Factor analysis models effectively summarise the covariance structure of high dimensional data,but the solutions are typically hard to interpret. This motivates attempting to find a disjoint partition, i.e. a simple clustering, of observed variables into highly correlated subsets. We introduce a Bayesian nonparametric approach to this problem, and demonstrate advantages over heuristic methods proposed to date. Our Dirichlet process variable clustering (DPVC) model can discover blockdiagonal covariancestructures in data. We evaluate our method on both synthetic and gene expression analysis problems.

This paper explores unsupervised learning of parsing models along two directions. First, which models are identifiable from infinite data? We use a general technique for numerically checking identifiability based on the rank of a Jacobian matrix, and apply it to several standard constituency and dependency parsing models. Second, for identifiable models, how do we estimate the parameters efficiently? EM suffers from local optima, while recent work using spectral methods [1] cannot be directly applied since the topology of the parse tree varies across sentences. We develop a strategy, unmixing, which deals with this additional complexity for restricted classes of parsing models.

Links between probabilistic and non-probabilistic learning algorithms can arise by performing small-variance asymptotics, i.e., letting the variance of particular distributions in a graphical model go to zero. For instance, in the context of clustering, such an approach yields precise connections between the k-means and EM algorithms. In this paper, we explore small-variance asymptotics for exponential family Dirichlet process (DP) and hierarchical Dirichlet process (HDP) mixture models. Utilizing connections between exponential family distributions and Bregman divergences, we derive novel clustering algorithms from the asymptotic limit of the DP and HDP mixtures that feature the scalability of existing hard clustering methods as well as the flexibility of Bayesian nonparametric models. We focus on special cases of our analysis for discrete-data problems, including topic modeling, and we demonstrate the utility of our results by applying variants of our algorithms to problems arising in vision and document analysis.

We present a dynamic nonlinear generative model for visual motion based on a latent representation of binary-gated Gaussian variables. Trained on sequences of images, the model learns to represent different movement directions in different variables. We use an online approximate-inference scheme that can be mapped to the dynamics of networks of neurons. Probed with drifting grating stimuli and moving bars of light, neurons in the model show patterns of responses analogous to those of direction-selective simple cells in primary visual cortex. Most model neurons also show speed tuning and respond equally well to a range of motion directions and speeds aligned to the constraint line of their respective preferred speed. We show how these computations are enabled by a specific pattern of recurrent connections learned by the model.

Approaches to audio classification and retrieval tasks largely rely on detectionbased discriminativemodels. We submit that such models make a simplistic assumption inmapping acoustics directly to semantics, whereas the actual process is likely more complex. We present a generative model that maps acoustics in a hierarchical manner to increasingly higher-level semantics. Our model has two layers with the first layer modeling generalized sound units with no clear semantic associations, while the second layer models local patterns over these sound units. We evaluate our model on a large-scale retrieval task from TRECVID 2011, and report significant improvements over standard baselines.

A common challenge for Bayesian models of perception is the fact that the two fundamental Bayesian components, the prior distribution and the likelihood function, areformally unconstrained. Here we argue that a neural system that emulates Bayesian inference is naturally constrained by the way it represents sensory information inpopulations of neurons. More specifically, we show that an efficient coding principle creates a direct link between prior and likelihood based on the underlying stimulus distribution. The resulting Bayesian estimates can show biases awayfrom the peaks of the prior distribution, a behavior seemingly at odds with the traditional view of Bayesian estimation, yet one that has been reported in human perception. We demonstrate that our framework correctly accounts for the repulsive biases previously reported for the perception of visual orientation, and show that the predicted tuning characteristics of the model neurons match the reported orientation tuning properties of neurons in primary visual cortex. Our results suggest that efficient coding is a promising hypothesis in constraining Bayesianmodels of perceptual inference.

We consider the problem of performing efficient sum-product computations in an online setting over a tree. A natural application of our methods is to compute the marginal distribution at a vertex in a tree-structured Markov random field. Belief propagation can be used to solve this problem, but requires time linear in the size of the tree, and is therefore too slow in an online setting where we are continuously receiving new data and computing individual marginals. With our method we aim to update the data and compute marginals in time that is no more than logarithmic in the size of the tree, and is often significantly less. We accomplish this via a hierarchical covering structure that caches previous local sum-product computations. Our contribution is threefold: we i) give a linear time algorithm to find an optimal hierarchical cover of a tree; ii) give a sum-productlike algorithmto efficiently compute marginals with respect to this cover; and iii) apply "i" and "ii" to find an efficient algorithm with a regret bound for the online allocation problem in a multi-task setting.

The variational Bayesian (VB) approach is one of the best tractable approximations to the Bayesian estimation, and it was demonstrated to perform well in many applications. However, its good performance was not fully understood theoretically. For example, VB sometimes produces a sparse solution, which is regarded as a practical advantage of VB, but such sparsity is hardly observed in the rigorous Bayesian estimation. In this paper, we focus on probabilistic PCA and give more theoretical insight into the empirical success of VB. More specifically, for the situation where the noise variance is unknown, we derive a sufficient condition for perfect recovery of the true PCA dimensionality in the large-scale limit when the size of an observed matrix goes to infinity. In our analysis, we obtain bounds for a noise variance estimator and simple closed-form solutions for other parameters, which themselves are actually very useful for better implementation of VB-PCA.

We present a Bayesian nonparametric model for genetic sequence data in which a set of genetic sequences is modelled using a Markov model of partitions. The partitions at consecutive locations in the genome are related by their clusters first splitting and then merging. Our model can be thought of as a discrete time analogue of continuous time fragmentation-coagulation processes [Teh et al 2011], preserving the important properties of projectivity, exchangeability and reversibility, while being more scalable. We apply this model to the problem of genotype imputation, showing improved computational efficiency while maintaining the same accuracies as in [Teh et al 2011].

The expected return is a widely used objective in decision making under uncertainty. Manyalgorithms, such as value iteration, have been proposed to optimize it. In risk-aware settings, however, the expected return is often not an appropriate objective to optimize. We propose a new optimization objective for risk-aware planning and show that it has desirable theoretical properties. We also draw connections topreviously proposed objectives for risk-aware planing: minmax, exponential utility,percentile and mean minus variance. Our method applies to an extended class of Markov decision processes: we allow costs to be stochastic as long as they are bounded. Additionally, we present an efficient algorithm for optimizing theproposed objective. Synthetic and real-world experiments illustrate the effectiveness of our method, at scale.