Within the framework of probably approximately correct Markov decision processes (PAC-MDP), much theoretical work has focused on methods to attain near optimality after a relatively long period of learning and exploration. However, practical concerns require the attainment of satisfactory behavior within a short period of time. In this paper, we relax the PAC-MDP conditions to reconcile theoretically driven exploration methods and practical needs. We propose simple algorithms for discrete and continuous state spaces, and illustrate the benefits of our proposed relaxation via theoretical analyses and numerical examples. Our algorithms also maintain anytime error bounds and average loss bounds. Our approach accommodates both Bayesian and non-Bayesian methods.

We propose a probabilistic model for non-exhaustive and overlapping (NEO) bi-clustering. Our goal is to extract a few sub-matrices from the given data matrix, where entries of a sub-matrix are characterized by a specific distribution or parameters. Existing NEO biclustering methods typically require the number of sub-matrices to be extracted, which is essentially difficult to fix a priori. In this paper, we extend the plaid model, known as one of the best NEO bi-clustering algorithms, to allow infinite bi-clustering; NEO bi-clustering without specifying the number of sub-matrices. Our model can represent infinite sub-matrices formally. We develop a MCMC inference without the finite truncation, which potentially addresses all possible numbers of sub-matrices. Experiments quantitatively and qualitatively verify the usefulness of the proposed model. The results reveal that our model can offer more precise and in-depth analysis of sub-matrices.

Buoyed by the success of deep multilayer neural networks, there is renewed interest in scalable learning of Bayesian neural networks. Here, we study algorithms that utilize recent advances in Bayesian inference to efficiently learn distributions over network weights. In particular, we focus on recently proposed assumed density filtering based methods for learning Bayesian neural networks -- Expectation and Probabilistic backpropagation. Apart from scaling to large datasets, these techniques seamlessly deal with non-differentiable activation functions and provide parameter (learning rate, momentum) free learning. In this paper, we first rigorously compare the two algorithms and in the process develop several extensions, including a version of EBP for continuous regression problems and a PBP variant for binary classification. Next, we extend both algorithms to deal with multiclass classification and count regression problems. On a variety of diverse real world benchmarks, we find our extensions to be effective, achieving results competitive with the state-of-the-art.

Bayesian models provide a framework for probabilistic modelling of complex datasets. Many such models are computationally demanding, especially in the presence of large datasets. In sensor network applications, statistical (Bayesian) parameter estimation usually relies on decentralized algorithms, in which both data and computation are distributed across the nodes of the network. In this paper we propose a framework for decentralized Bayesian learning using Bregman Alternating Direction Method of Multipliers (B-ADMM). We demonstrate the utility of our framework, with Mean Field Variational Bayes (MFVB) as the primitive for distributed affine structure from motion (SfM).

We study the robustness of active learning (AL) algorithms against prior misspecification: whether an algorithm achieves similar performance using a perturbed prior as compared to using the true prior. In both the average and worst cases of the maximum coverage setting, we prove that all alpha-approximate algorithms are robust (i.e., near alpha-approximate) if the utility is Lipschitz continuous in the prior. We further show that robustness may not be achieved if the utility is non-Lipschitz. This suggests we should use a Lipschitz utility for AL if robustness is required. For the minimum cost setting, we can also obtain a robustness result for approximate AL algorithms. Our results imply that many commonly used AL algorithms are robust against perturbed priors. We then propose the use of a mixture prior to alleviate the problem of prior misspecification. We analyze the robustness of the uniform mixture prior and show experimentally that it performs reasonably well in practice.

