# Causal Disentanglement for Regulating Social Influence Bias in Social
Recommendation

Li Wang<EMAIL_ADDRESS>Min Xu<EMAIL_ADDRESS>Quangui Zhang
<EMAIL_ADDRESS>Yunxiao Shi<EMAIL_ADDRESS>Qiang Wu
<EMAIL_ADDRESS>
###### Abstract

Social recommendation systems face the problem of social influence bias, which
can lead to an overemphasis on recommending items that friends have interacted
with. Addressing this problem is crucial, and existing methods often rely on
techniques such as weight adjustment or leveraging unbiased data to eliminate
this bias. However, we argue that not all biases are detrimental, i.e., some
items recommended by friends may align with the user’s interests. Blindly
eliminating such biases could undermine these positive effects, potentially
diminishing recommendation accuracy. In this paper, we propose a Causal
Disentanglement-based framework for Regulating Social influence Bias in social
recommendation, named CDRSB, to improve recommendation performance. From the
perspective of causal inference, we find that the user social network could be
regarded as a confounder between the user and item embeddings (treatment) and
ratings (outcome). Due to the presence of this social network confounder, two
paths exist from user and item embeddings to ratings: a non-causal social
influence path and a causal interest path. Building upon this insight, we
propose a disentangled encoder that focuses on disentangling user and item
embeddings into interest and social influence embeddings. Mutual information-
based objectives are designed to enhance the distinctiveness of these
disentangled embeddings, eliminating redundant information. Additionally, a
regulatory decoder that employs a weight calculation module to dynamically
learn the weights of social influence embeddings for effectively regulating
social influence bias has been designed. Experimental results on four large-
scale real-world datasets Ciao, Epinions, Dianping, and Douban book
demonstrate the effectiveness of CDRSB compared to state-of-the-art baselines.

###### keywords:

Graph Neural Network (GNN) , Social Recommendation , Causal Inference ,
Disentanglement , Mutual Information

††journal: Nuclear Physics B

[first]organization=School of Electrical and Data Engineering, University of
Technology Sydney,addressline=15, Broadway, Ultimo, city=Sydney,
postcode=2000, state=NSW, country=Australia [second]organization=School of
Artificial Intelligence, Chongqing University of Arts and
Sciences,addressline=319, Honghe Avenue, Yongchuan District, city=Chongqing,
postcode=402160, country=China

##  1 Introduction

Social recommendation systems (SR) play a crucial role in addressing the data-
sparsity challenge and enhancing recommendation performance by incorporating
social network information [1, 2, 3]. These systems leverage data from users’
social interactions, encompassing friendships, shared content, comments and
likes on social networks, to learn comprehensive and personalized user and
item representations. Notable methods like SocialMF [4], GraphRec [5], and
DiffNet [2] have introduced innovative approaches, such as integrating social
network information into traditional matrix factorization methods or utilizing
Graph Neural Networks (GNN) to model high-order social relationships.

Despite these advancements, a critical limitation arises due to the potential
presence of social influence bias in the acquired user and item
representations, which may not accurately reflect users’ genuine interests.
This bias originates from the phenomenon where individuals, under the
influence of their social circles, might make choices that deviate from their
personal preferences. In recent years, some existing methods [6, 7, 8] have
focused on mitigating social influence bias generated from network
information. For example, SIDR [6] disentangles user and item representations
into three latent factors: user interest, item popularity, and user social
influence, and then mitigates the social influence bias. DENC [7] proposes an
exposure model and a deconfounding model to effectively control and eliminate
social influence bias. Conversely, D2Rec [8] utilizes network information to
disentangle user and item representations into exposure, confounder, and
prediction factors. It designs a reweighting function to mitigate social
influence bias. While SIDR [6] employs causal disentanglement to separate
social influence, its primary emphasis is on mitigating social influence bias
rather than strategically leveraging it.

Rather than indiscriminately mitigating social influence bias, we argue that
it is crucial to recognize that not all biases are harmful. Some users
perceive recommendations from friends as thoughtful selections, indicating
high quality and alignment with their interests. In such cases, the influence
exerted by friends has a positive impact on users, and these products are
worth recommending. Blindly mitigating this bias may lead to the loss of
essential information, preventing the recommendations that align with users’
interests. Thus, a dilemma arises: eliminating social influence bias
sacrifices meaningful recommendations, while preserving it may lead to
undesirable social conformity. Therefore, it is crucial and urgent to propose
a method that can reasonably regulate social influence bias to enhance
recommendation performance. Such a method should preserve positive social
influence bias while mitigating its negative counterpart.

(a) Fork structure of causal graph.

(b) Causal graph of social recommendations.

(c) Causal graph of CDRSB.

Figure 1: (a) Fork structure of causal graph: confounder affects both the
treatment and the outcome. (b) In social recommendations, we treat the social
network as a confounder, with user and item embeddings as the treatment and
user-item ratings as the outcome. Due to the existence of the social network
confounder, there are two paths between user and item embeddings and user-item
ratings: a non-causal social influence path and a causal interest path. (c)
CDRSB disentangles the user and item embeddings into social influence and
interest components and learns dynamic weights of social influence embeddings
to fuse them, thereby effectively regulating social influence bias. $C$:
social network, $T$: user and item embeddings, $R$: user-item ratings,
$T_{S}$: social influence embeddings, $T_{I}$: interest embeddings,
$T^{\prime}$: reconstructed user and item representations, $\alpha$: the
weight of social influence embeddings.

To gain a deeper understanding of how social influence affects
recommendations, we introduce the causal graph to analyze this process.
Motivated by the fork structure of the causal model proposed by Pearl [9], as
shown in Figure 1a, the confounder is a variable that is related to both the
treatment variable (the cause) and the outcome variable (the effect). The
presence of a confounder can lead to a spurious correlation between the
treatment and outcome variables, making it challenging to establish the causal
relationship. In the context of social recommendations, as illustrated in
Figure 1b, we can regard user and item embeddings as the treatment and user-
item ratings as the outcome. The social network emerges as a potential
confounder since it exerts simultaneous influence on both the user and item
embeddings as well as user-item ratings. Due to the existence of the social
network confounder, there are two paths from the user and item embeddings
(treatment) $T$ and the user-item ratings (outcome) $R$, including the non-
causal social influence path ($C\to T\to R$) introduced by the confounder and
the causal interest ($T\to R$) path which represents the reason why a user
likes an item. We refer to the bias introduced by the social influence path as
social influence bias. This bias has the undesirable effect of bias
amplification because it increases the exposure probability of items that
friends interact with, even if these items do not match the user’s interests.
However, some of the items recommended by friends may align with the user’s
interests and deserve to be recommended. Therefore, it’s crucial to design a
method that can effectively regulate social influence bias, preserving its
positive effects while mitigating the negative ones.

Based on the above analysis, we propose a causal disentanglement-based
framework for regulating social influence bias in social recommendations,
named CDRSB, as illustrated in Figure 1c. We assume that the treatment (user
and item embeddings) can be causally decomposed into two independent
embeddings: interest embedding which represents the user’s real preferences,
and social influence embedding which indicates the social influence bias. We
design a disentangled encoder aimed at separating interest and social
influence embeddings, along with a regulatory decoder that designs a weight
calculation module to reasonably regulate social influence bias. Specifically,
for the disentangled encoder, we first learn user and item embeddings via GNN-
based learning networks with the user social network and user-item interaction
network. Then, we design a causal disentanglement component to separate the
user and item embeddings into interest and social influence embeddings. To
make these two components independent of each other and contain more semantic
information, we introduce mutual information-based objectives. Regarding the
regulatory decoder, we first introduce a weight calculation module to learn
varying weights of social influence embeddings, which could regulate the
social influence bias. These weights are then utilized to fuse interest and
social influence embeddings to learn more accurate user and item
representations. The main contributions of this work are as follows:

  * 1.

Based on the non-causal social influence path and the causal interest path
introduced by the social network confounder, we propose a disentangled
encoder. This encoder disentangles user and item embeddings into interest and
social influence embeddings. Mutual information-based objectives are designed
to ensure the separation of these disentangled embeddings.

  * 2.

We propose a regulatory decoder that introduces a weight calculation module to
regulate social influence bias and learn more accurate user and item
representations, enhancing the model’s performance.

  * 3.

Extensive experiments are conducted on four large-scale real-world datasets
Ciao, Epinions, Dianping, and Douban book. The comprehensive results
demonstrate the effectiveness of CDRSB compared to several state-of-the-art
baselines.

