Generative Supervised Classification Using Dirichlet Process Priors.

Choosing the appropriate parameter prior distributions associated to a given Bayesian model is a challenging problem. Conjugate priors can be selected for simplicity motivations. However, conjugate priors can be too restrictive to accurately model the available prior information. This paper studies a new generative supervised classifier which assumes that the parameter prior distributions conditioned on each class are mixtures of Dirichlet processes. The motivations for using mixtures of Dirichlet processes is their known ability to model accurately a large class of probability distributions. A Monte Carlo method allowing one to sample according to the resulting class-conditional posterior distributions is then studied. The parameters appearing in the class-conditional densities can then be estimated using these generated samples (following Bayesian learning). The proposed supervised classifier is applied to the classification of altimetric waveforms backscattered from different surfaces (oceans, ices, forests, and deserts). This classification is a first step before developing tools allowing for the extraction of useful geophysical information from altimetric waveforms backscattered from nonoceanic surfaces

Classification of chirp signals using hierarchical bayesian learning and MCMC methods

This paper addresses the problem of classifying chirp signals using hierarchical Bayesian learning together with Markov chain Monte Carlo (MCMC) methods. Bayesian learning consists of estimating the distribution of the observed data conditional on each class from a set of training samples. Unfortunately, this estimation requires to evaluate intractable multidimensional integrals. This paper studies an original implementation of hierarchical Bayesian learning that estimates the class conditional probability densities using MCMC methods. The performance of this implementation is first studied via an academic example for which the class conditional densities are known. The problem of classifying chirp signals is then addressed by using a similar hierarchical Bayesian learning implementation based on a Metropolis-within-Gibbs algorithm

Maximum likelihood parameter estimation for latent variable models using sequential Monte Carlo

We present a sequential Monte Carlo (SMC) method for maximum likelihood (ML) parameter estimation in latent variable models. Standard methods rely on gradient algorithms such as the Expectation- Maximization (EM) algorithm and its Monte Carlo variants. Our approach is different and motivated by similar considerations to simulated annealing (SA); that is we propose to sample from a sequence of artificial distributions whose support concentrates itself on the set of ML estimates. To achieve this we use SMC methods. We conclude by presenting simulation results on a toy problem and a nonlinear non-Gaussian time series model

A Unified View of TD Algorithms; Introducing Full-Gradient TD and Equi-Gradient Descent TD

International audienceThis paper addresses the issue of policy evaluation in Markov Decision Processes, using linear function approximation. It provides a unified view of algorithms such as TD(lambda), LSTD(lambda), iLSTD, residual-gradient TD. It is asserted that they all consist in minimizing a gradient function and differ by the form of this function and their means of minimizing it. Two new schemes are introduced in that framework: Full-gradient TD which uses a generalization of the principle introduced in iLSTD, and EGD TD, which reduces the gradient by successive equi-gradient descents. These three algorithms form a new intermediate family with the interesting property of making much better use of the samples than TD while keeping a gradient descent scheme, which is useful for complexity issues and optimistic policy iteration

Sparse Temporal Difference Learning using LASSO

International audienceWe consider the problem of on-line value function estimation in reinforcement learning. We concentrate on the function approximator to use. To try to break the curse of dimensionality, we focus on non parametric function approximators. We propose to fit the use of kernels into the temporal difference algorithms by using regression via the LASSO. We introduce the equi-gradient descent algorithm (EGD) which is a direct adaptation of the one recently introduced in the LARS algorithm family for solving the LASSO. We advocate our choice of the EGD as a judicious algorithm for these tasks. We present the EGD algorithm in details as well as some experimental results. We insist on the qualities of the EGD for reinforcement learning

Equi-Gradient Temporal Difference Learning

Equi-Gradient Temporal Difference Learnin

Robust Unsupervised Speaker Segmentation for Audio Diarization

Audio diarization is the process of partitioning an input audio stream into homogeneous regions according to their specific audio sources. These sources can include audio type (speech, music, background noise, ect.), speaker identity and channel characteristics. With the continually increasing number of larges volumes of spoken documents including broadcasts, voice mails, meetings and telephone conversations, diarization has received a great deal of interest in recent years which significantly impacts performances of automatic speech recognition and audio indexing systems. A subtype of audio diarization, where the speech segments of the signal are broken into different speakers, is speaker diarization. It generally answers to the question "Who spoke when?" and it is divided in two modules: speaker segmentation and speaker clustering. This chapter discusses the problem of automatically detecting speaker change points presented in a given audio stream, without prior acoustic information on the speakers. We introduce a new unsupervised speaker segmentation technique based on One Class Support Vector Machines (1-SVMs) robust to different acoustic conditions. We evaluated the robustness improvements of this method by segmenting different types of audio stream (broadcast news, meetings and telephone conversations) and comparing the results with model selection segmentation techniques based on the Bayesian information criterion (BIC)

Joint segmentation of piecewise constant autoregressive processes by using a hierarchical model and a Bayesian sampling approach

International audienceWe propose a joint segmentation algorithm for piecewise constant autoregressive (AR) processes recorded by several independent sensors. The algorithm is based on a hierarchical Bayesian model. Appropriate priors allow to introduce correlations between the change locations of the observed signals. Numerical problems inherent to Bayesian inference are solved by a Gibbs sampling strategy. The proposed joint segmentation methodology yields improved segmentation results when compared to parallel and independent individual signal segmentations. The initial algorithm is derived for piecewise constant AR processes whose orders are fixed on each segment. However, an extension to models with unknown model orders is also discussed. Theoretical results are illustrated by many simulations conducted with synthetic signals and real arc-tracking and speech signals

Online bayesian inference in some time-frequency representations of non-stationary processes

The use of Bayesian inference in the inference of time-frequency representations has, thus far, been limited to offline analysis of signals, using a smoothing spline based model of the time-frequency plane. In this paper we introduce a new framework that allows the routine use of Bayesian inference for online estimation of the time-varying spectral density of a locally stationary Gaussian process. The core of our approach is the use of a likelihood inspired by a local Whittle approximation. This choice, along with the use of a recursive algorithm for non-parametric estimation of the local spectral density, permits the use of a particle filter for estimating the time-varying spectral density online. We provide demonstrations of the algorithm through tracking chirps and the analysis of musical data