Equal Experience in Recommender Systems Jaewoong Cho1 Moonseok Choi2Changho Suh2 Abstract

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Equal Experience in Recommender Systems

Jaewoong Cho 1 * Moonseok Choi 2Changho Suh 2

Abstract

We explore the fairness issue that arises in rec-

ommender systems. Biased data due to inher-

ent stereotypes of particular groups (e.g., male

students’ average rating on mathematics is often

higher than that on humanities, and vice versa

for females) may yield a limited scope of sug-

gested items to a certain group of users. Our main

contribution lies in the introduction of a novel

fairness notion (that we call equal experience),

which can serve to regulate such unfairness in

the presence of biased data. The notion captures

the degree of the equal experience of item recom-

mendations across distinct groups. We propose

an optimization framework that incorporates the

fairness notion as a regularization term, as well

as introduce computationally-efﬁcient algorithms

that solve the optimization. Experiments on syn-

thetic and benchmark real datasets demonstrate

that the proposed framework can indeed mitigate

such unfairness while exhibiting a minor degrada-

tion of recommendation accuracy.

1. Introduction

Recommender systems are everywhere, playing a crucial

role to support decision making and to decide what we ex-

perience in our daily life. One recent challenge concerning

fairness arises when the systems are built upon biased his-

torical data. Biased data due to polarized preferences of

particular groups for certain items may often yield limited

recommendation service. For instance, if female students

exhibit high ratings on literature subjects and less interest

in math and science relative to males, the subject recom-

mender system trained based on such data may provide a

narrow scope of recommended subjects to the female group,

thereby yielding unequal experience. This unequal experi-

ence across groups may result in amplifying the gender gap

issue in science, technology, engineering, and mathematics

KRAFTON Inc., Seoul, Korea

KAIST, Daejeon, Korea. Cor-

respondence to: Changho Suh <chsuh@kaist.ac.kr>.

*This work was done when Jaewoong Cho was with KAIST as a

PhD candidate.

(STEM) ﬁelds.

Among various works for fair recommender systems (Yao

& Huang,2017;Li et al.,2021;Kamishima & Akaho,2017;

Xiao et al.,2017;Beutel et al.,2019;Burke,2017), one

recent and most relevant work is (Yao & Huang,2017).

They focus on a scenario in which unfairness occurs mainly

due to distinct recommendation accuracies across different

groups. They propose novel fairness measures that quantify

the degree of such unfairness via the difference between rec-

ommendation accuracies, and also develop an optimization

framework that well trades the fairness measures against

the average accuracy. However, it comes with a challenge

in ensuring fairness w.r.t. the unequal experience. This is

because similar accuracy performances between different

groups do not guarantee a variety of recommendations to

an underrepresented group with historical data bearing low

preferences and/or scarce ratings for certain items. For in-

stance, in the subject recommendation, the fairness notion

may not serve properly, as long as female students exhibit

low ratings (and/or lack of ratings) on math and science

subjects due to societal/cultural inﬂuences (and/or sampling

biases). Furthermore, if the recommended items are selected

only according to the overall preference, the biased pref-

erence for a speciﬁc item group will further increase, and

the exposure to the unpreferred item group will gradually

decrease.

Contribution:

In an effort to address the challenge, we

introduce a new fairness notion that we call equal experi-

ence. At a high level, the notion represents how equally

various items are suggested even for an underrepresented

group preserving such biased historical data. Inspired by an

information-theoretic notion “mutual information” (Cover,

1999) and its key property “chain rule”, we quantify our

notion so as to control the level of independence between

preference predictions and items for any group of users.