The remainder of this work is organized as follows: In Section 2, we provide
an overview of the relevant work. Section 3 presents the detailed methodology
of the CDRSB. We then conduct extensive experiments on four public datasets
and compare the results with baselines in Section 4. Finally, in Section 5, we
provide a conclusion summarizing our work and outline future research
directions.

##  2 Related Work

In this section, we present several relevant studies related to social
recommendation, disentangled representation learning in recommendation, and
causal recommendation.

Social Recommendation. In recent years, social recommendation systems have
gained significant attention due to the widespread adoption of social media
platforms and the increasing number of users. The social network provides rich
social relationships and interaction information among users, which can solve
the long-standing data-sparsity problem [10, 11, 12]. Existing social
recommendations could be categorized as matrix factorization (MF)-based [4,
13] and graph neural network (GNN)-based approaches [2, 5, 14, 15]. MF-based
methods usually jointly factorize the user-item interaction matrix and user-
social relationship matrix or add a regularizer to restrain user and item
embeddings. SocialMF [4] incorporates the user’s social network into
traditional collaborative filtering models for recommendation. In [13],
authors introduce a social regularization term to incorporate users’ social
relationships into the recommendation model. In contrast, GNN-based methods
utilize the connectivity of graphs to directly model user and item embeddings.
GraphRec [5] introduce a graph attention mechanism with both the user social
network and the user-item interaction graph to learn user and item embeddings.
ConsisRec [14] is an improved version of GraphRec that addresses the social
inconsistency problem. To improve the performance of social recommendation,
DiffNet [2] and DiffNet++ [15] learn the social influence diffusion process.
However, these methods ignore the problem of social influence bias, which may
degrade the recommendation performance.

Disentangled Representation Learning in Recommendation. Disentangled
representation learning has been recognized as an effective way to enhance the
robustness and interpretability of models [16, 17]. Disentangled
representation learning has been applied in generative recommendations [18,
19, 20] and graph recommendations [21, 22, 23]. Authors in [18] propose a
model called MacridVAE, which is a disentangled variational auto-encoder
capable of learning representations from user behavior. This model achieves
both macro-disentanglement of high-level concepts and micro-disentanglement of
isolated low-level factors. DGCF [21] learns disentangled representations that
capture fine-grained user intents from the user-item interaction graph.
DisenHAN [22] learns disentangled user/item representations from various
aspects in a heterogeneous information network, utilizing meta relations to
decompose high-order connectivity between node pairs. Recently, disentangled
representation learning has been applied to causal recommendation systems [24,
25, 26]. DICE [24] constructs cause-specific data according to causal effect
and disentangles user and item embeddings into interest and conformity
components. DIB [25] mitigates confounding bias by decomposing user and item
embeddings into unbiased and biased components via information bottleneck.
Authors in [26] utilize user search data to decouple corresponding actual
preferences, providing a model-agnostic approach to causal embedding learning
in recommendation systems. Nevertheless, these methods may not be suitable for
social recommendations where social influence plays an important role in
modeling user preferences.

Causal Recommendation. In contrast to traditional recommendation systems that
predominantly emphasize correlational patterns, causal recommendation systems
delve into the realm of causality. Their objective is to discern and address
the causal relationships between user actions and the recommended outcomes
[27]. These systems leverage methodologies rooted in causal inference, such as
inverse propensity weighting [7, 28], backdoor adjustment [29, 30], frontdoor
adjustment [31, 32], and counterfactual inference [33, 34], to understand and
mitigate various biases like confounding bias, selection bias or spurious
correlations. For example, AutoDebias [35] leverages uniform data collected by
a random logging policy and meta-learning technique to mitigate various
biases. Zhang et al. [28] introduce the Multi-IPW model, employing a multi-
task learning approach to estimate Inverse Propensity Scores (IPS) and
simultaneously mitigate selection bias. DCR [29] introduces the notion of item
confounding features and employs backdoor adjustment combined with a mixture-
of-experts (MoE) strategy to alleviate the spurious correlations arising from
them. DCCF [31] utilizes frontdoor adjustment to alleviate the confounding
bias. Wei et al. [33] focus specifically on countering popularity bias through
the application of counterfactual inference. Recently, some causal
disentanglement-based methods have been proposed to achieve unbiased
recommendations [7, 8]. For example, DENC [7] and D2Rec [8] both focus on
disentangling three causes: inherent, confounder, and exposure factors, and
mitigating bias produced by network information. Nevertheless, these
approaches mainly eliminate biases, it is worth noting that certain biases,
such as popularity bias and social influence bias, can occasionally be
beneficial for learning user preferences [36].

##  3 Methodology

In this part, we first present the definitions and notations used in this
paper and then provide a concise overview of the overall framework. Following
that, we introduce each component in detail.

###  3.1 Definitions and Notations

Let $U=\\{u_{1},u_{2},...,u_{n}\\}$ and $V=\\{v_{1},v_{2},...,v_{m}\\}$ denote
the sets of users and items, where $n$ and $m$ are the number of users and
items, respectively. $\textbf{p}_{i}\in\mathbb{R}^{d}$ represents the ID
embedding of user $u_{i}$ and $\textbf{q}_{j}\in\mathbb{R}^{d}$ denotes the ID
embedding of item $v_{j}$, $d$ is the embedding size.
$\bf{Y}\in\mathbb{R}^{m\times n}$ represents the user-item rating matrix,
where $y_{ij}\in\textbf{Y}$ denotes the rating given by user $u_{i}$ to item
$v_{j}$. Let use $\bf{T}\in\mathbb{R}^{n\times n}$ to denote the user social
network, where $T_{ij}=1$ if there is a relation between $u_{i}$ and $u_{j}$.
$\textbf{e}_{ij}^{u}$ represents the rating embedding of user $u_{i}$ on item
$v_{j}$ that $u_{i}$ has interacted with, and $\textbf{e}_{ji}^{v}$ denotes
the rating embedding of item $v_{j}$ rated by user $u_{i}$. We use
$\textbf{z}_{i}^{u}$, $\textbf{c}_{i}^{u}$, $\textbf{z}_{j}^{v}$, and
$\textbf{c}_{j}^{v}$ to denote the interest embedding and social influence
embedding of user $u_{i}$ and item $v_{j}$, respectively. $\textbf{x}_{i}^{u}$
and $\textbf{x}_{j}^{v}$ represent the embeddings learned by a GNN-based
network of user $u_{i}$ and item $v_{j}$. In addition, $\textbf{h}_{i}^{u}$
and $\textbf{h}_{j}^{v}$ denote the reconstructed user and item
representations. The mathematical notations used in this paper are summarized
in Table 1.

Table 1: Notations. Symbols | Definitions and Notations
---|---
Y | user-item rating matrix
$U$ | user set
$V$ | item set
T | user social network
$C(i)$ | the set of items which user $u_{i}$ have interacted with
$N(i)$ | the set of neighbouring users connected to user $u_{i}$
$B(j)$ | the set of users who interact with item $v_{j}$
$\textbf{p}_{i}$ | ID embedding of user $u_{i}$
$\textbf{q}_{j}$ | ID embedding of item $v_{j}$
$\textbf{x}_{i}^{u}$ |  embedding learned from a GNN-based network of user $u_{i}$
$\textbf{x}_{j}^{v}$ |  embedding learned from a GNN-based network of item $v_{j}$
$\textbf{z}_{i}^{u}$ | interest embedding of user $u_{i}$
$\textbf{c}_{i}^{u}$ | social influence embedding of user $u_{i}$
$\textbf{z}_{j}^{v}$ | interest embedding of item $v_{j}$
$\textbf{c}_{j}^{v}$ | social influence embedding of item $v_{j}$
$\textbf{e}_{ij}^{u}$ |  rating embedding of user $u_{i}$ for item $v_{j}$ that $u_{i}$ has interacted with
$\textbf{e}_{ji}^{v}$ | rating embedding of item $v_{j}$ by user $u_{i}$
$\textbf{r}_{ij}^{v}$ | item embedding from item set $C(i)$ of user $u_{i}$
$\textbf{r}_{ji}^{u}$ | user embedding from user set $B(j)$ of item $v_{j}$
$\textbf{t}_{ij}^{u}$ | user embedding from user set $N(i)$ of user $u_{i}$
$\textbf{h}_{i}^{u}$ | reconstructed representation of user $u_{i}$
$\textbf{h}_{j}^{v}$ | reconstructed representation of item $v_{j}$

###  3.2 An overview of the proposed model

We propose a causal disentanglement-based framework for regulating social
influence bias in social recommendation, named CDRSB. Figure 2 shows the
overall architecture of the model.

