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 paper is concerned with fairness in recommendations. Specifically, there are groups of users and groups of items. Previous work has modelled fairness as the constraint of all user groups having the same accuracy or as the prediction probability being independent of the item group or the user group. In this work, the notion is generalized so that the prediction is independent of both the item and user group. Optimization algorithms are shown to solve this problem along with experimental results.