Speciﬁcally, the notion encourages prediction

(e.g., 1 if

a user prefers an item; 0 otherwise) to be independent of

the following two: (i) user group

Zuser

(e.g., 0 for male;

and 1 for female); and (ii) item group

Zitem

(e.g., 0 for

mathematics; and 1 for literature). In other words, it pro-

motes

Y⊥(Zuser, Zitem)

; which in turns ensures all of

the following four types of independence that one can

think of:

Y⊥Zitem

Y⊥Zuser

Y⊥Zitem|Zuser

, and

Y⊥Zuser|Zitem

. This is inspired by the fact that mutual

arXiv:2210.05936v1 [cs.LG] 12 Oct 2022

Equal Experience in Recommender Systems

information being zero is equivalent to the independence

between associated random variables, as well as the chain

rule:

I(e

Y;Zuser, Zitem) = I(e

Y;Zitem) + I(e

Y;Zuser|Zitem)

=I(e

Y;Zuser) + I(e

Y;Zitem|Zuser).

(1)

See Section 3.1 for details. The higher independence, the

more diverse recommendation services are offered for every

group. We also develop an optimization framework that

incorporates the quantiﬁed notion as a regularization term

into a conventional optimization in recommender systems

(e.g., the one based on matrix completion (Koren,2008;

Koren et al.,2009)). Here one noticeable feature of our

framework is that the fairness performances w.r.t. the above

four types of independence conditions can be gracefully

controlled via a single uniﬁed regularization term. This is

in stark contrast to prior works (Yao & Huang,2017;Li

et al.,2021;Kamishima & Akaho,2017;Mehrotra et al.,

2018), each of which promotes only one independence con-

dition or two via two separate regularization terms. See

below

Related works

for details. In order to enable an

efﬁcient implementation of the fairness constraint, we em-

ploy recent methodologies developed in the context of fair

classiﬁers, such as the ones building upon kernel density

estimation (Cho et al.,2020a), mutual information (Zhang

et al.,2018;Kamishima et al.,2012;Cho et al.,2020b), or

covariance (Zafar et al.,2017a;b). We also conduct exten-

sive experiments both on synthetic and two benchmark real

datasets: MovieLens 1M (Harper & Konstan,2015) and

Last FM 360K (Celma,2010). As a result, we ﬁrst identify

two primary sources of biases that incur unequal experi-

ence: population imbalance and observation bias (Yao &

Huang,2017). In addition, we demonstrate that our fairness

notion can help improve the fairness measure w.r.t. equal

experience (to be deﬁned in Section 3.1; see Deﬁnition 3.2)

while exhibiting a small degradation of recommendation

accuracy. Furthermore, we provide an extension of our fair-

ness notion to the context of top-

recommendation from

an end-ranked list. We also demonstrate the effectiveness of

the proposed framework in top-

recommendation setting.

Related works:

In addition to (Yao & Huang,2017), nu-

merous fairness notions and algorithms have been proposed

for fair recommender systems (Xiao et al.,2017;Beutel

et al.,2019;Singh & Joachims,2018;Zehlike et al.,2017;

Narasimhan et al.,2020;Biega et al.,2018;Li et al.,2021;

Kamishima & Akaho,2017;Mehrotra et al.,2018;Schnabel

et al.,2016). (Xiao et al.,2017) develop fairness notions

that encourage similar recommendations for users within

the same group. (Beutel et al.,2019) consider similar met-

rics as that in (Yao & Huang,2017) yet in the context of

pairwise recommender systems wherein pairewise prefer-

ences are given as training data. (Li et al.,2021) propose

a fairness measure that quantiﬁes the irrelevancy of pref-

erence predictions to user groups, like demographic par-

ity in the fairness literature (Feldman et al.,2015;Zafar

et al.,2017a;b). Speciﬁcally, they consider the indepen-

dence condition between prediction

and user group

Zuser

Y⊥Zuser

. Actually this was also considered as another

fairness measure in (Yao & Huang,2017). Similarly, other

works with a different direction consider the similar no-

tion concerning the independence w.r.t. item group

Zitem

Y⊥Zitem

(Kamishima & Akaho,2017;Singh & Joachims,

2018;Biega et al.,2018). (Mehrotra et al.,2018) incorporate

both measures to formulate a multi-objective optimization.