Figure 2: The overall framework of CDRSB. It contains two modules: (1) a
disentangled encoder that disentangles user and item embeddings learned from a
GNN-based network into interest and social influence embeddings. We minimize
mutual information-based objectives to reduce redundancy and ensure the
separation of these disentangled embeddings. (2) a regulatory decoder that
learns dynamic weights to combine interest and social influence embeddings
into final user and item representations, achieving reasonable utilization of
social influence bias.

This framework mainly includes two modules: (1) Disentangled Encoder. We aim
to disentangle user and item embeddings learned from network information into
interest and social influence embeddings. (2) Regulatory Decoder. We introduce
a weight calculation module to regulate the social influence bias, which could
improve the recommendation performance.

###  3.3 Disentangled Encoder

In this section, based on the non-causal social influence path and causal
interest path of the causal graph for social recommendations, our focus is on
disentangling user and item embeddings into interest and social influence
embeddings. Initially, we employ a GNN-based learning network with the user-
item interaction graph and user-social graph to learn user and item
embeddings. Subsequently, we introduce independent MLP layers to disentangle
interest and social influence embeddings.

####  3.3.1 GNN-based Learning Network

Motivated by the approach introduced in [5], we design a similar GNN-based
method to learn the initial user and item embeddings, which contains two
layers: the embedding layer and the concatenation layer.

Embedding layer: We input the user social network and user-item interaction
network into the embedding layer to learn the ID embedding, neighboring item
embedding, and neighboring user embedding of user $u_{i}$. In addition, we
also consider each user-item rating in the user-item interaction network,
which represents the user’s preference level.

$\displaystyle\textbf{p}_{i}=\delta(\textbf{W}\cdot\textbf{o}_{i}+\textbf{b}),$
(1) $\displaystyle\textbf{r}_{ij,\forall j\in
C(i)}^{v}=\delta(\textbf{W}\cdot\textbf{o}_{ij}^{r}+\textbf{b}),$
$\displaystyle\textbf{e}_{ij,\forall j\in
C(i)}^{u}=\delta(\textbf{W}\cdot\textbf{o}_{ij}^{e}+\textbf{b}),$
$\displaystyle\textbf{t}_{ij,\forall j\in
N(i)}^{u}=\delta(\textbf{W}\cdot\textbf{o}_{ij}^{t}+\textbf{b}),$

where $\textbf{p}_{i}$ and $\textbf{o}_{i}$ represent the ID embedding and
one-hot vectors of user $u_{i}$. $\textbf{r}_{ij}^{v}$ and
$\textbf{o}_{ij}^{r}$ are the embedding and one-hot vectors of item $v_{j}$
that user $u_{i}$ has interacted with. $\textbf{e}_{ij}^{u}$ and
$\textbf{o}_{ij}^{e}$ are the rating embedding and one-hot vectors of user
$u_{i}$ for the item $v_{j}$ that user $u_{i}$ has interacted with.
$\textbf{t}_{ij}^{u}$ and $\textbf{o}_{ij}^{t}$ are the embedding and one-hot
vectors of user $u_{j}$ that user $u_{i}$ has connected with. $\delta$ denotes
the non-linear activation function, W and b represent the weight matrix and
bias vector, respectively.

Concatenation layer: In this part, we concatenate user ID embedding
$\textbf{p}_{i}$, neighboring item embedding $\textbf{r}_{ij}^{v}$, and rating
embedding $\textbf{e}_{ij}^{u}$ from the user-item interaction network, as
well as the neighboring user embedding $\textbf{t}_{ij}^{u}$ from the user-
social network to learn the user embedding $\textbf{x}_{i}^{u}$.

$\begin{split}\textbf{x}_{i}^{u}=\delta(\textbf{W}\cdot(\textbf{p}_{i}&\oplus
Agg_{items}({\textbf{r}_{ij}^{v},\forall j\in C(i)})\\\ &\oplus
Agg_{ratings}({\textbf{e}_{ij}^{u},\forall j\in C(i)})\\\ &\oplus
Agg_{users}({\textbf{t}_{ij}^{u},\forall j\in N(i)}))+\textbf{b}),\end{split}$
(2)

where $Agg_{items}$ represents the aggregation operation for items,
$Agg_{ratings}$ represents the aggregation operation for user-item ratings,
and $Agg_{users}$ represents the user aggregation function. We have tried
various aggregation methods, including sum aggregation, mean aggregation, and
neural network aggregation. Among them, the mean aggregation obtained the best
results. $C(i)$ is a set of items that user $u_{i}$ has interacted with.
$N(i)$ is the set of neighboring users trusted by user $u_{i}$. $\oplus$
represents the concatenation operation.

Similarly, we utilize the user-item interaction network to learn the item
embedding $\textbf{x}_{j}^{v}$.

$\displaystyle\textbf{q}_{j}=\delta(\textbf{W}\cdot\textbf{o}_{j}+\textbf{b}),$
(3) $\displaystyle\textbf{r}_{ji,\forall i\in
B(j)}^{u}=\delta(\textbf{W}\cdot\textbf{o}_{ji}^{r}+\textbf{b}),$
$\displaystyle\textbf{e}_{ji,\forall i\in
B(j)}^{v}=\delta(\textbf{W}\cdot\textbf{o}_{ji}^{e}+\textbf{b}),$
$\begin{split}\textbf{x}_{j}^{v}=\delta(\textbf{W}\cdot(\textbf{q}_{j}\oplus
Agg_{users}({\textbf{r}_{ji}^{u},\forall i\in B(j)})\oplus\\\
Agg_{ratings}({\textbf{e}_{ji}^{v},\forall i\in
B(j)}))+\textbf{b}),\end{split}$ (4)

where $B(j)$ is the set of users who interacted with item $v_{j}$.

####  3.3.2 Causal Disentanglement

In this subsection, we design four independent MLP networks to decompose user
and item embeddings into interest and social influence embeddings.
Specifically, for the user embedding $\textbf{x}_{i}^{u}$, we extract two
independent interest and social influence components. We feed
$\textbf{x}_{i}^{u}$ into two separate MLP layers,

$\textbf{z}_{i}^{u}=MLP(\textbf{x}_{i}^{u};\Theta_{0});\qquad\textbf{c}_{i}^{u}=MLP(\textbf{x}_{i}^{u};\Theta_{1}).$
(5)

Similarly, the decomposing process of item embedding $\textbf{x}_{j}^{v}$ is
as follows,

$\textbf{z}_{j}^{v}=MLP(\textbf{x}_{j}^{v};\Theta_{2});\qquad\textbf{c}_{j}^{v}=MLP(\textbf{x}_{j}^{v};\Theta_{3}),$
(6)

where $\Theta_{0},\Theta_{1},\Theta_{2}$ and $\Theta_{3}$ refer to all the
parameters for the respective MLP layers.

Despite using separate networks to learn interest and social influence
embeddings, we cannot guarantee the absence of redundant information.
Therefore, we aim to minimize the mutual information between them to ensure
their independence. Mutual information is a statistical measure that
quantifies the amount of information one random variable contains about
another, indicating the level of dependence between these two variables. High
mutual information indicates a strong relationship or dependency between the
variables, while low mutual information suggests independence or little shared
information.

Traditionally, mutual information is calculated based on examples $a_{i}$ and
$b_{i}$ sampled from two distributions $A$ and $B$. However, in our case, the
true distributions of $A$ and $B$ are unknown. Taking inspiration from recent
advancements in contrastive learning and sample-based mutual information
estimation, such as the CLUB framework [37], we estimate mutual information
using the difference in conditional probabilities between positive and
negative sample pairs. We regard a sample pair with the same index as a
positive pair, such as $(a_{i},b_{i})$, and consider a sample pair with a
different index as a negative pair, such as $(a_{i},b_{j})$.

