Bayesian Heteroskedastic Choice Modeling on Non-identically Distributed Linkages

Abstract

Choice modeling (CM) aims to describe and predict choices according to attributes of subjects and options. If we presume each choice making as the formation of link between subjects and options, immediately CM can be bridged to link analysis and prediction (LAP) problem. However, such a mapping is often not trivial and straightforward. In LAP problems, the only available observations are links among objects but their attributes are often inaccessible. Therefore, we extend CM into a latent feature space to avoid the need of explicit attributes. Moreover, LAP is usually based on binary linkage assumption that models observed links as positive instances and unobserved links as negative instances. Instead, we use a weaker assumption that treats unobserved links as pseudo negative instances. Furthermore, most subjects or options may be quite heterogeneous due to the long-tail distribution, which is failed to capture by conventional LAP approaches. To address above challenges, we propose a Bayesian heteroskedastic choice model to represent the non-identically distributed linkages in the LAP problems. Finally, the empirical evaluation on real-world datasets proves the superiority of our approach.

Improving the Quality of Recommendations for Users and Items in the Tail of Distribution

“…As a result, we call this variant MF model heteroscedastic MF (HMF). From a probabilistic view, the variance parameter σ 2 ij controls the confidence level [Hu et al 2014]. Specifically, a smaller σ 2 ij implies higher confidence and less uncertainty of the observation Y ij , i.e., a large w ij is applied to more tightly fitting Y ij .…”

“…Apart from the MF approach, some other models have also achieved success in this field. For example, in the literature, choice modeling [Train 2003] is strongly related to the recommendation problem, and Hu et al [2014] proposed a latent-featurebased Bayesian heteroscedastic choice model (BHCM) to represent heterogeneities between users and items. Additionally, with the prevalence of deep learning techniques [Bengio et al 2013], restricted Boltzmann machines (RBM) have also been applied in RSs [Georgiev and Nakov 2013].…”

“…However, explicit feedback is not always available in the real world while implicit feedback, e.g., click logs, can be obtained more easily. Implicit feedback is often represented by binary values, that is, 1 for observed choices and 0 for others [Hu et al 2014;Pan et al 2008]. These unobserved choices have zero values, but they do not mean true negative instances.…”

“…These unobserved choices have zero values, but they do not mean true negative instances. Therefore, a strategy that is often used to assign a larger confidence level to the observed choices to represent the high certainty of users' explicit likes while a much smaller confidence level is assigned to unobserved choices to represent the small certainty of dislike [Hu et al 2014;Hu et al 2008;Pan et al 2008]. For instance, Bayesian personalized ranking (BPR) [Rendle et al 2009] assumes that users show a stronger like for their chosen items than for unobserved ones.…”

“…This implicit rating data is usually modeled as a unary preference because the blank entries do not necessarily indicate user dislike, but, instead, are a result of the users' lack of awareness [Herlocker et al 2004]. Hence, we can assign a higher confidence level to observed entries and a much lower confidence level to blank entries [Hu et al 2014;Hu et al 2008]. Recall that the confidence level is associated with the variance parameter, i.e., the inverse of weight (cf.…”