In Section 2.2, we will elaborate on why the above prior

fairness notions cannot fully address the challenge w.r.t.

unequal experience.

There has been a proliferation of fairness notions in the

context of fair classiﬁers: (i) group fairness (Feldman et al.,

2015;Zafar et al.,2017b;Hardt et al.,2016;Woodworth

et al.,2017); (ii) individual fairness (Dwork et al.,2012;

Garg et al.,2018); (iii) causality-based fairness (Kusner

et al.,2017;Nabi & Shpitser,2018;Russell et al.,2017;Wu

et al.,2019;Zhang & Bareinboim,2018b;a). Among various

prominent group fairness notions, demographic parity and

equalized odds give an inspiration to our work in the process

of applying the chain rule, reﬂected in

(1)

. Concurrently,

a multitude of fairness algorithms have been developed

with the use of covariance (Zafar et al.,2017a;b), mutual

information (Zhang et al.,2018;Kamishima et al.,2012;

Cho et al.,2020b), kernel density estimation (Cho et al.,

2020a) or R

enyi correlation (Mary et al.,2019) to name a

few. In this work, we also demonstrate that our proposed

framework (to be presented in Section 3) embraces many of

these approaches; See Remark 3.4 for details.

2. Problem Formulation

As a key technique for operating recommender systems, we

consider collaborative ﬁltering which estimates user ratings

on items. We ﬁrst formulate an optimization problem build-

ing upon one prominent approach, matrix completion. We

then introduce a couple of fairness measures proposed by

recent prior works (Yao & Huang,2017;Li et al.,2021;

Kamishima & Akaho,2017), and present an extended opti-

mization framework that incorporates the fairness measures

as regularization terms.

2.1. Optimization based on matrix completion

As a well-known approach for operating recommender sys-

tems, we consider matrix completion (Fazel,2002;Koren

et al.,2009;Cand

es & Recht,2009). Let

M∈Rn×m

the ground-truth rating matrix where

and

denote the

number of users and items respectively. Each entry, denoted

Mij

, can be of any type. It could be binary, ﬁve-star

Equal Experience in Recommender Systems

rating, or any real number. Denote by

Ω

the set of observed

entries of

. For simplicity, we assume noiseless obser-

vation. Denote by

M∈Rn×m

an estimate of the rating

matrix.

Matrix completion can be done via the rank minimization

that exploits the low-rank structure of the rating matrix.

However, since the problem is NP-hard (Fazel,2002), we

consider a well-known relaxation approach that intends to

minimize instead the squared error between

and

the observed entries:

min

(i,j)∈Ω

(Mij −c

Mij )2.(2)

There are two well-known approaches for solving the opti-

mization in

(2)

: (i) matrix factorization (Abadir & Magnus,

2005;Koren et al.,2009); and (ii) neural-net-based parame-

terization (Salakhutdinov et al.,2007;Sedhain et al.,2015;

He et al.,2017). Matrix factorization assumes a certain struc-

ture on the rating matrix:

M=LR

where

L∈Rn×r

and

R∈Rr×m

. One natural way to search for optimal

L∗

and

R∗

is to apply gradient descent (Robbins & Monro,1951)

w.r.t. all of the

Lij

’s and

Rij

’s, although it does not ensure

the convergence of the optimal point due to non-convexity.

The second approach is to parameterize

via neural net-

works such as restricted Boltzmann machine (Salakhutdinov

et al.,2007) and autoencoder (Sedhain et al.,2015;Lee et al.,

2018). For instance, one may employ an autoencoder-type

neural network which outputs a completed matrix

fed

by the partially-observed version of

. For a user-based

autoencoder (Sedhain et al.,2015), an observed row vec-

tor of

is fed into the autoencoder, while an observed

column vector serves as an input for an item-based autoen-

coder (Sedhain et al.,2015). In this work, we consider the

two approaches in our experiments: matrix factorization

with gradient descent; and autoencoder-based parameteriza-

tion.

