Logistic-normal topic models can effectively discover correlation structures among latent topics. However, their inference remains a challenge because of the non-conjugacy between the logistic-normal prior and multinomial topic mixing proportions. Existing algorithms either make restricting mean-field assumptions or are not scalable to large-scale applications. This paper presents a partially collapsed Gibbs sampling algorithm that approaches the provably correct distribution by exploring the ideas of data augmentation. To improve time efficiency, we further present a parallel implementation that can deal with large-scale applications and learn the correlation structures of thousands of topics from millions of documents. Extensive empirical results demonstrate the promise.

We introduce a new objective function for pool-based Bayesian active learning with probabilistic hypotheses. This objective function, called the policy Gibbs error, is the expected error rate of a random classifier drawn from the prior distribution on the examples adaptively selected by the active learning policy. Exact maximization of the policy Gibbs error is hard, so we propose a greedy strategy that maximizes the Gibbs error at each iteration, where the Gibbs error on an instance is the expected error of a random classifier selected from the posterior label distribution on that instance. We apply this maximum Gibbs error criterion to three active learning scenarios: non-adaptive, adaptive, and batch active learning. In each scenario, we prove that the criterion achieves near-maximal policy Gibbs error when constrained to a fixed budget. For practical implementations, we provide approximations to the maximum Gibbs error criterion for Bayesian conditional random fields and transductive Naive Bayes. Our experimental results on a named entity recognition task and a text classification task show that the maximum Gibbs error criterion is an effective active learning criterion for noisy models.

Given a Markov Decision Process (MDP) with $n$ states and $m$ actions per state, we study the number of iterations needed by Policy Iteration (PI) algorithms to converge to the optimal $\gamma$-discounted optimal policy. We consider two variations of PI: Howard's PI that changes the actions in all states with a positive advantage, and Simplex-PI that only changes the action in the state with maximal advantage. We show that Howard's PI terminates after at most $ O \left( \frac{ n m}{1-\gamma} \log \left( \frac{1}{1-\gamma} \right)\right) $ iterations, improving by a factor $O(\log n)$ a result by Hansen et al. (2013), while Simplex-PI terminates after at most $ O \left( \frac{n^2 m}{1-\gamma} \log \left( \frac{1}{1-\gamma} \right)\right) $ iterations, improving by a factor $O(\log n)$ a result by Ye (2011). Under some structural assumptions of the MDP, we then consider bounds that are independent of the discount factor~$\gamma$: given a measure of the maximal transient time $\tau_t$ and the maximal time $\tau_r$ to revisit states in recurrent classes under all policies, we show that Simplex-PI terminates after at most $ \tilde O \left( n^3 m^2 \tau_t \tau_r \right) $ iterations. This generalizes a recent result for deterministic MDPs by Post & Ye (2012), in which $\tau_t \le n$ and $\tau_r \le n$. We explain why similar results seem hard to derive for Howard's PI. Finally, under the additional (restrictive) assumption that the state space is partitioned in two sets, respectively states that are transient and recurrent for all policies, we show that Simplex-PI and Howard's PI terminate after at most $ \tilde O(nm (\tau_t+\tau_r))$ iterations.

This paper addresses the problem of online planning in Markov decision processes using a randomized simulator, under a budget constraint. We propose a new algorithm which is based on the construction of a forest of planning trees, where each tree corresponds to a random realization of the stochastic environment. The trees are constructed using a "safe" optimistic planning strategy combining the optimistic principle (in order to explore the most promising part of the search space first) with a safety principle (which guarantees a certain amount of uniform exploration). In the decision-making step of the algorithm, the individual trees are aggregated and an immediate action is recommended. We provide a finite-sample analysis and discuss the tradeoff between the principles of optimism and safety. We also report numerical results on a benchmark problem. Our algorithm performs as well as state-of-the-art optimistic planning algorithms, and better than a related algorithm which additionally assumes the knowledge of all transition distributions.