Since we cannot directly compute the conditional distribution
$P(\textbf{c}_{i}^{u}|\textbf{z}_{i}^{u})$ and
$P(\textbf{c}_{j}^{v}|\textbf{z}_{j}^{v})$, we use variational distributions
$Q_{\theta_{u}}(\textbf{c}_{i}^{u}|\textbf{z}_{i}^{u})$ and
$Q_{\theta_{v}}(\textbf{c}_{j}^{v}|\textbf{z}_{j}^{v})$ with parameters
$\theta_{u}$ and $\theta_{v}$, which could be implemented by neural networks,
to approximate $P(\textbf{c}_{i}^{u}|\textbf{z}_{i}^{u})$ and
$P(\textbf{c}_{j}^{v}|\textbf{z}_{j}^{v})$. The output of
$Q_{\theta_{u}}(\textbf{c}_{i}^{u}|\textbf{z}_{i}^{u})$/$Q_{\theta_{v}}(\textbf{c}_{j}^{v}|\textbf{z}_{j}^{v})$
are mean $\mu_{i}^{u}$/$\mu_{j}^{v}$ and log variance
$log({\delta_{i}^{u}}^{2})$/$log({\delta_{j}^{v}}^{2})$. To update the
parameter $\theta_{u}$ and $\theta_{v}$, we maximize the corresponding
conditional log-likelihood loss function,

$\begin{split}L_{u}^{LLD}&=\frac{1}{N}\sum_{i=1}^{N}logQ_{\theta_{u}}(\textbf{c}_{i}^{u}|\textbf{z}_{i}^{u})\\\
&=\frac{1}{N}\sum_{i=1}^{N}-\frac{(\mu_{i}^{u}-\textbf{c}_{i}^{u})^{2}}{e^{log({\delta_{i}^{u}}^{2})}};\\\
L_{v}^{LLD}&=\frac{1}{N}\sum_{j=1}^{N}logQ_{\theta_{v}}(\textbf{c}_{j}^{v}|\textbf{z}_{j}^{v})\\\
&=\frac{1}{N}\sum_{i=1}^{N}-\frac{(\mu_{j}^{v}-\textbf{c}_{j}^{v})^{2}}{e^{log({\delta_{j}^{v}}^{2})}},\end{split}$
(7)

where $N$ is the number of samples. $\textbf{z}_{i}^{u}$,
$\textbf{c}_{i}^{u}$, $\textbf{z}_{j}^{v}$ and $\textbf{c}_{j}^{v}$ represent
the interest embedding and social influence embedding of user $u_{i}$ and item
$v_{j}$, respectively.

To ensure independence between the decomposed interest and social influence
embeddings, we introduce the mutual information loss function and minimize it,

$\begin{split}L_{u}^{MI}&=\frac{1}{N^{2}}\sum_{i=1}^{N}\sum_{k=1,k\not=i}^{N}[logQ_{\theta_{u}}(\textbf{c}_{i}^{u}|\textbf{z}_{i}^{u})-logQ_{\theta_{u}}(\textbf{c}_{k}^{u}|\textbf{z}_{i}^{u}))]\\\
&=\frac{1}{N}\sum_{i=1}^{N}[logQ_{\theta_{u}}(\textbf{c}_{i}^{u}|\textbf{z}_{i}^{u})-\frac{1}{N}\sum_{k=1,k\not=i}^{N}logQ_{\theta_{u}}(\textbf{c}_{k}^{u}|\textbf{z}_{i}^{u})]\\\
&=\frac{1}{N}\sum_{i=1}^{N}[\frac{(\mu_{i}^{u}-\textbf{c}_{i}^{u})^{2}}{e^{log({\delta_{i}^{u}}^{2})}}-\frac{1}{N}\sum_{k=1,k\not=i}^{N}\frac{(\mu_{i}^{u}-\textbf{c}_{k}^{u})^{2}}{e^{log({\delta_{i}^{u}}^{2})}}];\\\
L_{v}^{MI}&=\frac{1}{N^{2}}\sum_{j=1}^{N}\sum_{k=1,k\not=j}^{N}[logQ_{\theta_{v}}(\textbf{c}_{j}^{v}|\textbf{z}_{j}^{v})-logQ_{\theta_{v}}(\textbf{c}_{k}^{v}|\textbf{z}_{j}^{v})]\\\
&=\frac{1}{N}\sum_{j=1}^{N}[logQ_{\theta_{v}}(\textbf{c}_{j}^{v}|\textbf{z}_{j}^{v})-\frac{1}{N}\sum_{k=1,k\not=j}^{N}logQ_{\theta_{v}}(\textbf{c}_{k}^{v}|\textbf{z}_{j}^{v})]\\\
&=\frac{1}{N}\sum_{j=1}^{N}[\frac{(\mu_{j}^{v}-\textbf{c}_{j}^{v})^{2}}{e^{log({\delta_{j}^{v}}^{2})}}-\frac{1}{N}\sum_{k=1,k\not=i}^{N}\frac{(\mu_{j}^{v}-\textbf{c}_{k}^{v})^{2}}{e^{log({\delta_{j}^{v}}^{2})}}],\\\
\end{split}$ (8)

where
$(\textbf{c}_{i}^{u},\textbf{z}_{i}^{u})$/$(\textbf{c}_{j}^{v},\textbf{z}_{j}^{v})$
is the positive pair and
$(\textbf{c}_{k}^{u},\textbf{z}_{i}^{u})$/$(\textbf{c}_{k}^{v},\textbf{z}_{j}^{v})$
is the negative pair.

The total mutual information loss function and variational approximation loss
are as follows,

$\begin{split}L^{MI}&=L_{u}^{MI}+L_{v}^{MI},\\\
L^{LLD}&=-L_{u}^{LLD}-L_{v}^{LLD}.\end{split}$ (9)

###  3.4 Regulatory Decoder

In traditional causal recommendation methods, social influence bias is often
discarded. However, in our method, we argue that social influence bias is
individual-specific. The impact of social influence bias can be detrimental
when a user interacts with an item recommended by friends, deviating from
their genuine interests. Conversely, it can be beneficial when a user engages
with an item recommended by friends that is of high quality and aligns with
his interests. Blindly eliminating this bias may lead to suboptimal
recommendation performance. Therefore, we present a regulatory decoder
designed to regulate social influence bias by reasonably incorporating
positive social influence embeddings and mitigating the negative ones. This
decoder encompasses a dynamic weight calculation module and a fusion module.
The weight calculation module dynamically computes the weight of social
influence embeddings, while the fusion module integrates interest and social
influence embeddings into the final user and item representations.

Generally, when users click on or purchase a product recommended by their
friends that doesn’t align with their interests, these users are less inclined
to engage with similar items. Conversely, if the recommended product resonates
with the users’ genuine preferences, they are more likely to make subsequent
purchases of similar products. Therefore, for a user-item interaction pair
$(u_{i},v_{j})$ where $v_{j}$ is recommended by friends of user $u_{i}$, we
assume that if user $u_{i}$ interacts with another item $v_{k}$ that is
similar to $v_{j}$, the main reason for $u_{i}$ clicking on item $v_{j}$ is
that $u_{i}$ likes $v_{j}$. In such cases, the impact of friends is
beneficial, we should incorporate positive social influence embeddings.
Conversely, it might be attributed to the influence of herd mentality rather
than the personal preference for the item, we need to mitigate the negative
social influence embeddings. For the user-item interaction pair
$(u_{i},v_{j})$, if user $u_{i}$’s friends have interacted with the item
$v_{j}$, we consider $v_{j}$ to be recommended by $u_{i}$’s friends.

First, we calculate the maximum similarity between item $v_{j}$ and $v_{k}$,

$s=max_{v_{k}\in V_{h},k\not=j}f(v_{j},v_{k}),$ (10)

where $f$ is the similarity function, and $V_{h}=\\{v_{1},v_{2},...,v_{m}\\}$
represents the historical interaction records of user $u_{i}$.

The value of $s$ indicates the main reason why user $u_{i}$ clicks on the item
$v_{j}$. A higher value indicates that the user consistently clicks on items
similar to $v_{j}$. Multiple clicks mean that the user likes item $v_{j}$,
implying a positive impact from the social influence bias. Conversely, a small
value represents that the user dislikes the item $v_{j}$, signifying a
negative impact from the social influence bias. We set the similarity
threshold $s^{\prime}$ as 0.5 and we could obtain the weight of social
influence embeddings according to the similarity $s$,

$\alpha=\begin{cases}1,\quad s>s^{\prime}\\\ 0,\quad s<=s^{\prime}\end{cases}$
(11)

It is worth noting that within the user-item interaction pair $(u_{i},v_{j})$,
if the item $v_{j}$ is not recommended by the friends of user $u_{i}$, we
assume that $u_{i}$ clicked on item $v_{j}$ based on personal preferences,
entirely independent of any influence from the friends of user $u_{i}$.
Consequently, we set the weight $\alpha$ to $0$.

