying the quality-checking
mechanisms, we exclude $16$ participants from our results. The demographics of
our survey participants are as follows: $61.2\%$ indicated male and $38.8\%$
indicated female (no participant preferred not to disclose gender); the
majority of participant ages fall into the ranges of 21 to 30 ($56.3\%$) or 31
to 40 ($30.7\%$), with $6.0\%$ fall between 41 and 50, and the rest is older
than 50.

##  6\. User Study: Result Analysis

We now analyze the effectiveness of our evaluation score using the collected
human ratings, and answer the three research questions in Section 5.

###  6.1. RQ1: Is the proposed score correlated with real human judgment?

| Explainability | Informativeness | Effectiveness | Persuasiveness | Transparency | Trustworthiness | Satisfaction
---|---|---|---|---|---|---|---
Proposed | $\mathcal{CF}$ | 0.4436 | 0.4633 | 0.3653 | 0.3414 | 0.3701 | 0.3664 | 0.3499
$\mathcal{CF^{A}}$ | 0.4194 | 0.4199 | 0.3404 | 0.3467 | 0.3347 | 0.3424 | 0.3408
Baseline | Item-Sim | 0.3128 | 0.2619 | 0.2224 | 0.2394 | 0.2127 | 0.3048 | 0.2304
Genre-Jacc | 0.3553 | 0.2943 | 0.3221 | 0.2197 | 0.4554 | 0.3295 | 0.2957

Table 1. Pairwise correlation between each type of evaluation score and the
real human ratings. The higher is better.

We compute the correlation between each evaluation score and the average human
rating (over participants) across all questions. For both evaluation score and
human rating, the larger is the better the explanation quality is. Therefore a
more positive correlation means the evaluation score can represent real human
ratings better. Table 1 shows the pairwise correlation between each evaluation
score and the human rating from each assessing dimension. We have two main
observations. First, $\mathcal{CF}$ and $\mathcal{CF^{A}}$ have higher
correlation than the other two baselines in 6 out of 7 assessing dimensions.
We will explain why our method is underperformed by Genre-Jacc in Transparency
dimension shortly after. Second, $\mathcal{CF}$ and $\mathcal{CF^{A}}$ share a
similar correlation, which suggests that the approximation in
$\mathcal{CF^{A}}$ does not significantly downgrade the effectiveness in
serving as a proxy of human judgments. ($\mathcal{CF^{A}}$ even slightly
outperforms $\mathcal{CF}$ in Persuasiveness. However the difference is
small.) Hence, in practice $\mathcal{CF^{A}}$ can be used as a reasonably good
evaluation score while saving much computational cost.

Understand Transparency. To understand why our proposed scores are
underperformed in Transparency, we investigate the explanations that users
wrote when rating Transparency. We find when giving a high rating on
Tranparecny, many users regarded an explanation’s easiness to be understood as
the deciding factor. For example, “It’s easy to understand the system.”
(P302), “I can nearly understand how the system works.”(P174), “Easy to
understand.” (P143) etc. And many users mentioned that sharing similar genres
(between the recommended movie and the explaining movies) eased their
understanding. For example, “They almost match the movies before for genre. I
got it.” (P81), “The explanation share the similar genre. It makes sense to
me.” (P324), “The genres are matched. I can understand it.” (P253) etc. Hence
it is possible that Transparency is a dimension that users are naturally
inclined to associate with genre similarity because of the intuitiveness.

| Explainability | Informativeness | Effectiveness | Persuasiveness | Transparency | Trustworthiness | Satisfaction
---|---|---|---|---|---|---|---
Proposed | $\mathcal{CF}$ | 0.0093 | 0.0101 | 0.0089 | 0.0059 | 0.0032 | 0.0018 | 0.0011
$\mathcal{CF^{A}}$ | 0.0096 | 0.0113 | 0.0093 | 0.0061 | 0.0036 | 0.0022 | 0.0013
Baseline | Item-Sim | 0.0105 | 0.0142 | 0.0114 | 0.0067 | 0.0039 | 0.0059 | 0.0015
Genre-Jacc | 0.0141 | 0.0121 | 0.0139 | 0.0081 | 0.0029 | 0.0031 | 0.0037

Table 2. Testing mean squared error (MSE) of linear regression models that
predict human ratings from evaluation scores. The lower MSE is, the better the
evaluation score can serve as a predictor of real human ratings.

| Explainability | Informativeness | Effectiveness | Persuasiveness | Transparency | Trustworthiness | Satisfaction
---|---|---|---|---|---|---|---
| High-$\mathcal{CF}$
---
Mean $\pm$ Std
| 4.119 $\pm$ 0.953
---
| 3.995 $\pm$ 1.126
---
| 4.115 $\pm$ 0.975
---
| 4.221 $\pm$ 0.878
---
| 4.341 $\pm$ 0.776
---
| 4.290 $\pm$ 0.811
---
| 4.331 $\pm$ 0.750
---
| Low-$\mathcal{CF}$
---
Mean $\pm$ Std
| 3.571 $\pm$ 1.101
---
| 3.594 $\pm$ 1.140
---
| 3.543 $\pm$ 1.064
---
| 3.737 $\pm$ 1.107
---
| 3.756 $\pm$ 1.078
---
| 3.664 $\pm$ 1.091
---
| 3.824 $\pm$ 1.080
---
t-statistic | 6.518 | 4.297 | 6.422 | 2.0424 | 5.928 | 7.529 | 5.897
p-value | 2.470e-10 | 1.311e-5 | 4.223e-10 | 5.978e-9 | 3.992e-12 | 6.851e-13 | 7.027e-9