We propose a novel class of algorithms for low rank matrix completion. Our approach builds on novel penalty functions on the singular values of the low rank matrix. By exploiting a mixture model representation of this penalty, we show that a suitably chosen set of latent variables enables to derive an Expectation-Maximization algorithm to obtain a Maximum A Posteriori estimate of the completed low rank matrix. The resulting algorithm is an iterative soft-thresholded algorithm which iteratively adapts the shrinkage coefficients associated to the singular values. The algorithm is simple to implement and can scale to large matrices. We provide numerical comparisons between our approach and recent alternatives showing the interest of the proposed approach for low rank matrix completion.

The idea of computer vision as the Bayesian inverse problem to computer graphics has a long history and an appealing elegance, but it has proved difficult to directly implement. Instead, most vision tasks are approached via complex bottom-up processing pipelines. Here we show that it is possible to write short, simple probabilistic graphics programs that define flexible generative models and to automatically invert them to interpret real-world images. Generative probabilistic graphics programs consist of a stochastic scene generator, a renderer based on graphics software, a stochastic likelihood model linking the renderer's output and the data, and latent variables that adjust the fidelity of the renderer and the tolerance of the likelihood model. Representations and algorithms from computer graphics, originally designed to produce high-quality images, are instead used as the deterministic backbone for highly approximate and stochastic generative models. This formulation combines probabilistic programming, computer graphics, and approximate Bayesian computation, and depends only on general-purpose, automatic inference techniques. We describe two applications: reading sequences of degraded and adversarially obscured alphanumeric characters, and inferring 3D road models from vehicle-mounted camera images. Each of the probabilistic graphics programs we present relies on under 20 lines of probabilistic code, and supports accurate, approximately Bayesian inferences about ambiguous real-world images.

People can learn a new visual class from just one example, yet machine learning algorithms typically require hundreds or thousands of examples to tackle the same problems. Here we present a Hierarchical Bayesian model based on compositionality and causality that can learn a wide range of natural (although simple) visual concepts, generalizing in human-like ways from just one image. We evaluated performance on a challenging one-shot classification task, where our model achieved a human-level error rate while substantially outperforming two deep learning models. We also used a visual Turing test" to show that our model produces human-like performance on other conceptual tasks, including generating new examples and parsing."

Many powerful Monte Carlo techniques for estimating partition functions, such as annealed importance sampling (AIS), are based on sampling from a sequence of intermediate distributions which interpolate between a tractable initial distribution and an intractable target distribution. The near-universal practice is to use geometric averages of the initial and target distributions, but alternative paths can perform substantially better. We present a novel sequence of intermediate distributions for exponential families: averaging the moments of the initial and target distributions. We derive an asymptotically optimal piecewise linear schedule for the moments path and show that it performs at least as well as geometric averages with a linear schedule. Moment averaging performs well empirically at estimating partition functions of restricted Boltzmann machines (RBMs), which form the building blocks of many deep learning models, including Deep Belief Networks and Deep Boltzmann Machines.

Structure learning algorithms for graphical models have focused almost exclusively on stable environments in which the underlying generative process does not change; that is, they assume that the generating model is globally stationary. In real-world environments, however, such changes often occur without warning or signal. Real-world data often come from generating models that are only locally stationary. In this paper, we present LoSST, a novel, heuristic structure learning algorithm that tracks changes in graphical model structure or parameters in a dynamic, real-time manner. We show by simulation that the algorithm performs comparably to batch-mode learning when the generating graphical structure is globally stationary, and significantly better when it is only locally stationary.

A long term goal of Interactive Reinforcement Learning is to incorporate non-expert human feedback to solve complex tasks. State-of-the-art methods have approached this problem by mapping human information to reward and value signals to indicate preferences and then iterating over them to compute the necessary control policy. In this paper we argue for an alternate, more effective characterization of human feedback: Policy Shaping. We introduce Advise, a Bayesian approach that attempts to maximize the information gained from human feedback by utilizing it as direct labels on the policy. We compare Advise to state-of-the-art approaches and highlight scenarios where it outperforms them and importantly is robust to infrequent and inconsistent human feedback.