One common way to promote a fair recommender system is

to incorporate a fairness measure, say

Lfair

(which we will

relate to an estimated matrix

), as a regularization term

into the above base optimization in (2):

min

(1 −λ)X

(i,j)∈Ω

(Mij −c

Mij )2+λ· Lfair (3)

where

λ∈[0,1]

denotes a normalized regularization factor

that balances prediction accuracy against the fairness con-

straint. For the fairness-regularization term

Lfair

, several

fairness measures have been introduced.

2.2. Fairness measures in prior works (Yao & Huang,

2017;Kamishima & Akaho,2017;Li et al.,2021)

We list three of them, which are mostly relevant to our frame-

work to be presented in Section 3. For illustrative purpose,

we will explain them in a simple setting where there are two

groups of users, say the male group

and the female group

. The ﬁrst is value unfairness proposed by (Yao & Huang,

2017). It quantiﬁes the difference between prediction errors

across the two groups of users over the entire items:

VAL := 1

j=1 

|MΩ|X

(i,j)∈Ω:i∈M

(Mij −c

Mij )

| {z }

prediction error w.r.t. M

−1

|FΩ|X

(i,j)∈Ω:i∈F

(Mij −c

Mij )

| {z }

prediction error w.r.t. F



(4)

where

MΩ

and

FΩ

denote the male and female group w.r.t.

observed entries, respectively. While the measure promotes

fairness w.r.t. prediction accuracy across distinct groups,

it may not ensure fairness w.r.t. the diversity of recom-

mended items to users. To see this clearly, consider an

extreme scenario in which the ground truth rating is very

small

Mij∗≈0

for a certain item

j∗

(say science subject)

for all

i∈ F

. In this case, minimizing VAL may encourage

Mij∗≈0

for all

i∈ F

. This then incurs almost no recom-

mendation of the science subject to the females, thus giving

no opportunity to experience the subject. This motivates

us to propose a new fairness measure (to be presented in

Section 3.1) that helps mitigate such unfairness.

On the other hand, (Kamishima & Akaho,2017) introduce

another fairness measure, which bears a similar spirit to

demographic parity in the fairness literature (Feldman et al.,

2015;Zafar et al.,2017a;b). The measure, named Calders

and Verwer’s discrimination score (

CVS

), quantiﬁes the

level of irrelevancy between preference predictions and item

groups. To describe it in detail, let us introduce some nota-

tions. Let

Zitem

be a sensitive attribute w.r.t. item groups,

e.g.,

Zitem = 0

(literature) and

Zitem = 1

(science). Let

be a generic random variable w.r.t. estimated ratings

Mij

’s.

To capture the preference prediction, let us consider a simple

binary preference setting in which

Y:= 1{b

Y≥τ}

where

indicates a certain threshold. Specializing the measure

into the one like demographic parity, it can be quantiﬁed

as:

CVS := |P(e

Y= 1|Zitem = 1) −P(e

Y= 1|Zitem = 0)|.(5)

Minimizing the measure encourages the independence be-

tween

and

Zitem

, thereby promoting the same rating statis-

tics across different groups. However, it does not necessarily

ensure the same statistics when we focus on a certain group

of users. It guarantees the independence only in the average

sense. To see this clearly, consider a simple scenario in

which there are two groups of users, say female and male.

Let

Zuser

be another sensitive attribute w.r.t. user groups,

Equal Experience in Recommender Systems

111000

000111

Figure 1.

An example in which

Y⊥Zitem

but

Y6⊥ Zitem|Zuser

Here

Y:= 1{

Y≥τ}

;

is a generic random variable w.r.t.

estimated ratings

Mij

’s; and

indicates a certain threshold. The

(i, j)

entry of an estimated preference matrix with 6 users (row)

and 6 items (column) indicates 1{

Mij ≥τ}.

e.g.,

Zuser = 0

(female) and

Zuser = 1

(male). Fig. 1il-

lustrates a concrete example where

is independent of

Zitem.

