Equal Experience in Recommender Systems

1 INTRODUCTION . Recommender systems are everywhere , playing a crucial role to support decision making and to decide what we experience in our daily life . One recent challenge concerning fairness arises when the systems are built upon biased historical 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 recommender system trained based on such data may provide a narrow scope of recommended subjects to the female group , thereby yielding unequal experience . This unequal experience across groups may result in amplifying the gender gap issue in science , technology , engineering , and mathematics ( 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 recommendation 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 instance , 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 preference 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 experience . 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 informationtheoretic 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 Ỹ ( 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 promotes Ỹ ⊥ ( Zuser , Zitem ) ; which in turns ensures all of the following four types of independence that one can think of : Ỹ ⊥ Zitem , Ỹ ⊥ Zuser , Ỹ ⊥ Zitem|Zuser , and Ỹ ⊥ Zuser|Zitem . This is inspired by the fact that mutual information being zero is equivalent to the independence between associated random variables , as well as the chain rule : I ( Ỹ ; Zuser , Zitem ) = I ( Ỹ ; Zitem ) + I ( Ỹ ; Zuser|Zitem ) = I ( Ỹ ; Zuser ) + I ( Ỹ ; 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 for collaborative filtering 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 condition 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 employ 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 extensive 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 experience : 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 2 ) while exhibiting a small degradation of recommendation accuracy . Related works : In addition to Yao & Huang ( 2017 ) , numerous 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 metrics as that in Yao & Huang ( 2017 ) yet in the context of pairwise recommender systems wherein pairewise preferences are given as training data . Li et al . ( 2021 ) propose a fairness measure that quantifies the irrelevancy of preference predictions to user groups , like demographic parity in the fairness literature ( Feldman et al. , 2015 ; Zafar et al. , 2017a ; b ) . Specifically , they consider the independence condition between prediction Ỹ and user group Zuser : Ỹ ⊥ Zuser . Actually this was also considered as another fairness measure in Yao & Huang ( 2017 ) . Similarly , other works with a different direction consider the similar notion concerning the independence w.r.t . item group Zitem : Ỹ ⊥ 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 can not 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 equation 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 Rényi 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 1 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 for collaborative filtering building 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 optimization framework that incorporates the fairness measures as regularization terms . 2.1 OPTIMIZATION BASED ON MATRIX COMPLETION . As a well-known approach for operating recommender systems , we consider matrix completion ( Fazel , 2002 ; Koren et al. , 2009 ; Candès & Recht , 2009 ) . Let M ∈ Rn×m be the ground-truth rating matrix where n and m denote the number of users and items respectively . Each entry , denoted by Mij , can be of any type . It could be binary , five-star rating , or any real number . Denote by Ω the set of observed entries of M . For simplicity , we assume noiseless observation . Denote by M̂ ∈ 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 M and M̂ in the observed entries : min M̂ ∑ ( i , j ) ∈Ω ( Mij − M̂ij ) 2 . ( 2 ) There are two well-known approaches for solving the optimization in equation 2 : ( i ) matrix factorization ( Abadir & Magnus , 2005 ; Koren et al. , 2009 ) ; and ( ii ) neural-net-based parameterization ( Salakhutdinov et al. , 2007 ; Sedhain et al. , 2015 ; He et al. , 2017 ) . Matrix factorization assumes a certain structure 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 M̂ via neural networks 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 M̂ fed by the partially-observed version of M . For a user-based autoencoder ( Sedhain et al. , 2015 ) , an observed row vector of M is fed into the autoencoder , while an observed column vector serves as an input for an item-based autoencoder ( Sedhain et al. , 2015 ) . In this work , we consider the two approaches in our experiments : matrix factorization with gradient descent ; and autoencoder-based parameterization . 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 M̂ ) , as a regularization term into the above base optimization in equation 2 : min M̂ ( 1− λ ) ∑ ( i , j ) ∈Ω ( Mij − M̂ij ) 2 + λ · Lfair ( 3 ) where λ ∈ [ 0 , 1 ] denotes a normalized regularization factor that balances prediction accuracy against the fairness constraint . For the fairness-regularization term Lfair , several fairness measures have been introduced .

Summary: The presented study argued that a fair recommendation should be independent of both user and item. Therefore, the study introduced a new fairness notion, i.e., equal experience, and further incorporated this fairness notion as a regularisation term in the matrix completion framework to construct a fair recommender system. The proposed method was evaluated with three datasets (one synthetic and two real datasets).