Subsequently, a more accurate user representation $\textbf{h}_{i}^{u}$ and
item representation $\textbf{h}_{j}^{v}$ can be learned as follows,

$\begin{split}\textbf{h}_{i}^{u}&=\textbf{z}_{i}^{u}+\alpha\textbf{c}_{i}^{u},\\\
\textbf{h}_{j}^{v}&=\textbf{z}_{j}^{v}+\alpha\textbf{c}_{j}^{v}.\end{split}$
(12)

After reconstructing the user representation $\textbf{h}_{i}^{u}$ and item
representation $\textbf{h}_{j}^{v}$, we concatenate them and put them into the
final prediction layers,

$\hat{y}_{ij}=MLP(\textbf{h}_{i}^{u}\oplus\textbf{h}_{j}^{v}).$ (13)

We aim to minimize the following loss function,

$L^{O}=\frac{1}{N}\sum_{i,j=1}^{N}l(y_{ij}-\hat{y}_{ij}),$ (14)

where $N$ is the batch size, $l$ denotes the mean squared error in the rating
prediction task and the cross-entropy loss function in the ranking task.

Finally, we optimize all parameters by minimizing the final loss function $L$,

$L=L^{O}+\lambda(L^{MI}+L^{LLD}),$ (15)

where $\lambda$ is the weight parameter.

##  4 Experiments

In this section, we conduct a series of comprehensive experiments on four
publicly available datasets to evaluate the performance of our proposed model
CDRSB in the rating prediction task and ranking task. We aim to answer the
following questions.

  * 1.

RQ1: Does our model achieve superior performance compared to other state-of-
the-art baseline methods?

  * 2.

RQ2: How do different components, such as mutual information-based objectives
and social influence embeddings, affect the outcomes of our model?

  * 3.

RQ3: Are the interest and social influence embeddings we’ve acquired genuinely
disentangled?

  * 4.

RQ4: How does our model’s performance vary with different hyper-parameters?

  * 5.

RQ5: What is the primary reason for user interaction with an item?

###  4.1 Experimental Settings

####  4.1.1 Datasets

We conduct experiments on four large-scale datasets:
Ciao111http://www.cse.msu.edu/ tangjili/trust.html, Epinions††footnotemark: ,
Dianping222https://lihui.info/data/dianping/, and Douban
book333https://www.dropbox.com/s/u2ejjezjk08lz1o/Douban.tar.gz?e=1&dl=0. These
datasets comprise user-item ratings along with user trust relationships. The
Ciao and Epinions datasets are collected from popular social websites
Ciao444http://www.ciao.co.uk and Epinions555http://www.epinions.com, where
users have the ability to rate items and establish social connections by
adding friends. The Dianping dataset is collected from a leading local
restaurant search and review platform in China666https://www.dianping.com.
This dataset is crawled by authors in [38]. The Douban book dataset is
extracted from a Chinese book forum777https://book.douban.com/. The rating
scale in all datasets ranges from 1 to 5. For the ranking task, we discretize
the ratings into binary values of 0 and 1 to indicate whether the user has
interacted with the item or not. To ensure data quality and address sparsity
issues, we apply filtering criteria to remove records with insufficient
interactions. For the Epinions dataset, we delete records with fewer than five
interactions. For the Ciao dataset, we remove samples with less than three
interactions between users and items. For the Dianping and Douban book
datasets, samples involving less than ten interactions between users and items
are omitted. Given the substantial data volume in both Dianping and Douban
book datasets, we employ random sampling to enhance training efficiency. Table
2 provides an overview of the basic statistics of these datasets.

Table 2: Statistic of the datasets: Ciao, Epinions, Dianping and Douban book

.  Datasets Ciao Epinions Dianping Douban book # Users 7108 20461 20000 7000 #
Items 21978 31678 9511 16421 # Ratings 184960 545861 725637 443334 Rating
Density 0.119% 0.084% 0.380% 0.386% # Social Connections 53019 311235 77146
11267 Social Connection Density 0.105% 0.074% 0.019% 0.023%

####  4.1.2 Evaluation Metrics

To assess the recommendation performance of the CDRSB model and baselines, we
depend on rating prediction and ranking metrics.

Rating Prediction Metrics. We utilize two commonly used evaluation metrics:
root mean squared error (RMSE) and mean absolute error (MAE). These metrics
are widely employed in collaborative prediction algorithms [39]. RMSE measures
the square root of the average squared difference between the predicted
ratings $\hat{y}_{i}$ and the true ratings $y_{i}$ for a set of $N$ instances.
A lower RMSE indicates better accuracy in predicting ratings. MAE calculates
the average absolute difference between the predicted ratings $\hat{y}_{i}$
and the true ratings $y_{i}$.

Ranking Metrics. We utilize two widely adopted metrics, Hit Rate (HR) and
Normalized Discounted Cumulative Gain (NDCG), to assess the ranking
performance. HR measures the proportion of samples where a user-interacted
item appears within the top-K recommended items. NDCG considers both the
relevance and the position of the recommended items, assigning higher weights
to items ranked higher in the list.

####  4.1.3 Baseline Methods

To verify the effectiveness of our model, we compare the performance of CDRSB
with three sets of baseline methods: traditional recommendation systems,
social recommendation systems, and causal recommendation systems. We carefully
selected several of the most representative methods from each category. This
comprehensive comparison allows us to assess the relative performance of CDRSB
against different types of recommendation approaches and gain insights into
its strengths and advantages. Furthermore, distinct sets of baselines are
employed for the rating prediction and ranking tasks, as outlined in Table 3.

Table 3: Summary of baselines for rating prediction and ranking tasks. | Rating Prediction | Ranking
---|---|---
Traditional recommendations | NeuMF | NeuMF
PMF | LightGCN
Social recommendations | SocialMF | DiffNet
GraphRec | DiffNet++
ConsisRec |
Causal recommendations | CausE | DICE
D2Rec | D2Rec
IPS-MF | SIDR

  * 1.

Traditional recommendation systems

    * (a)

PMF [40] is a traditional recommendation method that decomposes the user-item
rating matrix into low-dimensional latent feature matrices. It learns the
relationships among these latent features for rating prediction.

    * (b)

NeuMF [41] combines collaborative filtering and neural network techniques to
capture user-item interactions and make accurate predictions. For the rating
prediction task, we modify its loss function to the square loss.

    * (c)

LightGCN [42] is a simple GCN model that directly propagates user and item
embeddings through the user-item interaction graph without introducing complex
operations or auxiliary information.

  * 2.

Social recommendation systems

    * (a)

SocialMF [4] incorporates user trust information into a matrix factorization
model, leveraging user social relationships to infer user ratings for items.

    * (b)

GraphRec [5] proposes a framework for social recommendation that leverages
Graph Neural Networks to learn user and item representations with user-item
interactions and user social networks.

    * (c)

ConsisRec [14] is an enhanced method based on GraphRec that effectively
addresses the issue of social inconsistency by leveraging consistent neighbor
aggregation.

    * (d)

DiffNet [2] proposes a deep influence propagation model to simulate how users
are influenced by the recursive social diffusion process for social
recommendation.

    * (e)

DiffNet++ [15] is an improved model based on DiffNet, incorporating the
modeling of interest diffusion with a user-item graph.

  * 3.

Causal recommendation systems

    * (a)

IPS-MF [43] utilizes inverse propensity score (IPS) to mitigate the selection
bias produced by exposure data.

    * (b)

CausE [44] proposes a domain adaptation method that trains the model by
utilizing biased data and predicts recommendation results based on random
exposure.

    * (c)

DICE [24] first disentangles user and item embeddings into interest and
conformity with cause-specific data and then eliminates the confounding effect
of popularity bias.

    * (d)

D2Rec [8] disentangles user and item representations into inherent,
confounder, and exposure factors, and then mitigates social influence bias by
a reweighting function.

    * (e)

SIDR [6] causally disentangles the user and item latent features to mitigate
social influence bias in implicit feedback for social recommendation.

