The efficacy of family-based approaches to mixture model-based clustering and classification depends on the selection of parsimonious models. Current wisdom suggests the Bayesian information criterion (BIC) for mixture model selection. However, the BIC has well-known limitations, including a tendency to overestimate the number of components as well as a proclivity for, often drastically, underestimating the number of components in higher dimensions. While the former problem might be soluble through merging components, the latter is impossible to mitigate in clustering and classification applications. In this paper, a LASSO-penalized BIC (LPBIC) is introduced to overcome this problem. This approach is illustrated based on applications of extensions of mixtures of factor analyzers, where the LPBIC is used to select both the number of components and the number of latent factors. The LPBIC is shown to match or outperform the BIC in several situations.

We consider the inverse reinforcement learning problem, that is, the problem of learning from, and then predicting or mimicking a controller based on state/action data. We propose a statistical model for such data, derived from the structure of a Markov decision process. Adopting a Bayesian approach to inference, we show how latent variables of the model can be estimated, and how predictions about actions can be made, in a unified framework. A new Markov chain Monte Carlo (MCMC) sampler is devised for simulation from the posterior distribution. This step includes a parameter expansion step, which is shown to be essential for good convergence properties of the MCMC sampler. As an illustration, the method is applied to learning a human controller.

We apply the spike-and-slab Restricted Boltzmann Machine (ssRBM) to texture modeling. The ssRBM with tiled-convolution weight sharing (TssRBM) achieves or surpasses the state-of-the-art on texture synthesis and inpainting by parametric models. We also develop a novel RBM model with a spike-and-slab visible layer and binary variables in the hidden layer. This model is designed to be stacked on top of the TssRBM. We show the resulting deep belief network (DBN) is a powerful generative model that improves on single-layer models and is capable of modeling not only single high-resolution and challenging textures but also multiple textures.

A basic assumption of statistical learning theory is that train and test data are drawn from the same underlying distribution. Unfortunately, this assumption doesn't hold in many applications. Instead, ample labeled data might exist in a particular `source' domain while inference is needed in another, `target' domain. Domain adaptation methods leverage labeled data from both domains to improve classification on unseen data in the target domain. In this work we survey domain transfer learning methods for various application domains with focus on recent work in Computer Vision.

We present a general construction for dependent random measures based on thinning Poisson processes on an augmented space. The framework is not restricted to dependent versions of a specific nonparametric model, but can be applied to all models that can be represented using completely random measures. Several existing dependent random measures can be seen as specific cases of this framework. Interesting properties of the resulting measures are derived and the efficacy of the framework is demonstrated by constructing a covariate-dependent latent feature model and topic model that obtain superior predictive performance.

Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input variables of the model. When the statistics of the output event are known, these input variables have to be chosen in a specific way for the output to have the prescribed statistics. Because the probability distribution of the input random variables is not directly known but dictated implicitly by the statistics of the output random variables, this problem is usually intractable for classical sampling methods. Based on Markov Chain Monte Carlo we propose a novel method to sample random inputs to such models by introducing a modification to the standard Metropolis-Hastings algorithm. As an example we consider a system described by a stochastic differential equation (sde) and demonstrate how sample paths of a random process satisfying this sde can be generated with our technique.

Dependent nonparametric processes extend distributions over measures, such as the Dirichlet process and the beta process, to give distributions over collections of measures, typically indexed by values in some covariate space. Such models are appropriate priors when exchangeability assumptions do not hold, and instead we want our model to vary fluidly with some set of covariates. Since the concept of dependent nonparametric processes was formalized by MacEachern [1], there have been a number of models proposed and used in the statistics and machine learning literatures. Many of these models exhibit underlying similarities, an understanding of which, we hope, will help in selecting an appropriate prior, developing new models, and leveraging inference techniques.

Structure learning of Bayesian networks is an important problem that arises in numerous machine learning applications. In this work, we present a novel approach for learning the structure of Bayesian networks using the solution of an appropriately constructed traveling salesman problem. In our approach, one computes an optimal ordering (partially ordered set) of random variables using methods for the traveling salesman problem. This ordering significantly reduces the search space for the subsequent greedy optimization that computes the final structure of the Bayesian network. We demonstrate our approach of learning Bayesian networks on real world census and weather datasets. In both cases, we demonstrate that the approach very accurately captures dependencies between random variables. We check the accuracy of the predictions based on independent studies in both application domains.

We develop a Bayesian nonparametric extension of the popular Plackett-Luce choice model that can handle an infinite number of choice items. Our framework is based on the theory of random atomic measures, with the prior specified by a gamma process. We derive a posterior characterization and a simple and effective Gibbs sampler for posterior simulation. We develop a time-varying extension of our model, and apply it to the New York Times lists of weekly bestselling books.

This paper advocates the exploration of the full state of recorded real-time strategy (RTS) games, by human or robotic players, to discover how to reason about tactics and strategy. We present a dataset of StarCraft games encompassing the most of the games' state (not only player's orders). We explain one of the possible usages of this dataset by clustering armies on their compositions. This reduction of armies compositions to mixtures of Gaussian allow for strategic reasoning at the level of the components. We evaluated this clustering method by predicting the outcomes of battles based on armies compositions' mixtures components