Causal Structure Learning with Recommendation System

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Shuyuan Xu†, Da Xu‡, Evren Korpeoglu‡, Sushant Kumar‡

Stephen Guo§, Kannan Achan‡, Yongfeng Zhang†

†Rutgers University ‡Walmart Labs §Indeed

shuyuan.xu@rutgers.edu,{da.xu,EKorpeoglu,Sushant.Kumar}@walmart.com

sguo@indeed.com,kannan.achan@walmart.com,yongfeng.zhang@rutgers.edu

ABSTRACT

A fundamental challenge of recommendation systems (RS) is under-

standing the causal dynamics underlying users’ decision making.

Most existing literature addresses this problem by using causal

structures inferred from domain knowledge. However, there are

numerous phenomenons where domain knowledge is insucient,

and the causal mechanisms must be learnt from the feedback data.

Discovering the causal mechanism from RS feedback data is both

novel and challenging, since RS itself is a source of intervention

that can inuence both the users’ exposure and their willingness

to interact. Also for this reason, most existing solutions become

inappropriate since they require data collected free from any RS.

In this paper, we rst formulate the underlying causal mechanism

as a causal structural model and describe a general causal structure

learning framework grounded in the real-world working mecha-

nism of RS. The essence of our approach is to acknowledge the

unknown nature of RS intervention. We then derive the learning ob-

jective from our framework and propose an augmented Lagrangian

solver for ecient optimization. We conduct both simulation and

real-world experiments to demonstrate how our approach com-

pares favorably to existing solutions, together with the empirical

analysis from sensitivity and ablation studies.

KEYWORDS

Recommender Systems, Causal Discovery, Explainability, Graphical

Model, Structural Equation, Unknown Intervention

1 INTRODUCTION

In recent years, there has been growing interest in understanding

how the actions taken by a recommendation system (RS) can in-

duce changes to the subsequent feedback data. This type of causal

reasoning is critical to the explainability, fairness, and transparency

of RS. In contrast to machine learning who primarily focuses on

data-driven problem solving, causal discovery investigates into the

data generating mechanism and tries to understand how the ob-

servations are formed. Therefore, depending on the question of

interest, the fact that RS itself can interfere with the users’ feedback

can be both troublesome and useful.

For example, most machine learning model assumes that the col-

lected data is generated by a static distribution. However, making

a recommendation is likely to intervene with the user’s decision

making, thus changing the potential feedback [

]. Also, notice that

RS interventions are often systematic, meaning they are designed

by developers in specic patterns rather than being purely ran-

dom, which is very dierent from ordinary statistical uctuations

[

]. Therefore, when it comes to machine learning and evaluation,

those interventions will cause various types of bias, and a great

deal of literature has been devoted to addressing such issues [

On the other hand, discovering causal relationships can benet sig-

nicantly from systematic interventions. The reason is that when

an intervention takes place during the data-generation process, the

systematic changes it causes provides an opportunity for us to track

down the underlying cause-eect mechanisms.

To our knowledge, discovering causal mechanisms with RS has

rarely been studied previously due to various challenges. Most ex-

isting solutions cannot handle unknown interventions made by

RS that are unrelated to causal discovery. Consequently, the RS

community relies primarily on causal mechanism inferred from

domain knowledge [

], but they often lack the coverage, ver-

satility, and ability to explain many phenomenons of interest. With

causal inference emerging as a key instrument for many RS studies

and applications, it becomes imperative to learn the desired causal

mechanism from RS feedback data.

However, unlike other scientic elds (such as clinical trials, etc.)

where interventions are purposefully made to elucidate the causal

mechanisms of interest [

], the interventions made by RS are pri-

marily designed to increase the users’ engagement and revenue.

Worse yet, we may not even be able to tell whether a recommenda-

tion has indeed changed the users’ decision making, which means

the intervention from RS is of an unknown nature. As a result,

with the existing solutions, it is nearly impossible to identify the

underlying causal mechanisms using RS feedback data alone.

An important observation that makes causal discovery possible,

even with unknown intervention, is that an eect given its causes

remains invariant to changes in the mechanism that generates the

causes [

]. It implies that while the recommendation made by

RS can interfere with what causes a user to give the feedback, the

causal mechanism behind the user’s decision making is unaltered

regardless of the interference. The opposite statement is not true,

that the occurrence of a cause given the eect will not be invariant

under outside interference. As we discuss later, this critical asym-

metry can help us identify the cause-eect relationship in the RS

feedback data.

Rather than making unrealistic assumptions to consolidate the

unknown interventions of RS, we propose a novel modelling tech-

nique through a mixture of competing mechanisms. The high-level

intuition is similar to that of the classical mixture of distributions

[32], but we make two signicant progress:

(1)

the expectations are now taken with respect to an

expert

–

which is a stochastic indicator function – that judges the winner

of the competing mechanisms, namely, the recommendation

mechanisms and the causal mechanism;

arXiv:2210.10256v1 [cs.IR] 19 Oct 2022

Conference’17, July 2017, Washington, DC, USA Shuyuan Xu et al.

(2)

rather than using the traditional expectation-maximization (EM)

optimization which is dicult to adapt to the mixture mech-

anism setting, we propose using the more advanced

Gumbel

reparameterization

approach [

] to address the gradient-

over-expectation challenge.