####  4.1.4 Parameter Settings

We implement the CDRSB model using Python with the Pytorch framework, all
baseline methods are conducted based on their GitHub source code and carefully
adjusted the hyperparameters. We randomly split datasets into training, test,
and validation sets according to an 8:1:1 ratio. The optimal hyperparameters
are obtained by optimizing the loss function (15) using the RMSprop optimizer.
Based on the validation set, we evaluate the performance of the model using
different parameter combinations. The embedding size of original embedding,
decomposing embedding, and batch size are searched within the range of [8, 16,
32, 64, 128, 256]. Ultimately, we set them to 64, 64, and 128, respectively.
We conduct tests with different learning rates [0.0001, 0.0005, 0.001, 0.005,
0.01, 0.05, 0.1] and $\lambda$ values [0.0001, 0.001, 0.01, 0.1]. We determine
that the optimal learning rate is 0.0001, and we set $\lambda$ to 0.001. To
prevent overfitting, we apply batch normalization, dropout, and early stopping
techniques where the training is stopped when the test evaluation metrics
increase for 5 epochs.

###  4.2 Results and Analysis (RQ1)

We evaluate the performance of CDRSB and the baselines using commonly used
evaluation metrics for rating prediction task w.r.t. RMSE and MAE and ranking
task w.r.t. HR@10 and NDCG@10 on four datasets. The results for each task are
shown in Table 4 and Table 5.

Table 4: Overall performance comparison for the rating prediction task. The optimal performance is highlighted using bold fonts, and the second-best performance is denoted by underlines. Method type | Method | Epinions | Ciao | Dianping | Douban book
---|---|---|---|---|---
RMSE | MAE | RMSE | MAE | RMSE | MAE | RMSE | MAE
Traditional recommendations | PMF | 1.2905 | 1.0203 | 1.1309 | 0.9107 | 1.0260 | 0.8530 | 1.0176 | 0.8425
NeuMF | 1.1290 | 0.9040 | 1.0713 | 0.8145 | 0.9606 | 0.7887 | 0.9513 | 0.7802
Social recommendations | SociaMF | 1.0934 | 0.8442 | 1.0534 | 0.8223 | 0.9512 | 0.7945 | 0.9428 | 0.7845
GraphRec | 1.0657 | 0.8134 | 0.9978 | 0.7523 | 0.8205 | 0.6023 | 0.8116 | 0.5928
ConsisRec | 1.0467 | 0.8096 | 0.9823 | 0.7436 | 0.8073 | 0.5796 | 0.8025 | 0.5768
Causal recommendations | IPS-MF | 1.1023 | 0.8813 | 1.0423 | 0.7904 | 0.9649 | 0.7514 | 0.9584 | 0.7461
CausE | 1.1145 | 0.8956 | 1.0378 | 0.7810 | 0.8546 | 0.6481 | 0.8475 | 0.6362
D2Rec | 1.0223 | 0.8545 | 0.9394 | 0.7103 | 0.7256 | 0.5478 | 0.7124 | 0.5405
CDRSB | 0.9404 | 0.7078 | 0.8246 | 0.5950 | 0.6759 | 0.5128 | 0.6695 | 0.5277
| Imp.% |  $\uparrow$ 8.19% |  $\uparrow$ 14.67% |  $\uparrow$ 11.48% |  $\uparrow$ 11.53% |  $\uparrow$ 4.97% |  $\uparrow$ 3.50% |  $\uparrow$ 4.29% |  $\uparrow$ 1.28%
Table 5: Overall performance comparison for ranking task. The optimal performance is highlighted using bold fonts, and the second-best performance is denoted by underlines. Method type | Method | Epinions | Ciao | Dianping | Douban book
---|---|---|---|---|---
HR@10 | NDCG@10 | HR@10 | NDCG@10 | HR@10 | NDCG@10 | HR@10 | NDCG@10
Traditional recommendations | NeuMF | 0.3815 | 0.2389 | 0.3393 | 0.2231 | 0.4123 | 0.2701 | 0.4163 | 0.2572
LightGCN | 0.4013 | 0.2527 | 0.3456 | 0.2367 | 0.4234 | 0.2825 | 0.4389 | 0.2826
Social recommendations | DiffNet | 0.4264 | 0.2756 | 0.3589 | 0.2501 | 0.4495 | 0.3026 | 0.4527 | 0.3009
DiffNet++ | 0.4479 | 0.3016 | 0.3670 | 0.2704 | 0.4726 | 0.3313 | 0.4848 | 0.3428
Causal recommendations | DICE | 0.6735 | 0.3902 | 0.5572 | 0.3301 | 0.6972 | 0.4231 | 0.7026 | 0.4237
D2Rec | 0.6703 | 0.3876 | 0.5674 | 0.3356 | 0.7004 | 0.4294 | 0.7128 | 0.4162
SIDR | 0.6824 | 0.4036 | 0.5863 | 0.3528 | 0.7183 | 0.4368 | 0.7345 | 0.4596
CDRSB | 0.8082 | 0.5434 | 0.7599 | 0.4772 | 0.7768 | 0.5146 | 0.8260 | 0.5791
| Imp.% |  $\uparrow$ 12.58% |  $\uparrow$ 13.98% |  $\uparrow$ 17.36% |  $\uparrow$ 12.44% |  $\uparrow$ 5.85% |  $\uparrow$ 7.78% |  $\uparrow$ 9.15% |  $\uparrow$ 11.95%

  * 1.

Our model, CDRSB, outperforms other baselines in terms of metrics for rating
prediction (RMSE and MAE) and ranking (HR@10 and NDCG@10) on four datasets.
CDRSB demonstrates superior performance, achieving average improvements of up
to 39.04% and 26.49% in terms of HR@10 and NDCG@10 over the best baseline
model LightGCN in traditional recommendation methods. Furthermore, it
outperforms the best baseline model DiffNet++ by an average of 34.97% and
21.71% in terms of HR@10 and NDCG@10 in social recommendation methods.
Additionally, CDRSB exhibits better performance than the best baseline model
D2Rec, with improvements of 7.23% and 7.75% in terms of RMSE and MAE in causal
recommendation methods. The results indicate the effectiveness and rationality
of CDRSB.

  * 2.

Compared to D2Rec and SIDR, which mitigate social influence bias, CDRSB
achieves the highest performance. This demonstrates that properly regulating
social influence bias could improve the model’s overall performance.

  * 3.

Social recommendation methods based on causal debiasing, such as D2Rec and
SIDR, outperform traditional social recommendation methods across all
evaluation metrics. This emphasizes the significance of mitigating social
influence bias in enhancing recommendation performance.

  * 4.

SocialMF, GraphRec, and ConsisRec, which incorporate social network
information, outperform traditional recommendation models NeuMF and PMF. This
is attributed to the fact that social networks can complement user
preferences, particularly when user features are sparse.

  * 5.

Both NeuMF and PMF utilize rating information for recommendations. However,
NeuMF outperforms PMF, indicating the superior learning capability of deep
learning models in recommendation systems.

  * 6.

GraphRec outperforms SocialMF by an average of 8.63% and 12.12% in terms of
RMSE and MAE across four datasets. These results highlight the advantages of
GNN and the incorporation of rating information into the learning process of
user and item embeddings.

###  4.3 Ablation Studies (RQ2)

To evaluate the effectiveness of each component in CDRSB, we conduct ablation
experiments on four datasets. We create three variants of CDRSB, denoted as
w/o wt, w/o sl, and w/o mi by removing specific components.

  * 1.

w/o wt: It eliminates the weight calculation module, thereby fixing the
weights of social influence embeddings at 1.

  * 2.

w/o sl: It removes user and item social influence embeddings and only uses
user and item interest embeddings for recommendation.

  * 3.

w/o mi: It eliminates the mutual information minimization objective from the
joint loss.

The results of the ablation studies for rating prediction and ranking tasks
are presented in Table 6 and Table 7.

