Inference in matrix-variate Gaussian models has major applications for multioutput prediction and joint learning of row and column covariances from matrixvariate data. Here, we discuss an approach for efficient inference in such models that explicitly account for iid observation noise. Computational tractability can be retained by exploiting the Kronecker product between row and column covariance matrices. Using this framework, we show how to generalize the Graphical Lasso in order to learn a sparse inverse covariance between features while accounting for a low-rank confounding covariance between samples. We show practical utility on applications to biology, where we model covariances with more than 100,000 dimensions. We find greater accuracy in recovering biological network structures and are able to better reconstruct the confounders.

Recently, image categorization has been an active research topic due to the urgent need to retrieve and browse digital images via semantic keywords. This paper formulates image categorization as a multi-label classification problem using recent advances in matrix completion. Under this setting, classification of testing data is posed as a problem of completing unknown label entries on a data matrix that concatenates training and testing features with training labels. We propose two convex algorithms for matrix completion based on a Rank Minimization criterion specifically tailored to visual data, and prove its convergence properties.

Most state-of-the-art techniques for multi-class image segmentation and labeling use conditional random fields defined over pixels or image regions. While regionlevel models often feature dense pairwise connectivity, pixel-level models are considerably larger and have only permitted sparse graph structures. In this paper, we consider fully connected CRF models defined on the complete set of pixels in an image. The resulting graphs have billions of edges, making traditional inference algorithms impractical. Our main contribution is a highly efficient approximate inference algorithm for fully connected CRF models in which the pairwise edge potentials are defined by a linear combination of Gaussian kernels. Our experiments demonstrate that dense connectivity at the pixel level substantially improves segmentation and labeling accuracy.

Multi-instance learning (MIL) considers input as bags of instances, in which labels are assigned to the bags. MIL is useful in many real-world applications. For example, in image categorization semantic meanings (labels) of an image mostly arise from its regions (instances) instead of the entire image (bag). Existing MIL methods typically build their models using the Bag-to-Bag (B2B) distance, which are often computationally expensive and may not truly reflect the semantic similarities. To tackle this, in this paper we approach MIL problems from a new perspective using the Class-to-Bag (C2B) distance, which directly assesses the relationships between the classes and the bags.

Traditional approaches to probabilistic inference such as loopy belief propagation and Gibbs sampling typically compute marginals for it all the unobserved variables in a graphical model. However, in many real-world applications the user's interests are focused on a subset of the variables, specified by a query. In this case it would be wasteful to uniformly sample, say, one million variables when the query concerns only ten. In this paper we propose a query-specific approach to MCMC that accounts for the query variables and their generalized mutual information with neighboring variables in order to achieve higher computational efficiency. Surprisingly there has been almost no previous work on query-aware MCMC. We demonstrate the success of our approach with positive experimental results on a wide range of graphical models.

We introduce a variational Bayesian inference algorithm which can be widely applied to sparse linear models. The algorithm is based on the spike and slab prior which, from a Bayesian perspective, is the golden standard for sparse inference. We apply the method to a general multi-task and multiple kernel learning model in which a common set of Gaussian process functions is linearly combined with task-specific sparse weights, thus inducing relation between tasks. This model unifies several sparse linear models, such as generalized linear models, sparse factor analysis and matrix factorization with missing values, so that the variational algorithm can be applied to all these cases. We demonstrate our approach in multi-output Gaussian process regression, multi-class classification, image processing applications and collaborative filtering.

Topic models are learned via a statistical model of variation within document collections, but designed to extract meaningful semantic structure. Desirable traits include the ability to incorporate annotations or metadata associated with documents; the discovery of correlated patterns of topic usage; and the avoidance of parametric assumptions, such as manual specification of the number of topics. We propose a doubly correlated nonparametric topic (DCNT) model, the first model to simultaneously capture all three of these properties. The DCNT models metadata via a flexible, Gaussian regression on arbitrary input features; correlations via a scalable square-root covariance representation; and nonparametric selection from an unbounded series of potential topics via a stick-breaking construction. We validate the semantic structure and predictive performance of the DCNT using a corpus of NIPS documents annotated by various metadata.

We consider the problem of Ising and Gaussian graphical model selection given n i.i.d. samples from the model. We propose an efficient threshold-based algorithm for structure estimation based known as conditional mutual information test. This simple local algorithm requires only low-order statistics of the data and decides whether two nodes are neighbors in the unknown graph. Under some transparent assumptions, we establish that the proposed algorithm is structurally consistent (or sparsistent) when the number of samples scales as n= Omega(J_{min}^{-4} log p), where p is the number of nodes and J_{min} is the minimum edge potential. We also prove novel non-asymptotic necessary conditions for graphical model selection.

We consider the problem of estimating neural spikes from extracellular voltage recordings. Most current methods are based on clustering, which requires substantial human supervision and produces systematic errors by failing to properly handle temporally overlapping spikes. We formulate the problem as one of statistical inference, in which the recorded voltage is a noisy sum of the spike trains of each neuron convolved with its associated spike waveform. Joint maximum-a-posteriori (MAP) estimation of the waveforms and spikes is then a blind deconvolution problem in which the coefficients are sparse. We develop a block-coordinate descent method for approximating the MAP solution. We validate our method on data simulated according to the generative model, as well as on real data for which ground truth is available via simultaneous intracellular recordings. In both cases, our method substantially reduces the number of missed spikes and false positives when compared to a standard clustering algorithm, primarily by recovering temporally overlapping spikes. The method offers a fully automated alternative to clustering methods that is less susceptible to systematic errors.

A Bayesian approach to partitioning distance matrices is presented. It is inspired by the 'Translation-Invariant Wishart-Dirichlet' process (TIWD) in (Vogt et al., 2010) and shares a number of advantageous properties like the fully probabilistic nature of the inference model, automatic selection of the number of clusters and applicability in semi-supervised settings. In addition, our method (which we call 'fastTIWD') overcomes the main shortcoming of the original TIWD, namely its high computational costs. The fastTIWD reduces the workload in each iteration of a Gibbs sampler from O(n^3) in the TIWD to O(n^2). Our experiments show that this cost reduction does not compromise the quality of the inferred partitions. With this new method it is now possible to 'mine' large relational datasets with a probabilistic model, thereby automatically detecting new and potentially interesting clusters.