We introduce a Gaussian process (GP) framework, stochastic relational models (SRM), for learning social, physical, and other relational phenomena where interactions between entities are observed. The key idea is to model the stochastic structure of entity relationships (i.e., links) via a tensor interaction of multiple GPs, each defined on one type of entities. These models in fact define a set of nonparametric priors on infinite dimensional tensor matrices, where each element represents a relationship between a tuple of entities. By maximizing the marginalized likelihood, information is exchanged between the participating GPs through the entire relational network, so that the dependency structure of links is messaged to the dependency of entities, reflected by the adapted GP kernels. The framework offers a discriminative approach to link prediction, namely, predicting the existences, strengths, or types of relationships based on the partially observed linkage network as well as the attributes of entities (if given).

Stochastic relational models provide a rich family of choices for learning and predicting dyadic data between two sets of entities. Previously empirical Bayesian inference was applied, which is however not scalable when the size of either object sets becomes tens of thousands. In this paper, we introduce a Markov chain Monte Carlo (MCMC) algorithm to scale the model to very large-scale dyadic data. Both superior scalability and predictive accuracy are demonstrated on a collaborative filtering problem, which involves tens of thousands users and a half million items.

Stochastic relational models provide a rich family of choices for learning and predicting dyadic data between two sets of entities. Previously empirical Bayesian inference was applied, which is however not scalable when the size of either object sets becomes tens of thousands. In this paper, we introduce a Markov chain Monte Carlo (MCMC) algorithm to scale the model to very large-scale dyadic data. Both superior scalability and predictive accuracy are demonstrated on a collaborative filtering problem, which involves tens of thousands users and a half million items. Papers published at the Neural Information Processing Systems Conference.

Stochastic relational models (SRMs) [15] provide a rich family of choices for learning and predicting dyadic data between two sets of entities. The models generalize matrixfactorization to a supervised learning problem that utilizes attributes of entities in a hierarchical Bayesian framework. Previously variational Bayes inference wasapplied for SRMs, which is, however, not scalable when the size of either entity set grows to tens of thousands. In this paper, we introduce a Markov chain Monte Carlo (MCMC) algorithm for equivalent models of SRMs in order to scale the computation to very large dyadic data sets. Both superior scalability and predictive accuracy are demonstrated on a collaborative filtering problem, which involves tens of thousands users and half million items.

We introduce a Gaussian process (GP) framework, stochastic relational models (SRM), for learning social, physical, and other relational phenomena where interactions between entities are observed. The key idea is to model the stochastic structure of entity relationships (i.e., links) via a tensor interaction of multiple GPs, each defined on one type of entities. These models in fact define a set of nonparametric priors on infinite dimensional tensor matrices, where each element represents a relationship between a tuple of entities. By maximizing the marginalized likelihood, information is exchanged between the participating GPs through the entire relational network, so that the dependency structure of links is messaged to the dependency of entities, reflected by the adapted GP kernels. The framework offers a discriminative approach to link prediction, namely, predicting the existences, strengths, or types of relationships based on the partially observed linkage network as well as the attributes of entities (if given). We discuss properties and variants of SRM and derive an efficient learning algorithm. Very encouraging experimental results are achieved on a toy problem and a user-movie preference link prediction task. In the end we discuss extensions of SRM to general relational learning tasks.

We introduce a Gaussian process (GP) framework, stochastic relational models (SRM), for learning social, physical, and other relational phenomena where interactions between entities are observed. The key idea is to model the stochastic structure of entity relationships (i.e., links) via a tensor interaction of multiple GPs, each defined on one type of entities. These models in fact define a set of nonparametric priors on infinite dimensional tensor matrices, where each element represents a relationship between a tuple of entities. By maximizing the marginalized likelihood, information is exchanged between the participating GPs through the entire relational network, so that the dependency structure of links is messaged to the dependency of entities, reflected by the adapted GP kernels. The framework offers a discriminative approach to link prediction, namely, predicting the existences, strengths, or types of relationships based on the partially observed linkage network as well as the attributes of entities (if given). We discuss properties and variants of SRM and derive an efficient learning algorithm. Very encouraging experimental results are achieved on a toy problem and a user-movie preference link prediction task. In the end we discuss extensions of SRM to general relational learning tasks.

We introduce a Gaussian process (GP) framework, stochastic relational models (SRM), for learning social, physical, and other relational phenomena where interactions betweenentities are observed. The key idea is to model the stochastic structure of entity relationships (i.e., links) via a tensor interaction of multiple GPs, each defined on one type of entities. These models in fact define a set of nonparametric priors on infinite dimensional tensor matrices, where each element represents a relationship between a tuple of entities. By maximizing the marginalized likelihood,information is exchanged between the participating GPs through the entire relational network, so that the dependency structure of links is messaged to the dependency of entities, reflected by the adapted GP kernels. The framework offers a discriminative approach to link prediction, namely, predicting the existences, strengths,or types of relationships based on the partially observed linkage network as well as the attributes of entities (if given). We discuss properties and variants of SRM and derive an efficient learning algorithm. Very encouraging experimental resultsare achieved on a toy problem and a user-movie preference link prediction task. In the end we discuss extensions of SRM to general relational learning tasks.