Learning from multi-view data is important in many applications, such as image classification and annotation. In this paper, we present a large-margin learning framework to discover a predictive latent subspace representation shared by multiple views. Our approach is based on an undirected latent space Markov network that fulfills a weak conditional independence assumption that multi-view observations and response variables are independent given a set of latent variables. We provide efficient inference and parameter estimation methods for the latent subspace model. Finally, we demonstrate the advantages of large-margin learning on real video and web image data for discovering predictive latent representations and improving the performance on image classification, annotation and retrieval.

We present a generative probabilistic model for learning general graph structures, which we term concept graphs, from text. Concept graphs provide a visual summary of the thematic content of a collection of documents-a task that is difficult to accomplish using only keyword search. The proposed model can learn different types of concept graph structures and is capable of utilizing partial prior knowledge about graph structure as well as labeled documents. We describe a generative model that is based on a stick-breaking process for graphs, and a Markov Chain Monte Carlo inference procedure. Experiments on simulated data show that the model can recover known graph structure when learning in both unsupervised and semi-supervised modes. We also show that the proposed model is competitive in terms of empirical log likelihood with existing structure-based topic models (such as hPAM and hLDA) on real-world text data sets. Finally, we illustrate the application of the model to the problem of updating Wikipedia category graphs.

Continuous Markov random fields are a general formalism to model joint probability distributions over events with continuous outcomes. We prove that marginal computation for constrained continuous MRFs is #P-hard in general and present a polynomial-time approximation scheme under mild assumptions on the structure of the random field. Moreover, we introduce a sampling algorithm to compute marginal distributions and develop novel techniques to increase its efficiency. Continuous MRFs are a general purpose probabilistic modeling tool and we demonstrate how they can be applied to statistical relational learning. On the problem of collective classification, we evaluate our algorithm and show that the standard deviation of marginals serves as a useful measure of confidence.

Bayesian approaches to preference elicitation (PE) are particularly attractive due to their ability to explicitly model uncertainty in users' latent utility functions. However, previous approaches to Bayesian PE have ignored the important problem of generalizing from previous users to an unseen user in order to reduce the elicitation burden on new users. In this paper, we address this deficiency by introducing a Gaussian Process (GP) prior over users' latent utility functions on the joint space of user and item features. We learn the hyper-parameters of this GP on a set of preferences of previous users and use it to aid in the elicitation process for a new user. This approach provides a flexible model of a multi-user utility function, facilitates an efficient value of information (VOI) heuristic query selection strategy, and provides a principled way to incorporate the elicitations of multiple users back into the model. We show the effectiveness of our method in comparison to previous work on a real dataset of user preferences over sushi types.

Heavy-tailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closed-form in graphical models which involve such heavy tailed distributions. In this work, we propose a novel simple linear graphical model for independent latent random variables, called linear characteristic model (LCM), defined in the characteristic function domain. Using stable distributions, a heavy-tailed family of distributions which is a generalization of Cauchy, L\'evy and Gaussian distributions, we show for the first time, how to compute both exact and approximate inference in such a linear multivariate graphical model. LCMs are not limited to only stable distributions, in fact LCMs are always defined for any random variables (discrete, continuous or a mixture of both). We provide a realistic problem from the field of computer networks to demonstrate the applicability of our construction. Other potential application is iterative decoding of linear channels with non-Gaussian noise.

To cope with concept drift, we placed a probability distribution over the location of the most-recent drift point. We used Bayesian model comparison to update this distribution from the predictions of models trained on blocks of consecutive observations and pruned potential drift points with low probability. We compare our approach to a non-probabilistic method for drift and a probabilistic method for change-point detection. In our experiments, our approach generally yielded improved accuracy and/or speed over these other methods.

Identifying the features of objects becomes a challenge when those features can change in their appearance. We introduce the Transformed Indian Buffet Process (tIBP), and use it to define a nonparametric Bayesian model that infers features that can transform across instantiations. We show that this model can identify features that are location invariant by modeling a previous experiment on human feature learning. However, allowing features to transform adds new kinds of ambiguity: Are two parts of an object the same feature with different transformations or two unique features? What transformations can features undergo? We present two new experiments in which we explore how people resolve these questions, showing that the tIBP model demonstrates a similar sensitivity to context to that shown by human learners when determining the invariant aspects of features.

This paper describes a probabilistic framework for studying associations between multiple genotypes, biomarkers, and phenotypic traits in the presence of noise and unobserved confounders for large genetic studies. The framework builds on sparse linear methods developed for regression and modified here for inferring causal structures of richer networks with latent variables. The method is motivated by the use of genotypes as ``instruments'' to infer causal associations between phenotypic biomarkers and outcomes, without making the common restrictive assumptions of instrumental variable methods. The method may be used for an effective screening of potentially interesting genotype phenotype and biomarker-phenotype associations in genome-wide studies, which may have important implications for validating biomarkers as possible proxy endpoints for early stage clinical trials. Where the biomarkers are gene transcripts, the method can be used for fine mapping of quantitative trait loci (QTLs) detected in genetic linkage studies. The method is applied for examining effects of gene transcript levels in the liver on plasma HDL cholesterol levels for a sample of sequenced mice from a heterogeneous stock, with $\sim 10^5$ genetic instruments and $\sim 47 \times 10^3$ gene transcripts.

Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of unbounded width and depth, where data can live at any node and are infinitely exchangeable. One can view our model as providing infinite mixtures where the components have a dependency structure corresponding to an evolutionary diffusion down a tree. By using a stick-breaking approach, we can apply Markov chain Monte Carlo methods based on slice sampling to perform Bayesian inference and simulate from the posterior distribution on trees. We apply our method to hierarchical clustering of images and topic modeling of text data.

We introduce a stochastic process with Wishart marginals: the generalised Wishart process (GWP). It is a collection of positive semi-definite random matrices indexed by any arbitrary dependent variable. We use it to model dynamic (e.g. time varying) covariance matrices. Unlike existing models, it can capture a diverse class of covariance structures, it can easily handle missing data, the dependent variable can readily include covariates other than time, and it scales well with dimension; there is no need for free parameters, and optional parameters are easy to interpret. We describe how to construct the GWP, introduce general procedures for inference and predictions, and show that it outperforms its main competitor, multivariate GARCH, even on financial data that especially suits GARCH. We also show how to predict the mean of a multivariate process while accounting for dynamic correlations.