Table 6: Results of the ablation studies on the rating prediction task. | Ciao | Epinions | Dianping | Douban book
---|---|---|---|---
Method | RMSE | MAE | RMSE | MAE | RMSE | MAE | RMSE | MAE
w/o wt | 0.8379 | 0.6126 | 0.9605 | 0.7274 | 0.6934 | 0.5326 | 0.6836 | 0.5529
w/o sl | 0.8345 | 0.6069 | 0.9592 | 0.7201 | 0.6883 | 0.5278 | 0.6796 | 0.5401
w/o mi | 0.8308 | 0.6006 | 0.9547 | 0.7156 | 0.6825 | 0.5234 | 0.6754 | 0.5357
CDRSB | 0.8246 | 0.5950 | 0.9404 | 0.7078 | 0.6759 | 0.5128 | 0.6695 | 0.5277
Table 7: Results of the ablation studies on the ranking task. | Ciao | Epinions | Dianping | Douban book
---|---|---|---|---
Method | HR@10 | NDCG@10 | HR@10 | NDCG@10 | HR@10 | NDCG@10 | HR@10 | NDCG@10
w/o wt | 0.7302 | 0.4501 | 0.7598 | 0.4938 | 0.7310 | 0.4709 | 0.7902 | 0.5313
w/o sl | 0.7268 | 0.4439 | 0.7603 | 0.4967 | 0.7278 | 0.4625 | 0.7810 | 0.5148
w/o mi | 0.7325 | 0.4503 | 0.7663 | 0.5015 | 0.7346 | 0.4739 | 0.7929 | 0.5393
CDRSB | 0.7599 | 0.4772 | 0.8082 | 0.5434 | 0.7768 | 0.5146 | 0.8260 | 0.5791

Based on the above results, we can observe that each component of the overall
model plays a crucial role. The model w/o mi, which eliminates mutual
information restraints, experiences a significant drop in performance. This
outcome might be attributed to the fact that mutual information minimization
ensures that the decoupled interest embedding and social influence embedding
have non-redundant information, leading to enhanced performance. Comparing
CDRSB with w/o wt, where negative social influence embeddings are
incorporated, it becomes evident that the weight calculation module plays a
pivotal role in effectively controlling social influence bias. Moreover, the
inferior performance of model w/o sl emphasizes the significant contributions
of the positive social influence embeddings to the outcome.

###  4.4 Visualization of Disentangled Embeddings (RQ3)

In this section, we aim to gain deeper insights into the impact of the
disentangled encoder on the representative learning process in CDRSB.
Specifically, we investigate whether the interest embedding and social
influence embedding become independent of each other during the training
process. We employ t-SNE [45], a data visualization technique that projects
high-dimensional data into a lower-dimensional space, to visualize this
phenomenon. The disentangled interest embedding and social influence embedding
for the rating prediction task on the Epinions dataset are visualized in
Figure 3 and Figure 4.

(a) Initialization (b) Convergence

Figure 3: Visualization of user’s interest embedding (red points) and social
influence embedding (blue points) for different stages: (a) initialization,
(b) convergence on the dataset Epinions.

(a) Initialization (b) Convergence

Figure 4: Visualization of item’s interest embedding (red points) and social
influence embedding (blue points) for different stages: (a) initialization,
(b) convergence on the dataset Epinions.

We observe that with an increasing number of model training iterations, a
distinction emerges between the interest embedding represented in red and the
social influence embedding represented in blue. This clear separation
validates the effectiveness of the disentangled encoder in disentangling and
distinguishing the interest and social influence within the embeddings.

###  4.5 Parameter Sensitivity (RQ4)

In this section, we evaluate the performance of CDRSB under various settings
of two crucial parameters: the decoupling embedding dimension and the weight
parameter $\lambda$.

  * 1.

The impact of decoupling embedding dimension. For the rating prediction and
ranking tasks, we present the comparative results in Figure 5 and Figure 6,
respectively. It is observed that optimal performance is achieved when the
dimension is set to 64. Increasing the dimension improves the model’s
effectiveness. However, it is important to note that too large embedding
dimensions may lead to overfitting. Thus, choosing an appropriate decoupled
embedding dimension is crucial to balance model complexity and performance.

(a)

(b)

Figure 5: RMSE and MAE on different decoupled embedding dimensions: (a) RMSE
(b) MAE.

  * 2.

The impact of weight parameter $\lambda$. The comparative results for rating
prediction and ranking tasks are shown in Figure 7 and Figure 8. It can be
observed that CDRSB obtains the optimal result when $\lambda$ is set to 0.001.
This indicates that a moderate weight parameter strikes a balance between
incorporating the mutual information minimization objective and preserving the
overall recommendation performance.

(a)

(b)

Figure 6: HR@10 and NDCG@10 on different decoupled embedding dimensions: (a)
HR@10 (b) NDCG@10.

(a)

(b)

Figure 7: RMSE and MAE on different $\lambda$: (a) RMSE (b) MAE.

(a)

(b)

Figure 8: HR@10 and NDCG@10 on different $\lambda$: (a) HR@10 (b) NDCG@10.

###  4.6 Case Study (RQ5)

In this section, we delve into the motivations behind user-item interactions,
exploring whether they primarily stem from individual preferences or are
influenced by herd mentality. We randomly sample 1000 users who received
recommendations from friends across all datasets and subsequently visualize
the different effects of social influence embeddings on each user-item
interaction pair for the rating prediction task, as shown in Figures 9 and 10.

(a)

(b)

Figure 9: The main reason for user-item interactions: (a) Ciao (b) Epinions.

(a)

(b)

Figure 10: The main reason for user-item interactions: (a) Dianping (b) Douban
book.

In the Figures 9 and 10, the green points denote that the social embeddings
have a positive effect, implying that recommendations from friends align with
users’ interests, showcasing interactions driven by personal preferences.
Conversely, the yellow points signify a negative effect of social influence
embeddings, indicating recommendations from friends that diverge from users’
interests and reflect interactions influenced by herd mentality.

##  5 Conclusion and Future Work

In this paper, we propose a causal disentanglement-based framework for
regulating social influence bias in social recommendation, named CDRSB. First,
due to the existence of the social network confounder, there are two paths
between user and item embeddings and user-item ratings in social
recommendations: a non-causal social influence path and a causal interest
path. Therefore, we propose a disentangled encoder that decomposes user and
item embeddings into interest and social influence embeddings. We leverage
mutual information minimization techniques to ensure the independence of these
two components from each other. Next, we present a regulatory decoder to
regulate social influence bias and integrate interest and social influence
embeddings into more accurate user and item representations. Experimental
results on four datasets Ciao, Epinions, Dianping, and Douban book demonstrate
the effectiveness of our proposed model CDRSB and its various components.

In the future, we plan to explore the following three directions. Firstly, we
will investigate other effective disentanglement methods that can enhance the
separation of user preferences and social influence bias. Secondly, we aim to
incorporate additional side information, such as user search data or review
texts, to assist in decomposing true preferences and social influence more
accurately. Additionally, we intend to further disentangle users’ interests
into finer-grained factors, such as clothing color, style, and price.

CRediT authorship contribution statement

Li Wang: Conceptualization, Investigation, Methodology, Software, Writing -
original draft, Writing - review & editing. Min Xu: Supervision, Writing -
review & editing. Quangui Zhang: Writing - review & editing. Yunxiao Shi: Data
curation. Qiang Wu: Supervision, Writing - review & editing.

