Divergences and distributions are deeply related concepts studied extensively in various fields. This paper is another attempt that casts their relations specifically into that of beta divergences and dispersion models and studies accordingly. The main consequence of this study is that beta divergence and (half of) statistical deviance are represented identical equations and they are, therefore, equivalent measures. In this respect, formulation of beta divergence is generalized and thus is extended beyond its Tweedie related classical forms [1], [2], [3], [4] and is aligned with exponential dispersion models. This is achieved by defining beta divergences as a function of so-called variance functions of exponential dispersion models. One immediate consequence is that we can compute beta divergence for non-Tweedie models such as negative binomial or hyperbolic secant distribution.

Discriminative latent-variable models are typically learned using EM or gradient-based optimization, which suffer from local optima. In this paper, we develop a new computationally efficient and provably consistent estimator for a mixture of linear regressions, a simple instance of a discriminative latent-variable model. Our approach relies on a low-rank linear regression to recover a symmetric tensor, which can be factorized into the parameters using a tensor power method. We prove rates of convergence for our estimator and provide an empirical evaluation illustrating its strengths relative to local optimization (EM).

Conditional independence tests (CI tests) have received special attention lately in Machine Learning and Computational Intelligence related literature as an important indicator of the relationship among the variables used by their models. In the field of Probabilistic Graphical Models (PGM)--which includes Bayesian Networks (BN) models--CI tests are especially important for the task of learning the PGM structure from data. In this paper, we propose the Full Bayesian Significance Test (FBST) for tests of conditional independence for discrete datasets. FBST is a powerful Bayesian test for precise hypothesis, as an alternative to frequentist's significance tests (characterized by the calculation of the \emph{p-value}).

The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov Random Field, from very limited samples. We propose a novel algorithm for solving the resulting optimization problem which is a regularized log-determinant program. In contrast to recent state-of-the-art methods that largely use first order gradient information, our algorithm is based on Newton's method and employs a quadratic approximation, but with some modifications that leverage the structure of the sparse Gaussian MLE problem. We show that our method is superlinearly convergent, and present experimental results using synthetic and real-world application data that demonstrate the considerable improvements in performance of our method when compared to other state-of-the-art methods.

Bayesian Reinforcement Learning (RL) is capable of not only incorporating domain knowledge, but also solving the exploration-exploitation dilemma in a natural way. As Bayesian RL is intractable except for special cases, previous work has proposed several approximation methods. However, these methods are usually too sensitive to parameter values, and finding an acceptable parameter setting is practically impossible in many applications. In this paper, we propose a new algorithm that greedily approximates Bayesian RL to achieve robustness in parameter space. We show that for a desired learning behavior, our proposed algorithm has a polynomial sample complexity that is lower than those of existing algorithms. We also demonstrate that the proposed algorithm naturally outperforms other existing algorithms when the prior distributions are not significantly misleading. On the other hand, the proposed algorithm cannot handle greatly misspecified priors as well as the other algorithms can. This is a natural consequence of the fact that the proposed algorithm is greedier than the other algorithms. Accordingly, we discuss a way to select an appropriate algorithm for different tasks based on the algorithms' greediness. We also introduce a new way of simplifying Bayesian planning, based on which future work would be able to derive new algorithms.

The performance of a modulation classifier is highly sensitive to channel signal-to-noise ratio (SNR). In this paper, we focus on amplitude-phase modulations and propose a modulation classification framework based on centralized data fusion using multiple radios and the hybrid maximum likelihood (ML) approach. In order to alleviate the computational complexity associated with ML estimation, we adopt the Expectation Maximization (EM) algorithm. Due to SNR diversity, the proposed multi-radio framework provides robustness to channel SNR. Numerical results show the superiority of the proposed approach with respect to single radio approaches as well as to modulation classifiers using moments based estimators.

When parts of the states in a goal POMDP are fully observable and some actions are deterministic it is possible to take advantage of these properties to efficiently generate approximate solutions. Actions that deterministically affect the fully observable component of the world state can be abstracted away and combined into macro actions, permitting a planner to converge more quickly. This processing can be separated from the main search procedure, allowing us to leverage existing POMDP solvers. Theoretical results show how a POMDP can be analyzed to identify the exploitable properties and formal guarantees are provided showing that the use of macro actions preserves solvability. The efficiency of the method is demonstrated with examples when used in combination with existing POMDP solvers.

Dynamic programming is a well-known approach for solving MDPs. In large state spaces, asynchronous versions like Real-Time Dynamic Programming have been applied successfully. If unfolded into equivalent trees, Monte-Carlo Tree Search algorithms are a valid alternative. UCT, the most popular representative, obtains good anytime behavior by guiding the search towards promising areas of the search tree. The Heuristic Search algorithm AO∗ finds optimal solutions for MDPs that can be represented as acyclic AND/OR graphs. We introduce a common framework, Trial-based Heuristic Tree Search, that subsumes these approaches and distinguishes them based on five ingredients: heuristic function, backup function, action selection, outcome selection, and trial length. Using this framework, we describe three new algorithms which mix these ingredients in novel ways in an attempt to combine their different strengths. Our evaluation shows that two of our algorithms not only provide superior theoretical properties to UCT, but also outperform state-of-the-art approaches experimentally.

We propose a novel receiver for orthogonal frequency division multiplexing (OFDM) transmissions in impulsive noise environments. Impulsive noise arises in many modern wireless and wireline communication systems, such as Wi-Fi and powerline communications, due to uncoordinated interference that is much stronger than thermal noise. We first show that the bit-error-rate optimal receiver jointly estimates the propagation channel coefficients, the noise impulses, the finite-alphabet symbols, and the unknown bits. We then propose a near-optimal yet computationally tractable approach to this joint estimation problem using loopy belief propagation. In particular, we merge the recently proposed "generalized approximate message passing" (GAMP) algorithm with the forward-backward algorithm and soft-input soft-output decoding using a "turbo" approach. Numerical results indicate that the proposed receiver drastically outperforms existing receivers under impulsive noise and comes within 1 dB of the matched-filter bound. Meanwhile, with N tones, the proposed factor-graph-based receiver has only O(N log N) complexity, and it can be parallelized.

A mean function in reproducing kernel Hilbert space, or a kernel mean, is an important part of many applications ranging from kernel principal component analysis to Hilbert-space embedding of distributions. Given finite samples, an empirical average is the standard estimate for the true kernel mean. We show that this estimator can be improved via a well-known phenomenon in statistics called Stein's phenomenon. After consideration, our theoretical analysis reveals the existence of a wide class of estimators that are better than the standard. Focusing on a subset of this class, we propose efficient shrinkage estimators for the kernel mean. Empirical evaluations on several benchmark applications clearly demonstrate that the proposed estimators outperform the standard kernel mean estimator.