Table 3. One-tailed (upper tail) paired t-statistics on user ratings on high-
and low-$\mathcal{CF}$ explanations. The high-$\mathcal{CF}$ explanations are
rated higher by users than low-$\mathcal{CF}$ explanations with statistical
significance ($p<0.05$) on all assessing dimensions.

###  6.2. RQ2: Can the proposed score be used to predict human judgment?

In addition to closely correlating with human ratings, an ideal evaluation
score should also serve as a good predictor of human ratings. To this end, we
build linear regression models that predict the human ratings from the
evaluation score. We randomly split the collected survey data into $70\%$
training set and $30\%$ testing set, train linear regression models on the
training set, and report the testing mean squared error (MSE) on the testing
set in Table 2. The lower testing MSE is, the better the evaluation score can
serve as a predictor of real human ratings. The observations are mainly
consistent with the previous correlation results. $\mathcal{CF}$ and
$\mathcal{CF^{A}}$ share a similar testing MSE, and achieve lower MSE than the
other two baselines except in Transparency dimension where Genre-Jacc performs
slightly better. The result shows that both $\mathcal{CF}$ and
$\mathcal{CF^{A}}$ can be used as reasonably good predictors of real human
ratings.

###  6.3. RQ3: Is an explanation with a high proposed score considered good by
humans?

Another way to show the evaluative power of $\mathcal{CF}$ is to compare the
human ratings on explanations with high and low $\mathcal{CF}$ (i.e. the
explanation candidate with the highest and the lowest $\mathcal{CF}$ among all
candidates, as mentioned in Section 5.2). To this end, we perform paired
t-test on the human ratings assigned to high- and low-$\mathcal{CF}$
explanations. We use one-tailed (upper tail) setting where the null hypothesis
is the high-$\mathcal{CF}$ and low-$\mathcal{CF}$ explanations share the same
average rating, and the alternative hypothesis is the average human ratings on
high-$\mathcal{CF}$ explanations is greater than low-$\mathcal{CF}$. Table 3
shows the corresponding t-statistics. Across all assessing dimensions, the
resulting p-value is less than 0.05, indicating we can reject the null
hypothesis. Therefore the high-$\mathcal{CF}$ explanations are rated higher by
users than low-$\mathcal{CF}$ explanations with statistical significance. In
addition, similar results are found between high- and low-$\mathcal{CF^{A}}$
explanations, thus we omit the results for brevity.

Similarly, we also compare between explanations assessed as high by
$\mathcal{CF}$ and by the other two baselines. We again perform the similar
paired t-test. Table 4 shows the results that compare high-$\mathcal{CF}$
explanations to high-Item-Sim and high-Genre-Jacc explanations. For both
baselines, we find that high-$\mathcal{CF}$ explanations are rated higher by
users than the other two baselines with statistical significance ($p<0.05$) on
all assessing dimensions.

| Explainability | Informativeness | Effectiveness | Persuasiveness | Transparency | Trustworthiness | Satisfaction
---|---|---|---|---|---|---|---
| High-$\mathcal{CF}$
---
Mean $\pm$ Std
| 4.119 $\pm$ 0.953
---
| 3.995 $\pm$ 1.126
---
| 4.115 $\pm$ 0.975
---
| 4.221 $\pm$ 0.878
---
| 4.341 $\pm$ 0.776
---
| 4.290 $\pm$ 0.811
---
| 4.331 $\pm$ 0.750
---
| High-Item-Sim
---
Mean $\pm$ Std
| 3.862 $\pm$ 0.774
---
| 3.847 $\pm$ 0.820
---
| 3.857 $\pm$ 0.866
---
| 3.972 $\pm$ 0.785
---
| 3.981 $\pm$ 0.762
---
| 3.889 $\pm$ 0.818
---
| 3.949 $\pm$ 0.793
---
t-statistic | 3.975 | 1.877 | 3.455 | 4.077 | 5.646 | 6.229 | 6.219
p-value | 4.796e-5 | 0.031 | 4.223e-10 | 3.315e-4 | 2.564e-8 | 1.204e-9 | 1.272e-9

(a) Between high-$\mathcal{CF}$ and high-Item-Sim explanations.

