Side Information Aware Bayesian A ffi nity Estimation

The estimation of affinity relationships between sets of entities can be aided by a variety of available sources of auxiliary information about these entities. Estimating the unknown affinity values given a few known values forms an important class of problems in data mining. This paper introduces a class of Bayesian mixture models Side Information Aware Bayesian Affinity Estimation (SABAE), that efficiently exploits all the available sources of information within a common framework to predict affinity relationships. In particular, the models relate multiple information sources such as available past affinities, independent entity attributes (covariates), and/or a neighborhood structure over entities (e.g. a social network), to accurately predict missing affinities between each entity pair. Utilizing side information allows seamless handling of both warm-start and cold-start within a single framework affinities for previously unseen entities can be estimated using the auxiliary information associated with these ‘new’ entities. We further embed a factorized representation of affinities in SABAE to leverage the predictive power of matrix factorization based approaches. The resulting ‘factorization aware Bayesian affinity estimation’ helps to achieve superior predictive capability. A Bayesian approach further allows us to infer the missing side information for the entities conditioned on the available affinities along with other auxiliary information. In particular, we show how missing entity attributes can be estimated within the SABAE framework. The estimated attributes can then be leveraged for future affinity predictions. Exploiting multiple sources of information entails the well-known feature selection problem. In this paper, we extend the SABAE framework for learning sparse homogeneous decompositions of the input affinity space that allows efficient feature selection from multiple available sources. Further, we provide efficient generative models for model selection among choices at varying resolutions. This joint feature and model selection framework results in more interpretable and actionable models. An important property of several datasets describing affinity relationships is that the available affinities are often recorded in a self-selecting manner. We incorporate this self-selecting property into SABAE by explicitly modeling the probability of observing an affinity between pairs of entities. This data observability model helps in unbiased parameter estimation, thereby improving the prediction accuracy of the missing affinities. Yet another property of these datasets is their dynamic nature characterized by constant arrival and/or departure of entities, continuously evolving preferences, tastes and hence affinity relationships. We incorporate this dynamic nature of the data into a Bayesian affinity estimation framework with temporal dynamics resulting in better suited models for each individual time stamp. Moreover in some applications, the learnt affinities are often used to generate a ranked preference list of one set of entities for another entity set. We further enhance the SABAE framework for a supervised ranking task that allows efficient learning of such rankings. Finally, we show how the models within the SABAE framework can be used in semi-supervised co-clustering settings, including an efficient modeling of the traditional must-link/cannot-link based constrained co-clustering. Efficient inferencing and learning algorithms for the SABAE framework based on variational mean field approximations are provided that allow scaling to large real-life datasets. Extensive experiments on simulated and real datasets illustrate the efficacy of the proposed models.