We propose a new matrix completion algorithm—Kernelized Probabilistic Matrix Factorization (KPMF), which effectively incorporates external side information into the matrix factorization process. Unlike Probabilistic Matrix Factorization (PMF) [14], which assumes an independent latent vector for each row (and each column) with Gaussian priors, KMPF works with latent vectors spanning all rows (and columns) with Gaussian Process (GP) priors. Hence, KPMF explicitly captures the underlying (nonlinear) covariance structures across rows and columns. This crucial difference greatly boosts the performance of KPMF when appropriate side information, e.g., users' social network in recommender systems, is incorporated. Furthermore, GP priors allow the KPMF model to fill in a row that is entirely missing in the original matrix based on the side information alone, which is not feasible for standard PMF formulation. In our paper, we mainly work on the matrix completion problem with a graph among the rows and/or columns as side information, but the proposed framework can be easily used with other types of side information as well. Finally, we demonstrate the efficacy of KPMF through two different applications: 1) recommender systems and 2) image restoration.

Probabilistic matrix factorization (PMF) methods have shown great promise in collaborative filtering. In this paper, we consider several variants and generalizations of PMF framework inspired by three broad questions: Are the prior distributions used in existing PMF models suitable, or can one get better predictive performance with different priors? Are there suitable extensions to leverage side information? Are there benefits to taking into account row and column biases? We develop new families of PMF models to address these questions along with efficient approximate inference algorithms for learning and prediction. Through extensive experiments on movie recommendation datasets, we illustrate that simpler models directly capturing correlations among latent factors can outperform existing PMF models, side information can benefit prediction accuracy, and accounting for row/column biases leads to improvements in predictive performance.

In recent years, matrix approximation for missing value prediction has emerged as an important problem in a variety of domains such as recommendation systems, e-commerce and online advertisement. While matrix factorization based algorithms typically have good approximation accuracy, such algorithms can be slow especially for large matrices. Further, such algorithms cannot naturally make prediction on new rows or columns. In this paper, we propose residual Bayesian co-clustering (RBC), which learns a generative model corresponding to the matrix from the non-missing entries, and uses the model to predict the missing entries. RBC is an extension of Bayesian co-clustering by taking row and column bias into consideration. The model allows mixed memberships of rows and columns to multiple clusters, and can naturally handle the prediction on new rows and columns which are not used in the training process, given only a few non-missing entries in them. We propose two variational inference based algorithms for learning the model and predicting missing entries. One of the proposed algorithms leads to a parallel RBC which can achieve significant speed-ups. The efficacy of RBC is demonstrated by extensive experimental comparisons with state-of-the-art algorithms on real world datasets.

Although mixed-membership models have achieved great success in unsupervised learning, they have not been widely applied to classification problems. In this paper, we propose a family of discriminative mixed-membership models for classification by combining unsupervised mixed-membership models with multi-class logistic regression. In particular, we propose two variants respectively applicable to text classification based on latent Dirichlet allocation and usual feature vector classification based on mixed-membership naive Bayes models. The proposed models allow the number of components in the mixed membership to be different from the number of classes. We propose two variational inference based algorithms for learning the models, including a fast variational inference which is substantially more efficient than mean-field variational approximation. Through extensive experiments on UCI and text classification benchmark datasets, we show that the models are competitive with the state of the art, and can discover components not explicitly captured by the class labels.

Cluster ensembles provide a framework for combining multiple base clusterings of a dataset to generate a stable and robust consensus clustering. There are important variants of the basic cluster ensemble problem, notably including cluster ensembles with missing values, as well as row-distributed or column-distributed cluster ensembles. Existing cluster ensemble algorithms are applicable only to a small subset of these variants. In this paper, we propose Bayesian Cluster Ensembles (BCE), which is a mixed-membership model for learning cluster ensembles, and is applicable to all the primary variants of the problem. We propose two methods, respectively based on variational approximation and Gibbs sampling, for learning a Bayesian cluster ensemble. We compare BCE extensively with several other cluster ensemble algorithms, and demonstrate that BCE is not only versatile in terms of its applicability, but also outperforms the other algorithms in terms of stability and accuracy.

In recent years, co-clustering has emerged as a powerful data mining tool that can analyze dyadic data connecting two entities. However, almost all existing co-clustering techniques are partitional, and allow individual rows and columns of a data matrix to belong to only one cluster. Several current applications, such as recommendation systems and market basket analysis, can substantially benefit from a mixed membership of rows and columns. In this paper, we present Bayesian co-clustering (BCC) models, that allow a mixed membership in row and column clusters. BCC maintains separate Dirichlet priors for rows and columns over the mixed membership and assumes each observation to be generated by an exponential family distribution corresponding to its row and column clusters. We propose a fast variational algorithm for inference and parameter estimation. The model is designed to naturally handle sparse matrices as the inference is done only based on the non-missing entries. In addition to finding a co-cluster structure in observations, the model outputs a low dimensional co-embedding, and accurately predicts missing values in the original matrix. We demonstrate the efficacy of the model through experiments on both simulated and real data.

In spite of the popularity of probabilistic mixture models for latent structure discovery from data, mixture models do not have a natural mechanism for handling sparsity, where each data point only has a few non-zero observations. In this paper, we introduce conditional naive-Bayes (CNB) models, which generalize naive-Bayes mixture models to naturally handle sparsity by conditioning the model on observed features. Further, we present latent Dirichlet conditional naive-Bayes (LD-CNB) models, which constitute a family of powerful hierarchical Bayesian models for latent structure discovery from sparse data. The proposed family of models are quite general and can work with arbitrary regular exponential family conditional distributions. We present a variational inference based EM algorithm for learning along with special case analyses for Gaussian and discrete distributions. The efficacy of the proposed models are demonstrated by extensive experiments on a wide variety of different datasets.

In this paper, we propose a novel cross-media retrieval method. The most important feature of it is to integrate the multi-modal data seamlessly via a cross-reference graph, and then based on the graph, it is able to use improved personalized PageRank to calculate how close the media object associates with the query on semantic and content level. It is also able to adjust the cross-reference graph according to user's relevance feedback, which refines the semantic relationship between the media objects, so as to improve the retrieval accuracy progressively. As demonstrated by the experiments, our method achieves satisfactory retrieval efficiency on multi-modal datasets.