We present a probabilistic factor analysis model which can be used for studying spatiotemporal datasets. The spatial and temporal structure is modeled by using Gaussian process priors both for the loading matrix and the factors. The posterior distributions are approximated using the variational Bayesian framework. High computational cost of Gaussian process modeling is reduced by using sparse approximations. Themodel is used to compute the reconstructions of the global sea surface temperatures from a historical dataset. The results suggest that the proposed model can outperform the state-of-the-art reconstruction systems.

Most of existing methods for DNA motif discovery consider only a single set of sequences to find an over-represented motif. In contrast, we consider multiple sets of sequences where we group sets associated with the same motif into a cluster, assuming that each set involves a single motif. Clustering sets of sequences yields clusters of coherent motifs, improving signal-to-noise ratio or enabling us to identify multiple motifs. We present a probabilistic model for DNA motif discovery where we identify multiple motifs through searching for patterns which are shared across multiple sets of sequences. Our model infers cluster-indicating latent variables and learns motifs simultaneously, where these two tasks interact with each other. We show that our model can handle various motif discovery problems, depending on how to construct multiple sets of sequences. Experiments on three different problems for discovering DNA motifs emphasize the useful behavior and confirm the substantial gains over existing methods where only single set of sequences is considered.

This paper proposes a fast and scalable alternating optimization technique to detect regionsof interest (ROIs) in cluttered Web images without labels. The proposed approachdiscovers highly probable regions of object instances by iteratively repeating the following two functions: (1) choose the exemplar set (i.e. a small number of highly ranked reference ROIs) across the dataset and (2) refine the ROIs of each image with respect to the exemplar set. These two subproblems are formulated as ranking in two different similarity networks of ROI hypotheses by link analysis. The experiments with the PASCAL 06 dataset show that our unsupervised localization performance is better than one of state-of-the-art techniques andcomparable to supervised methods. Also, we test the scalability of our approach with five objects in Flickr dataset consisting of more than 200K images.

Many nonlinear dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector autoregressive (VAR) process. In this paper, we present a nonparametric approach to the learning of an unknown number of persistent, smooth dynamical modes by utilizing a hierarchical Dirichlet process prior. We develop a sampling algorithm that combines a truncated approximation to the Dirichlet process with an efficient joint sampling of the mode and state sequences. The utility and flexibility of our model are demonstrated on synthetic data, sequences of dancing honey bees, and the IBOVESPA stock index.

We consider the question of computing Maximum A Posteriori (MAP) assignment in an arbitrary pair-wise Markov Random Field (MRF). We present a randomized iterative algorithm based on simple local updates. The algorithm, starting with an arbitrary initial assignment, updates it in each iteration by first, picking a random node, then selecting an (appropriately chosen) random local neighborhood and optimizing over this local neighborhood. Somewhat surprisingly, we show that this algorithm finds a near optimal assignment within $2n\ln n$ iterations on average and with high probability for {\em any} $n$ node pair-wise MRF with {\em geometry} (i.e. MRF graph with polynomial growth) with the approximation error depending on (in a reasonable manner) the geometric growth rate of the graph and the average radius of the local neighborhood -- this allows for a graceful tradeoff between the complexity of the algorithm and the approximation error. Through extensive simulations, we show that our algorithm finds extremely good approximate solutions for various kinds of MRFs with geometry.

In this paper we make several contributions towards accelerating approximate Bayesian structural inference for non-decomposable GGMs. Our first contribution is to show how to efficiently compute a BIC or Laplace approximation to the marginal likelihood of non-decomposable graphs using convex methods for precision matrix estimation. This optimization technique can be used as a fast scoring function inside standard Stochastic Local Search (SLS) for generating posterior samples. Our second contribution is a novel framework for efficiently generating large sets of high-quality graph topologies without performing local search. This graph proposal method, which we call Neighborhood Fusion" (NF), samples candidate Markov blankets at each node using sparse regression techniques. Our final contribution is a hybrid method combining the complementary strengths of NF and SLS. Experimental results in structural recovery and prediction tasks demonstrate that NF and hybrid NF/SLS out-perform state-of-the-art local search methods, on both synthetic and real-world datasets, when realistic computational limits are imposed."

Non-parametric Bayesian techniques are considered for learning dictionaries for sparse image representations, with applications in denoising, inpainting and compressive sensing (CS). The beta process is employed as a prior for learning the dictionary, and this non-parametric method naturally infers an appropriate dictionary size. The Dirichlet process and a probit stick-breaking process are also considered to exploit structure within an image. The proposed method can learn a sparse dictionary in situ; training images may be exploited if available, but they are not required. Further, the noise variance need not be known, and can be non-stationary. Another virtue of the proposed method is that sequential inference can be readily employed, thereby allowing scaling to large images. Several example results are presented, using both Gibbs and variational Bayesian inference, with comparisons to other state-of-the-art approaches.

The recent introduction of indefinite SVM by Luss and dAspremont [15] has effectively demonstrated SVM classification with a non-positive semi-definite kernel (indefinite kernel). This paper studies the properties of the objective function introduced there. In particular, we show that the objective function is continuously differentiable and its gradient can be explicitly computed. Indeed, we further show that its gradient is Lipschitz continuous. The main idea behind our analysis is that the objective function is smoothed by the penalty term, in its saddle (min-max) representation, measuring the distance between the indefinite kernel matrix and the proxy positive semi-definite one. Our elementary result greatly facilitates the application of gradient-based algorithms. Based on our analysis, we further develop Nesterovs smooth optimization approach [16,17] for indefinite SVM which has an optimal convergence rate for smooth problems. Experiments on various benchmark datasets validate our analysis and demonstrate the efficiency of our proposed algorithms.

While many perceptual and cognitive phenomena are well described in terms of Bayesian inference, the necessary computations are intractable at the scale of real-world tasks, and it remains unclear how the human mind approximates Bayesian inference algorithmically. We explore the proposal that for some tasks, humans use a form of Markov Chain Monte Carlo to approximate the posterior distribution over hidden variables. As a case study, we show how several phenomena of perceptual multistability can be explained as MCMC inference in simple graphical models for low-level vision.

Principal Components Analysis (PCA) has become established as one of the key tools for dimensionality reduction when dealing with real valued data. Approaches such as exponential family PCA and non-negative matrix factorisation have successfully extended PCA to non-Gaussian data types, but these techniques fail to take advantage of Bayesian inference and can suffer from problems of overfitting and poor generalisation. This paper presents a fully probabilistic approach to PCA, which is generalised to the exponential family, based on Hybrid Monte Carlo sampling. We describe the model which is based on a factorisation of the observed data matrix, and show performance of the model on both synthetic and real data.