## References

  * [1] W. Fan, Q. Li, M. Cheng, Deep modeling of social relations for recommendation, in: Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 32, 2018.
  * [2] L. Wu, P. Sun, Y. Fu, R. Hong, X. Wang, M. Wang, A neural influence diffusion model for social recommendation, in: Proceedings of the 42nd international ACM SIGIR conference on research and development in information retrieval, 2019, pp. 235–244.
  * [3] P. Zhu, D. Cheng, S. Luo, F. Yang, Y. Luo, W. Qian, A. Zhou, Si-news: Integrating social information for news recommendation with attention-based graph convolutional network, Neurocomputing 494 (2022) 33–42.
  * [4] M. Jamali, M. Ester, A matrix factorization technique with trust propagation for recommendation in social networks, in: Proceedings of the fourth ACM conference on Recommender systems, 2010, pp. 135–142.
  * [5] W. Fan, Y. Ma, Q. Li, Y. He, E. Zhao, J. Tang, D. Yin, Graph neural networks for social recommendation, in: The world wide web conference, 2019, pp. 417–426.
  * [6] P. Sheth, R. Guo, L. Cheng, H. Liu, K. S. Candan, Causal disentanglement for implicit recommendations with network information, ACM Transactions on Knowledge Discovery from Data 17 (7) (2023) 1–18.
  * [7] Q. Li, X. Wang, Z. Wang, G. Xu, Be causal: De-biasing social network confounding in recommendation, ACM Transactions on Knowledge Discovery from Data 17 (1) (2023) 1–23.
  * [8] P. Sheth, R. Guo, K. Ding, L. Cheng, K. S. Candan, H. Liu, Causal disentanglement with network information for debiased recommendations, in: International Conference on Similarity Search and Applications, Springer, 2022, pp. 265–273.
  * [9] J. Pearl, et al., Models, reasoning and inference, Cambridge, UK: CambridgeUniversityPress 19 (2) (2000) 3.
  * [10] H. Ma, H. Yang, M. R. Lyu, I. King, Sorec: social recommendation using probabilistic matrix factorization, in: Proceedings of the 17th ACM conference on Information and knowledge management, 2008, pp. 931–940.
  * [11] X. Wang, W. Pan, C. Xu, Hgmf: Hierarchical group matrix factorization for collaborative recommendation, in: Proceedings of the 23rd ACM International Conference on Conference on Information and Knowledge Management, 2014, pp. 769–778.
  * [12] J. Chen, C. Wang, S. Zhou, Q. Shi, Y. Feng, C. Chen, Samwalker: Social recommendation with informative sampling strategy, in: The World Wide Web Conference, 2019, pp. 228–239.
  * [13] H. Ma, D. Zhou, C. Liu, M. R. Lyu, I. King, Recommender systems with social regularization, in: Proceedings of the fourth ACM international conference on Web search and data mining, 2011, pp. 287–296.
  * [14] L. Yang, Z. Liu, Y. Dou, J. Ma, P. S. Yu, Consisrec: Enhancing gnn for social recommendation via consistent neighbor aggregation, in: Proceedings of the 44th international ACM SIGIR conference on Research and development in information retrieval, 2021, pp. 2141–2145.
  * [15] L. Wu, J. Li, P. Sun, R. Hong, Y. Ge, M. Wang, Diffnet++: A neural influence and interest diffusion network for social recommendation, IEEE Transactions on Knowledge and Data Engineering 34 (10) (2020) 4753–4766.
  * [16] X. Wang, H. Chen, S. Tang, Z. Wu, W. Zhu, Disentangled representation learning, arXiv preprint arXiv:2211.11695 (2022).
  * [17] J. Wu, X. Li, X. Ao, Y. Meng, F. Wu, J. Li, Improving robustness and generality of nlp models using disentangled representations, arXiv preprint arXiv:2009.09587 (2020).
  * [18] J. Ma, C. Zhou, P. Cui, H. Yang, W. Zhu, Learning disentangled representations for recommendation, Advances in neural information processing systems 32 (2019).
  * [19] C. P. Burgess, I. Higgins, A. Pal, L. Matthey, N. Watters, G. Desjardins, A. Lerchner, Understanding disentangling in $\beta$-vae (2018).  arXiv:1804.03599.
  * [20] D. Bouchacourt, R. Tomioka, S. Nowozin, Multi-level variational autoencoder: Learning disentangled representations from grouped observations, in: Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 32, 2018.
  * [21] X. Wang, H. Jin, A. Zhang, X. He, T. Xu, T.-S. Chua, Disentangled graph collaborative filtering, in: Proceedings of the 43rd international ACM SIGIR conference on research and development in information retrieval, 2020, pp. 1001–1010.
  * [22] Y. Wang, S. Tang, Y. Lei, W. Song, S. Wang, M. Zhang, Disenhan: Disentangled heterogeneous graph attention network for recommendation, in: Proceedings of the 29th ACM international conference on information & knowledge management, 2020, pp. 1605–1614.
  * [23] A. Li, Z. Cheng, F. Liu, Z. Gao, W. Guan, Y. Peng, Disentangled graph neural networks for session-based recommendation, IEEE Transactions on Knowledge and Data Engineering (2022).
  * [24] Y. Zheng, C. Gao, X. Li, X. He, Y. Li, D. Jin, Disentangling user interest and conformity for recommendation with causal embedding, in: Proceedings of the Web Conference 2021, 2021, pp. 2980–2991.
  * [25] D. Liu, P. Cheng, H. Zhu, Z. Dong, X. He, W. Pan, Z. Ming, Mitigating confounding bias in recommendation via information bottleneck, in: Proceedings of the 15th ACM Conference on Recommender Systems, 2021, pp. 351–360.
  * [26] Z. Si, X. Han, X. Zhang, J. Xu, Y. Yin, Y. Song, J.-R. Wen, A model-agnostic causal learning framework for recommendation using search data, in: Proceedings of the ACM Web Conference 2022, 2022, pp. 224–233.
  * [27] C. Gao, Y. Zheng, W. Wang, F. Feng, X. He, Y. Li, Causal inference in recommender systems: A survey and future directions, arXiv preprint arXiv:2208.12397 (2022).
  * [28] W. Zhang, W. Bao, X.-Y. Liu, K. Yang, Q. Lin, H. Wen, R. Ramezani, Large-scale causal approaches to debiasing post-click conversion rate estimation with multi-task learning, in: Proceedings of The Web Conference 2020, 2020, pp. 2775–2781.
  * [29] X. He, Y. Zhang, F. Feng, C. Song, L. Yi, G. Ling, Y. Zhang, Addressing confounding feature issue for causal recommendation, ACM Transactions on Information Systems 41 (3) (2023) 1–23.
  * [30] W. Wang, F. Feng, X. He, X. Wang, T.-S. Chua, Deconfounded recommendation for alleviating bias amplification, in: Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, 2021, pp. 1717–1725.
  * [31] S. Xu, J. Tan, S. Heinecke, V. J. Li, Y. Zhang, Deconfounded causal collaborative filtering, ACM Transactions on Recommender Systems 1 (4) (2023) 1–25.
  * [32] X. Zhu, Y. Zhang, F. Feng, X. Yang, D. Wang, X. He, Mitigating hidden confounding effects for causal recommendation, arXiv preprint arXiv:2205.07499 (2022).
  * [33] T. Wei, F. Feng, J. Chen, Z. Wu, J. Yi, X. He, Model-agnostic counterfactual reasoning for eliminating popularity bias in recommender system, in: Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, 2021, pp. 1791–1800.
  * [34] M. He, C. Li, X. Hu, X. Chen, J. Wang, Mitigating popularity bias in recommendation via counterfactual inference, in: International Conference on Database Systems for Advanced Applications, Springer, 2022, pp. 377–388.
  * [35] J. Chen, H. Dong, Y. Qiu, X. He, X. Xin, L. Chen, G. Lin, K. Yang, Autodebias: Learning to debias for recommendation, in: Proceedings of the 44th International ACM SIGIR Conference on Research and Development in Information Retrieval, 2021, pp. 21–30.
  * [36] J. Chen, H. Dong, X. Wang, F. Feng, M. Wang, X. He, Bias and debias in recommender system: A survey and future directions, ACM Transactions on Information Systems 41 (3) (2023) 1–39.
  * [37] P. Cheng, W. Hao, S. Dai, J. Liu, Z. Gan, L. Carin, Club: A contrastive log-ratio upper bound of mutual information, in: International conference on machine learning, PMLR, 2020, pp. 1779–1788.
  * [38] H. Li, D. Wu, W. Tang, N. Mamoulis, Overlapping community regularization for rating prediction in social recommender systems, in: Proceedings of the 9th ACM Conference on Recommender Systems, 2015, pp. 27–34.
  * [39] H. Wang, N. Wang, D.-Y. Yeung, Collaborative deep learning for recommender systems, in: Proceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining, 2015, pp. 1235–1244.
  * [40] A. Mnih, R. R. Salakhutdinov, Probabilistic matrix factorization, Advances in neural information processing systems 20 (2007).
  * [41] X. He, L. Liao, H. Zhang, L. Nie, X. Hu, T.-S. Chua, Neural collaborative filtering, in: Proceedings of the 26th international conference on world wide web, 2017, pp. 173–182.
  * [42] X. He, K. Deng, X. Wang, Y. Li, Y. Zhang, M. Wang, Lightgcn: Simplifying and powering graph convolution network for recommendation, in: Proceedings of the 43rd International ACM SIGIR conference on research and development in Information Retrieval, 2020, pp. 639–648.
  * [43] D. Liang, L. Charlin, D. M. Blei, Causal inference for recommendation, in: Causation: Foundation to Application, Workshop at UAI. AUAI, 2016.
  * [44] S. Bonner, F. Vasile, Causal embeddings for recommendation, in: Proceedings of the 12th ACM conference on recommender systems, 2018, pp. 104–112.
  * [45] L. Van der Maaten, G. Hinton, Visualizing data using t-sne., Journal of machine learning research 9 (11) (2008).