In this paper, we address the problem of learning the structure of a pairwise graphical model from samples in a high-dimensional setting. Our first main result studies the sparsistency, or consistency in sparsity pattern recovery, properties of a forward-backward greedy algorithm as applied to general statistical models. As a special case, we then apply this algorithm to learn the structure of a discrete graphical model via neighborhood estimation. As a corollary of our general result, we derive sufficient conditions on the number of samples n, the maximum node-degree d and the problem size p, as well as other conditions on the model parameters, so that the algorithm recovers all the edges with high probability. Our result guarantees graph selection for samples scaling as n = Omega(d log(p)), in contrast to existing convex-optimization based algorithms that require a sample complexity of Omega(d^2 log(p)). Further, the greedy algorithm only requires a restricted strong convexity condition which is typically milder than irrepresentability assumptions. We corroborate these results using numerical simulations at the end.

In this paper we describe a maximum likelihood likelihood approach for dictionary learning in the multiplicative exponential noise model. This model is prevalent in audio signal processing where it underlies a generative composite model of the power spectrogram. Maximum joint likelihood estimation of the dictionary and expansion coefficients leads to a nonnegative matrix factorization problem where the Itakura-Saito divergence is used. The optimality of this approach is in question because the number of parameters (which include the expansion coefficients) grows with the number of observations. In this paper we describe a variational procedure for optimization of the marginal likelihood, i.e., the likelihood of the dictionary where the activation coefficients have been integrated out (given a specific prior). We compare the output of both maximum joint likelihood estimation (i.e., standard Itakura-Saito NMF) and maximum marginal likelihood estimation (MMLE) on real and synthetical datasets. The MMLE approach is shown to embed automatic model order selection, akin to automatic relevance determination.

We propose a novel Adaptive Markov Chain Monte Carlo algorithm to compute the partition function. In particular, we show how to accelerate a flat histogram sampling technique by significantly reducing the number of ``null moves'' in the chain, while maintaining asymptotic convergence properties. Our experiments show that our method converges quickly to highly accurate solutions on a range of benchmark instances, outperforming other state-of-the-art methods such as IJGP, TRW, and Gibbs sampling both in run-time and accuracy. We also show how obtaining a so-called density of states distribution allows for efficient weight learning in Markov Logic theories.

Unlike existing nonparametric Bayesian models, which rely solely on specially conceived priors to incorporate domain knowledge for discovering improved latent representations, we study nonparametric Bayesian inference with regularization on the desired posterior distributions. While priors can indirectly affect posterior distributions through Bayes' theorem, imposing posterior regularization is arguably more direct and in some cases can be much easier. We particularly focus on developing infinite latent support vector machines (iLSVM) and multi-task infinite latent support vector machines (MT-iLSVM), which explore the large-margin idea in combination with a nonparametric Bayesian model for discovering predictive latent features for classification and multi-task learning, respectively. We present efficient inference methods and report empirical studies on several benchmark datasets. Our results appear to demonstrate the merits inherited from both large-margin learning and Bayesian nonparametrics.

The object people perceive in an image can depend on its orientation relative to the scene it is in (its reference frame). For example, the images of the symbols $\times$ and $+$ differ by a 45 degree rotation. Although real scenes have multiple images and reference frames, psychologists have focused on scenes with only one reference frame. We propose an ideal observer model based on nonparametric Bayesian statistics for inferring the number of reference frames in a scene and their parameters. When an ambiguous image could be assigned to two conflicting reference frames, the model predicts two factors should influence the reference frame inferred for the image: The image should be more likely to share the reference frame of the closer object ({\em proximity}) and it should be more likely to share the reference frame containing the most objects ({\em alignment}). We confirm people use both cues using a novel methodology that allows for easy testing of human reference frame inference.

Policy gradient is a useful model-free reinforcement learning approach, but it tends to suffer from instability of gradient estimates. In this paper, we analyze and improve the stability of policy gradient methods. We first prove that the variance ofgradient estimates in the PGPE (policy gradients with parameter-based exploration) method is smaller than that of the classical REINFORCE method under a mild assumption. We then derive the optimal baseline for PGPE, which contributes to further reducing the variance. We also theoretically show that PGPE with the optimal baseline is more preferable than REINFORCE with the optimal baseline in terms of the variance of gradient estimates. Finally, we demonstrate the usefulness of the improved PGPE method through experiments.

Log-linear models are widely used probability models for statistical pattern recognition. Typically, log-linear models are trained according to a convex criterion. In recent years, the interest in log-linear models has greatly increased. The optimization of log-linear model parameters is costly and therefore an important topic, in particular for large-scale applications. Different optimization algorithms have been evaluated empirically in many papers. In this work, we analyze the optimization problem analytically and show that the training of log-linear models can be highly ill-conditioned. We verify our findings on two handwriting tasks. By making use of our convergence analysis, we obtain good results on a large-scale continuous handwriting recognition task with a simple and generic approach.

It has been argued that perceptual multistability reflects probabilistic inference performed by the brain when sensory input is ambiguous. Alternatively, more traditional explanations of multistability refer to low-level mechanisms such as neuronal adaptation. We employ a Deep Boltzmann Machine (DBM) model of cortical processing to demonstrate that these two different approaches can be combined in the same framework. Based on recent developments in machine learning, we show how neuronal adaptation can be understood as a mechanism that improves probabilistic, sampling-based inference. Using the ambiguous Necker cube image, we analyze the perceptual switching exhibited by the model. We also examine the influence of spatial attention, and explore how binocular rivalry can be modeled with the same approach. Our work joins earlier studies in demonstrating how the principles underlying DBMs relate to cortical processing, and offers novel perspectives on the neural implementation of approximate probabilistic inference in the brain.

A common approach for handling the complexity and inherent ambiguities of 3D human pose estimation is to use pose priors learned from training data. Existing approaches however, are either too simplistic (linear), too complex to learn, or can only learn latent spaces from "simple data", i.e., single activities such as walking or running. In this paper, we present an efficient stochastic gradient descent algorithm that is able to learn probabilistic non-linear latent spaces composed of multiple activities. Furthermore, we derive an incremental algorithm for the online setting which can update the latent space without extensive relearning. We demonstrate the effectiveness of our approach on the task of monocular and multi-view tracking and show that our approach outperforms the state-of-the-art.

In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying graph structure of a sparse Gaussian Markov Random Field (GMRF). We present two novel greedy approaches to solving this problem. The first estimates the non-zero covariates of the overall inverse covariance matrix using a series of global forward and backward greedy steps. The second estimates the neighborhood of each node in the graph separately, again using greedy forward and backward steps, and combines the intermediate neighborhoods to form an overall estimate. The principal contribution of this paper is a rigorous analysis of the sparsistency, or consistency in recovering the sparsity pattern of the inverse covariance matrix. Surprisingly, we show that both the local and global greedy methods learn the full structure of the model with high probability given just $O(d\log(p))$ samples, which is a \emph{significant} improvement over state of the art $\ell_1$-regularized Gaussian MLE (Graphical Lasso) that requires $O(d^2\log(p))$ samples. Moreover, the restricted eigenvalue and smoothness conditions imposed by our greedy methods are much weaker than the strong irrepresentable conditions required by the $\ell_1$-regularization based methods. We corroborate our results with extensive simulations and examples, comparing our local and global greedy methods to the $\ell_1$-regularized Gaussian MLE as well as the Neighborhood Greedy method to that of nodewise $\ell_1$-regularized linear regression (Neighborhood Lasso).