We present the underlying causal mechanism as a structural causal

model (SCM), which consists of a set of structural equations and the

associated causal graph, representing by a directed acyclic graph

(DAG). We also leverage the recent advances in learning DAG

[

], and apply their continuous DAG constraint to our mixture-of-

mechanism learning object. We then integrate the above compo-

nents and techniques with the augmented Lagrangian solver [

]

that scales easily to causal mechanisms with hundreds of variables,

whereas most existing solutions handle only dozens of variables.

In Section 2, we rst develop a comprehensive view regarding

how feedback data is generated under the intervention of RS and

the causal mechanism of interest. We also provide the necessary

background and relevant work in this section. Then in Section 3,

we further expand on the challenges and solutions of unknown RS

interventions, and present the likelihood function (of users’ decision

making) as a mixture of competing mechanisms. We present the

complete causal structure learning procedure in Section 4, including

the optimization algorithm.

We examine the proposed causal structure learning approach

through both large-scale real-world RS datasets and simulation

studies. In addition to examining the learnt causal structures, we

also experiment on how causal structure learning can lead directly

to improved recommendations. In the simulation, we reveal the

accuracy of the proposed approach in recovering the ground truth

causal mechanisms compared with the existing causal discovery

solutions. We summarize our contributions as follow:

•

we describe a comprehensive causal structure learning frame-

work under unknown RS intervention;

•

we propose a principled causal structure learning solution via the

mixture of competing mechanisms, and develop an ecient opti-

mization procedure using reparameterization and the augmented

Lagrangian method;

•

the proposed approach is examined thoroughly via both real-data

experiments and simulation studies.

2 PRELIMINARIES AND RELATED WORK

We briey introduce the data generating mechanism of RS, and the

background of causal structure learning. We also discuss how our

work connects to a wide spectrum of recent literature in information

retrieval, causal inference, and machine learning.

2.1 Feedback generation under RS

Feedback data of RS are often generated as a result of interventions

made by the RS. This statement applies to a wide range of RS set-

tings where users are exposed to specic contents (e.g. product,

video, news, ads) made available by the historical or current RS

more general implicit feedback setting where the users’ response

does not suggest the degree of relevance, but is simply an indica-

tor of active interaction. It will be apparent that our development

extends directly to explicit feedback.

Figure 1: A simple illustration of how implicit feedback (click) is

generated considering the impact of both the RS and the indepen-

dent (causal) mechanism that underlies the user intent.

There is no doubt that users’ decision making is a highly complex

process resulting from the interaction of passive exposure and

active human reasoning. We refer to this intrinsic interaction as

user intent

. We also use the notion of

mechanism

to refer to

those modular, usable, and broadly applicable human intelligence

for reasoning [

], and being independent means they do not inform

or inuence each other. For instance, the complementariness of

Cable

is an independent mechanism since they are designed

in such way by human intelligence.

We illustrate in Figure 1 the interactive process of exposure,

independent mechanism, user intent that eventually leads to the

generation of user feedback. We mention that the existence of an

arrow in Figure 1 only suggests the possibility to make an inu-

ence. A critical implication from Figure 1 is that an interaction can

be caused via multiple pathways. It means the exposure and the

underlying independent mechanism may or may not have changed

the user intent, and we are not able to tell the dierence. As we

discuss later, the essence of our approach is not assuming a path-

way dominating the data generation process, which preserves the

unknown nature of RS interventions.

2.2 Characterizing causality and intervention

Recent causal inference literature has established rigorously con-

nection from independent mechanism to causality [

]. The

structural causal model, which consists of a joint distribution (can

be further factorized into a set of structural equations) and the as-

sociated directed acyclic graph (DAG), is often used to characterize

the causal relationships among variables [

]. In particular, the

model is dened by a distribution

𝑃𝑋

over the random variables

𝑋1, . . . , 𝑋𝑑

, and its factorization corresponds to the patterns of the

DAG. Each node in the DAG corresponds to a random variables

and each edge represents a direct causal relation. Given a DAG

under which the joint distribution 𝑃𝑋is Markovian, it holds:

𝑝𝑋(𝑥1, . . . , 𝑥𝑑)=

𝑑

𝑗=1

𝑝𝑗𝑥𝑗PaG(𝑥𝑗),(1)

where

PaG(𝑥𝑗)

is the set of parent node of

𝑥𝑗

according to

, and

the conditionals

𝑝𝑗, 𝑗 =

, . . . , 𝑑

can be thought of as independent

mechanisms that generate

𝑥𝑗

from its parents. In Figure 2, We show

an example of a structural causal model for the

product type

relationships among some electronics. The (weighted) adjacency

matrix of Gis denoted by 𝐴G∈R𝑑×𝑑

Structural causal model provides us a framework to understand

how the system responds to interventions – the systematic changes

that are being made to the target distribution [

]. Following the

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CausalStructureLearningwithRecommendationSystemShuyuanXu†,DaXu‡,EvrenKorpeoglu‡,SushantKumar‡StephenGuo§,KannanAchan‡,YongfengZhang††RutgersUniversity‡WalmartLabs§Indeedshuyuan.xu@rutgers.edu,{da.xu,EKorpeoglu,Sushant.Kumar}@walmart.comsguo@indeed.com,kannan.achan@walmart.com,yongfeng.zhang@rutgers....

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Causal Structure Learning with Recommendation System

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