Notice that the number of 1’s w.r.t.

Zitem = 0

(over the

entire user groups) is the same as that w.r.t.

Zitem = 1

However, focusing on a certain user group, say

Zuser =

is highly correlated with

Zitem

. Observe in the case

Zuser = 0

that the number of 1’s is 9 for

Zitem = 0

, while it

reads 0 for Zitem = 1.

(Li et al.,2021) consider a similar measure, named user-

oriented group fairness (

UGF

), yet which targets the inde-

pendence w.r.t. user groups. Similar to

CVS

, we can deﬁne

it by replacing Zitem with Zuser in (5):

UGF := |P(e

Y= 1|Zuser = 1) −P(e

Y= 1|Zuser = 0)|.(6)

However, by symmetry, the high correlation issue discussed

via Fig. 1still arises.

3. Proposed Framework

We ﬁrst propose new fairness measures that can regulate

fairness w.r.t. the opportunity to experience inherently-low

preference items, as well as address the high correlation

issue discussed as above. We then develop an integrated

optimization framework that uniﬁes the fairness measures as

a single regularization term. Finally we introduce concrete

methodologies that can implement the proposed optimiza-

tion.

3.1. New fairness measures

The common limitation of the prior fairness measures (Yao

& Huang,2017;Kamishima & Akaho,2017;Li et al.,2021)

is that the independence between preference predictions

and item groups may not be guaranteed for a certain group

of users. This motivates us to consider the conditional

independence as a new fairness notion, formally deﬁned as

below.

Deﬁnition 3.1

(Equalized Recommendation)

A recom-

mender system is said to respect “equalized recommen-

dation” if its prediction

is independent of item’s sen-

sitive attribute

Zitem

given user’s sensitive attribute

Zuser

Y⊥Zitem|Zuser.

Inspired by the quantiﬁcation methods w.r.t. equalized odds

in the fairness literature (Jiang et al.,2019;Donini et al.,

2018;Hardt et al.,2016;Woodworth et al.,2017), we quan-

tify the new notion via:

DER := X

z1∈Zuser X

z2∈Zitem P(e

Y= 1|Zuser =z1)

−P(e

Y= 1|Zitem =z2, Zuser =z1),

(7)

for arbitrary alphabet sizes

|Zuser|

and

|Zitem|

. Here

DER

stands for the difference w.r.t. two interested probabilities

that arise in equalized recommendation, and this naming

is similar to those in prior fairness metrics (Donini et al.,

2018;Jiang et al.,2019). It captures the degree of violating

equalized recommendation via the difference between the

conditional probability and its marginal given

Zuser

. No-

tice that the minimum

DER = 0

is achieved under “equal-

ized recommendation”. One may consider another measure

which takes “max” operation instead of “

” in

(7)

or a

different measure based on the ratio of the two associated

probabilities. We focus on

DER

(7)

for tractability of

an associated optimization problem that we will explain in

Section 3.2.

The constraint of “equalized recommendation” encourages

the same prediction statistics of items for every user group,

thereby promoting the equal chances of experiencing a vari-

ety of items for all individuals. However, the notion comes

with a limitation. The limitation comes from the fact that

conditional independence does not necessarily imply inde-

pendence (Cover,1999):

Y⊥Zitem|Zuser 6=⇒e

Y⊥Zitem.(8)

Actually, the ultimate goal of a fair recommender system is

to ensure all of the following four types of independence:

Y⊥Zitem,e

Y⊥Zuser|Zitem,

Y⊥Zuser,e

Y⊥Zitem|Zuser.(9)

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EqualExperienceinRecommenderSystemsJaewoongCho1*MoonseokChoi2ChanghoSuh2AbstractWeexplorethefairnessissuethatarisesinrec-ommendersystems.Biaseddataduetoinher-entstereotypesofparticulargroups(e.g.,malestudents'averageratingonmathematicsisoftenhigherthanthatonhumanities,andviceversaforfemales)mayyield...

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