| Explainability | Informativeness | Effectiveness | Persuasiveness | Transparency | Trustworthiness | Satisfaction
---|---|---|---|---|---|---|---
| High-$\mathcal{CF}$
---
Mean $\pm$ Std
| 4.119 $\pm$ 0.953
---
| 3.995 $\pm$ 1.126
---
| 4.115 $\pm$ 0.975
---
| 4.221 $\pm$ 0.878
---
| 4.341 $\pm$ 0.776
---
| 4.290 $\pm$ 0.811
---
| 4.331 $\pm$ 0.750
---
| High-Genre-Jacc
---
Mean $\pm$ Std
| 3.764 $\pm$ 1.018
---
| 3.677 $\pm$ 1.135
---
| 3.705 $\pm$ 1.122
---
| 4.014 $\pm$ 0.887
---
| 3.963 $\pm$ 0.925
---
| 3.995 $\pm$ 0.893
---
| 4.013 $\pm$ 0.933
---
t-statistic | 4.594 | 3.664 | 4.812 | 2.775 | 5.184 | 4.200 | 4.415
p-value | 3.699e-6 | 1.563e-4 | 1.402e-6 | 2.997e-3 | 2.486e-7 | 1.951e-5 | 7.959e-6

(b) Between high-$\mathcal{CF}$ and high-Genre-Jacc explanations.

Table 4. Paired t-statistics that compare user ratings on explanations
assessed as high by $\mathcal{CF}$ and assessed as high by the baselines.
High-$\mathcal{CF}$ explanations are rated higher by users than the other two
baselines with statistical significance ($p<0.05$) on all assessing
dimensions.

##  7\. Limitations

We point out several limitations in our work. First and foremost, our method
might be considered to be slow because of the need for retraining. Our focus
is to explore the direction of using the counterfactual approach to evaluate
explanations and to examine how close the resultant metric is related to human
judgments. We believe if the direction seems promising, then the future work
can improve efficiency, especially as machine unlearning techniques improve.
In addition, compared to conducting human studies, our method is still faster.
Second, we only consider item-based collaborative filtering logic mainly
because other logic would require different displaying user interfaces and
recommendation system designs, and therefore it is difficult to compare with
our method under a well-controlled setting. Third, there might exist some
other possible definitions on counterfactual scores other than the one
proposed in Eq (5). We do not list and examine all of them. Finally, we do not
build a real recommendation platform, hire participants to actually use it for
a certain period, and gather the data from the real user experience.

##  8\. Related Work

In addition to the related work mentioned in Section 2, we include more work
from other research areas.

Counterfactual Psychology. Psychological research on counterfactual thinking
(Mandel et al., 2005) starts in 1970s with studies that compare human memory
between counterfactual and factual inference (Carpenter, 1973; Fillenbaum,
1974). It is popularized by Kahneman and Tversky in the seminal paper
(Kahneman and Tversky, 1981), in which they examine and identify the
counterfactual thinking in everylife activities, e.g. consumer choice,
monetary decisions, and career plans, and connected to a wide range of
psychological behaviors. Later, researchers show counterfactual thinking might
imply causal inference (Epstude and Roese, 2008; Spellman and Mandel, 1999).
Some studies also point out that it serves as a preparative function (Markman
and McMullen, 2003; Roese, 1994) that helps humans plan for the future, which
fits the design of using counterfactual thinking in recommender systems to
provide actionable advice to users on how to change their recommendations
received in the future.

Machine Unlearning. Our counterfactual approach is closely related to the
ongoing research area of machine unlearning. The goal of machine unlearning is
to efficiently remove the impact of training samples on an already trained
model without fully retraining it. It concerns exactly how to obtain the
counterfactually trained model, which is our main computational bottleneck.
Similar to our method, the main challenge of machine unlearning is also how to
reduce the computational cost. We believe our method will become more and more
efficient as machine unlearning techniques develop.

Bourtoule et al.  (Bourtoule et al., 2021) propose to partition the training
dataset into sub-datasets, train an individual sub-model on each sub-dataset.
Then during inference time, the prediction is made by voting from all sub-
models. In this framework, removing the impact of a data sample is to discard
the corresponding sub-model trained on the sub-dataset that includes that
sample. In addition, Golatkar et al.  (Golatkar et al., 2020) use information
theory based methods to remove information from the trained model weights.
Furthermore, Golatkar et al.  (Golatkar et al., 2021) assume there is an
essential subset in the training dataset that will not be removed. They train
the model on both essential and non-essential datasets with separated model
weights. Then discarding non-essential model weights becomes relatively fast
because they do not need to change the essential model. Researchers also
propose to use caching information during training (Wu et al., 2020), or
design unlearning methods for a particular class of models like tree-based
(Brophy and Lowd, 2021).

##  9\. Conclusion

We propose an evaluation method using counterfactual logic that quantifies the
quality of explanations in a recommender system. Through an extensive user
study, we show that the evaluation scores produced by our method are closely
correlated with human judgments. It can serve as a reasonably good proxy of
human evaluation and replace the slow and expensive human evaluations. In
addition, we show that explanations with high proposed scores are rated higher
by humans than by the baselines. In summary, we believe the counterfactual
approach of evaluating recommendation explanations is promising.

We hope that our work can bring more attention to the research on evaluations
of recommendation explanations. We believe that practitioners and researchers
can benefit significantly from effective and practical evaluations in their
algorithm developments, as we see in the other areas.

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