Since the success of Independent Component Analysis (ICA) for solving the Blind Source Separation (BSS) problem [1, 2], ICA has received considerable attention in numerous areas, such as signal processing, statistical modeling, and unsupervised learning. The performance of ICA algorithms depends significantly on the choice of the contrast function measuring statistical independence of signals a...

Learning in decentralized systems: A nonparametric approach by XuanLong Nguyen Doctor of Philosophy in Computer Science and the Designated Emphasis in Communication, Computation, and Statistics University of California, Berkeley Professor Michael I. Jordan, Chair Rapid advances in information technology result in increased deployment of decentralized decision-making systems embedded within larg...

. Most of this book emphasizes frequentist methods, especially for nonparametric problems. However, there are Bayesian approaches to many nonparametric problems. In this chapter we present some of the most commonly used nonparametric Bayesian methods. These methods place priors on infinite dimensional spaces. The priors are based on certain stochastic processes called Dirichlet processes and Ga...

Probabilistic and statistical models for the occurrence of a recurrent event over time are described. These models have applicability in the reliability, engineering, biomedical and other areas where a series of events occurs for an experimental unit as time progresses. Nonparametric inference methods, in particular, the estimation of a relevant distribution function, are described.

Statistical analysis on landmark-based shape spaces has diverse applications in morphometrics, medical diagnostics, machine vision and other areas. These shape spaces are non-Euclidean quotient manifolds. To conduct nonparametric inferences, one may define notions of centre and spread on this manifold and work with their estimates. However, it is useful to consider full likelihood-based methods...

Nonparametric control charts are presented in order to figure out the problem of detecting changes in the process median (or mean)‎, ‎or changes in the variability process where there is limited knowledge regarding the underlying process‎. ‎When observations are reported imprecise‎, ‎then it is impossible to use classical nonparametric control charts‎. ‎This paper is devoted to the problem of c...

A common problem in statistics, and other disciplines , is to approximate adequately a function of several variables. In this paper we review some possible nonparametric Bayesian models with which we can perform this multiple regression problem. We shall also demonstrate how these basic models can be extended to allow the analysis of time series , both conventional and nancial, survival analysi...

Several nonparametric methods in a regression model are presented. First, the most classical ones: piecewise polynomial estimators, estimation with Spline bases, kernel estimators and projection estimators on orthonormal bases (such as Fourier or wavelet bases). Since these methods suffer from the curse of dimensionality, we also present Generalized Additive Models and CART regression models. T...