Bayesian models are established as one of the main successful paradigms for complex problems in machine learning. To handle intractable inference, research in this area has developed new approximation methods that are fast and effective. However, theoretical analysis of the performance of such approximations is not well developed. The paper furthers such analysis by providing bounds on the excess risk of variational inference algorithms and related regularized loss minimization algorithms for a large class of latent variable models with Gaussian latent variables. We strengthen previous results for variational algorithms by showing they are competitive with any point-estimate predictor.

Stochastic And-Or grammars compactly represent both compositionality and reconfigurability and have been used to model different types of data such as images and events. We present a unified formalization of stochastic And-Or grammars that is agnostic to the type of the data being modeled, and propose an unsupervised approach to learning the structures as well as the parameters of such grammars. Starting from a trivial initial grammar, our approach iteratively induces compositions and reconfigurations in a unified manner and optimizes the posterior probability of the grammar. In our empirical evaluation, we applied our approach to learning event grammars and image grammars and achieved comparable or better performance than previous approaches. Papers published at the Neural Information Processing Systems Conference.

Directed latent variable models that formulate the joint distribution as $p(x,z) p(z) p(x \mid z)$ have the advantage of fast and exact sampling. However, these models have the weakness of needing to specify $p(z)$, often with a simple fixed prior that limits the expressiveness of the model. Undirected latent variable models discard the requirement that $p(z)$ be specified with a prior, yet sampling from them generally requires an iterative procedure such as blocked Gibbs-sampling that may require many steps to draw samples from the joint distribution $p(x, z)$. We propose a novel approach to learning the joint distribution between the data and a latent code which uses an adversarially learned iterative procedure to gradually refine the joint distribution, $p(x, z)$, to better match with the data distribution on each step. GibbsNet is the best of both worlds both in theory and in practice.

Utilizing the structure of a probabilistic model can significantly increase its learning speed. Motivated by several recent applications, in particular bigram models in language processing, we consider learning low-rank conditional probability matrices under expected KL-risk. This choice makes smoothing, that is the careful handling of low-probability elements, paramount. We derive an iterative algorithm that extends classical non-negative matrix factorization to naturally incorporate additive smoothing and prove that it converges to the stationary points of a penalized empirical risk. We then derive sample-complexity bounds for the global minimizer of the penalized risk and show that it is within a small factor of the optimal sample complexity.

The most widely used technology to identify the proteins present in a complex biological sample is tandem mass spectrometry, which quickly produces a large collection of spectra representative of the peptides (i.e., protein subsequences) present in the original sample. In this work, we greatly expand the parameter learning capabilities of a dynamic Bayesian network (DBN) peptide-scoring algorithm, Didea, by deriving emission distributions for which its conditional log-likelihood scoring function remains concave. We show that this class of emission distributions, called Convex Virtual Emissions (CVEs), naturally generalizes the log-sum-exp function while rendering both maximum likelihood estimation and conditional maximum likelihood estimation concave for a wide range of Bayesian networks. Utilizing CVEs in Didea allows efficient learning of a large number of parameters while ensuring global convergence, in stark contrast to Didea's previous parameter learning framework (which could only learn a single parameter using a costly grid search) and other trainable models (which only ensure convergence to local optima). The newly trained scoring function substantially outperforms the state-of-the-art in both scoring function accuracy and downstream Fisher kernel analysis.

In large-scale applications of undirected graphical models, such as social networks and biological networks, similar patterns occur frequently and give rise to similar parameters. In this situation, it is beneficial to group the parameters for more efficient learning. We show that even when the grouping is unknown, we can infer these parameter groups during learning via a Bayesian approach. We impose a Dirichlet process prior on the parameters. Posterior inference usually involves calculating intractable terms, and we propose two approximation algorithms, namely a Metropolis-Hastings algorithm with auxiliary variables and a Gibbs sampling algorithm with stripped Beta approximation (Gibbs_SBA).

We propose a generalized Gibbs sampler algorithm for obtaining samples approximately distributed from a high-dimensional Gaussian distribution. Similarly to Hogwild methods, our approach does not target the original Gaussian distribution of interest, but an approximation to it. Contrary to Hogwild methods, a single parameter allows us to trade bias for variance. We show empirically that our method is very flexible and performs well compared to Hogwild-type algorithms. Papers published at the Neural Information Processing Systems Conference.

We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian inference. Moreover, the optimization problem induces a new regularization for the posterior embedding estimator, which is faster and has comparable performance to the squared regularization in kernel Bayes' rule. This regularization coincides with a former thresholding approach used in kernel POMDPs whose consistency remains to be established. Our theoretical work solves this open problem and provides consistency analysis in regression settings.

In sequential decision making, it is often important and useful for end users to understand the underlying patterns or causes that lead to the corresponding decisions. However, typical deep reinforcement learning algorithms seldom provide such information due to their black-box nature. In this paper, we present a probabilistic model, Q-LDA, to uncover latent patterns in text-based sequential decision processes. The model can be understood as a variant of latent topic models that are tailored to maximize total rewards; we further draw an interesting connection between an approximate maximum-likelihood estimation of Q-LDA and the celebrated Q-learning algorithm. We demonstrate in the text-game domain that our proposed method not only provides a viable mechanism to uncover latent patterns in decision processes, but also obtains state-of-the-art rewards in these games. Papers published at the Neural Information Processing Systems Conference.

Principal geodesic analysis (PGA) is a generalization of principal component analysis (PCA) for dimensionality reduction of data on a Riemannian manifold. Currently PGA is defined as a geometric fit to the data, rather than as a probabilistic model. Inspired by probabilistic PCA, we present a latent variable model for PGA that provides a probabilistic framework for factor analysis on manifolds. To compute maximum likelihood estimates of the parameters in our model, we develop a Monte Carlo Expectation Maximization algorithm, where the expectation is approximated by Hamiltonian Monte Carlo sampling of the latent variables. We demonstrate the ability of our method to recover the ground truth parameters in simulated sphere data, as well as its effectiveness in analyzing shape variability of a corpus callosum data set from human brain images.