Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on probability of evidence but does not have any guarantees in terms of relative or absolute error. Our proposed approximation is a randomized importance sampling scheme that uses the Markov inequality. However, a straight-forward application of the Markov inequality may lead to poor lower bounds. We therefore propose several heuristic measures to improve its performance in practice. Empirical evaluation of our scheme with state-of- the-art lower bounding schemes reveals the promise of our approach.

We propose a new Monte Carlo algorithm for complex discrete distributions. The algorithm is motivated by the N-Fold Way, which is an ingenious event-driven MCMC sampler that avoids rejection moves at any specific state. The N-Fold Way can however get "trapped" in cycles. We surmount this problem by modifying the sampling process. This correction does introduce bias, but the bias is subsequently corrected with a carefully engineered importance sampler.

Model-based Bayesian Reinforcement Learning (BRL) allows a found formalization of the problem of acting optimally while facing an unknown environment, i.e., avoiding the exploration-exploitation dilemma. However, algorithms explicitly addressing BRL suffer from such a combinatorial explosion that a large body of work relies on heuristic algorithms. This paper introduces BOLT, a simple and (almost) deterministic heuristic algorithm for BRL which is optimistic about the transition function. We analyze BOLT's sample complexity, and show that under certain parameters, the algorithm is near-optimal in the Bayesian sense with high probability. Then, experimental results highlight the key differences of this method compared to previous work.

Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of variational approximations inspired by nonparametric kernel density estimation. The locations of these kernels and their bandwidth are treated as variational parameters and optimized to improve an approximate lower bound on the marginal likelihood of the data. Using multiple kernels allows the approximation to capture multiple modes of the posterior, unlike most other variational approximations. We demonstrate the efficacy of the nonparametric approximation with a hierarchical logistic regression model and a nonlinear matrix factorization model. We obtain predictive performance as good as or better than more specialized variational methods and sample-based approximations. The method is easy to apply to more general graphical models for which standard variational methods are difficult to derive.

We present a max-margin nonparametric latent feature relational model, which unites the ideas of max-margin learning and Bayesian nonparametrics to discover discriminative latent features for link prediction and automatically infer the unknown latent social dimension. By minimizing a hinge-loss using the linear expectation operator, we can perform posterior inference efficiently without dealing with a highly nonlinear link likelihood function; by using a fully-Bayesian formulation, we can avoid tuning regularization constants. Experimental results on real datasets appear to demonstrate the benefits inherited from max-margin learning and fully-Bayesian nonparametric inference.

We study the convergence rate of stochastic optimization of exact (NP-hard) objectives, for which only biased estimates of the gradient are available. We motivate this problem in the context of learning the structure and parameters of Ising models. We first provide a convergence-rate analysis of deterministic errors for forward-backward splitting (FBS). We then extend our analysis to biased stochastic errors, by first characterizing a family of samplers and providing a high probability bound that allows understanding not only FBS, but also proximal gradient (PG) methods. We derive some interesting conclusions: FBS requires only a logarithmically increasing number of random samples in order to converge (although at a very low rate); the required number of random samples is the same for the deterministic and the biased stochastic setting for FBS and basic PG; accelerated PG is not guaranteed to converge in the biased stochastic setting.

We present a framework for online inference in the presence of a nonexhaustively defined set of classes that incorporates supervised classification with class discovery and modeling. A Dirichlet process prior (DPP) model defined over class distributions ensures that both known and unknown class distributions originate according to a common base distribution. In an attempt to automatically discover potentially interesting class formations, the prior model is coupled with a suitably chosen data model, and sequential Monte Carlo sampling is used to perform online inference. Our research is driven by a biodetection application, where a new class of pathogen may suddenly appear, and the rapid increase in the number of samples originating from this class indicates the onset of an outbreak.

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the sample covariance matrix. In this paper we consider the situation where the data variance is already partially explained by other factors, for example sparse conditional dependencies between the covariates, or temporal correlations leaving some residual variance. We decompose the residual variance into its components through a generalised eigenvalue problem, which we call residual component analysis (RCA). We explore a range of new algorithms that arise from the framework, including one that factorises the covariance of a Gaussian density into a low-rank and a sparse-inverse component. We illustrate the ideas on the recovery of a protein-signaling network, a gene expression time-series data set and the recovery of the human skeleton from motion capture 3-D cloud data.

This paper revisits the problem of analyzing multiple ratings given by different judges. Different from previous work that focuses on distilling the true labels from noisy crowdsourcing ratings, we emphasize gaining diagnostic insights into our in-house well-trained judges. We generalize the well-known DawidSkene model (Dawid & Skene, 1979) to a spectrum of probabilistic models under the same "TrueLabel + Confusion" paradigm, and show that our proposed hierarchical Bayesian model, called HybridConfusion, consistently outperforms DawidSkene on both synthetic and real-world data sets.

Chordal graphs can be used to encode dependency models that are representable by both directed acyclic and undirected graphs. This paper discusses a very simple and efficient algorithm to learn the chordal structure of a probabilistic model from data. The algorithm is a greedy hill-climbing search algorithm that uses the inclusion boundary neighborhood over chordal graphs. In the limit of a large sample size and under appropriate hypotheses on the scoring criterion, we prove that the algorithm will find a structure that is inclusion-optimal when the dependency model of the data-generating distribution can be represented exactly by an undirected graph. The algorithm is evaluated on simulated datasets.