The Dirichlet process mixtures (DPM) can automatically infer the model complexity from data. Hence it has attracted significant attention recently, and is widely used for model selection and clustering. As a generative model, it generally requires prior base distribution to learn component parameters by maximizing posterior probability. In contrast, discriminative classifiers model the conditional probability directly, and have yielded better results than generative classifiers.In this paper, we propose a maximum margin Dirichlet process mixture for clustering, which is different from the traditional DPM for parameter modeling. Our model takes a discriminative clustering approach, by maximizing a conditional likelihood to estimate parameters. In particular, we take a EM-like algorithm by leveraging Gibbs sampling algorithm for inference, which in turn can be perfectly embedded in the online maximum margin learning procedure to update model parameters. We test our model and show comparative results over the traditional DPM and other nonparametric clustering approaches.

In recent years, several probabilistic techniques have been applied to various debugging problems. However, most existing probabilistic debugging systems use relatively simple statistical models, and fail to generalize across multiple programs. In this work, we propose Tractable Fault Localization Models (TFLMs) that can be learned from data, and probabilistically infer the location of the bug. While most previous statistical debugging methods generalize over many executions of a single program, TFLMs are trained on a corpus of previously seen buggy programs, and learn to identify recurring patterns of bugs. Widely-used fault localization techniques such as TARANTULA evaluate the suspiciousness of each line in isolation; in contrast, a TFLM defines a joint probability distribution over buggy indicator variables for each line. Joint distributions with rich dependency structure are often computationally intractable; TFLMs avoid this by exploiting recent developments in tractable probabilistic models (specifically, Relational SPNs). Further, TFLMs can incorporate additional sources of information, including coverage-based features such as TARANTULA. We evaluate the fault localization performance of TFLMs that include TARANTULA scores as features in the probabilistic model. Our study shows that the learned TFLMs isolate bugs more effectively than previous statistical methods or using TARANTULA directly.

A key challenge in complex activity recognition is the fact that a complex activity can often be performed in several different ways, with each consisting of its own configuration of atomic actions and their temporal dependencies. This leads us to define an atomic activity-based probabilistic framework that employs Allen's interval relations to represent local temporal dependencies. The framework introduces a latent variable from the Chinese Restaurant Process to explicitly characterize these unique internal configurations of a particular complex activity as a variable number of tables.It can be analytically shown that the resulting interval network satisfies the transitivity property, and as a result, all local temporal dependencies can be retained and are globally consistent.Empirical evaluations on benchmark datasets suggest our approach significantly outperforms the state-of-the-art methods.

Noisy and incomplete data restoration is a critical preprocessing step in developing effective learning algorithms, which targets to reduce the effect of noise and missing values in data. By utilizing attribute correlations and/or instance similarities, various techniques have been developed for data denoising and imputation tasks. However, current existing data restoration methods are either specifically designed for a particular task, or incapable of dealing with mixed-attribute data. In this paper, we develop a new probabilistic model to provide a general and principled method for restoring mixed-attribute data. The main contributions of this study are twofold: a) a unified generative model, utilizing a generic random mixed field (RMF) prior, is designed to exploit mixed-attribute correlations; and b) a structured mean-field variational approach is proposed to solve the challenging inference problem of simultaneous denoising and imputation. We evaluate our method by classification experiments on both synthetic data and real benchmark datasets. Experiments demonstrate, our approach can effectively improve the classification accuracy of noisy and incomplete data by comparing with other data restoration methods.

We present a discriminative nonparametric latent feature relational model (LFRM) for link prediction to automatically infer the dimensionality of latent features. Under the generic RegBayes (regularized Bayesian inference) framework, we handily incorporate the prediction loss with probabilistic inference of a Bayesian model; set distinct regularization parameters for different types of links to handle the imbalance issue in real networks; and unify the analysis of both the smooth logistic log-loss and the piecewise linear hinge loss. For the nonconjugate posterior inference, we present a simple Gibbs sampler via data augmentation, without making restricting assumptions as done in variational methods. We further develop an approximate sampler using stochastic gradient Langevin dynamics to handle large networks with hundreds of thousands of entities and millions of links, orders of magnitude larger than what existing LFRM models can process. Extensive studies on various real networks show promising performance.