Recent progress in Bayesian methods largely focus on non-conjugate models featured with extensive use of black-box functions: continuous functions implemented with neural networks. Using deep neural networks, Bayesian models can reasonably fit big data while at the same time capturing model uncertainty. This thesis targets at a more challenging problem: how do we model general random objects, including discrete ones, using random functions? Our conclusion is: many (discrete) random objects are in nature a composition of Poisson processes and random functions}. Thus, all discreteness is handled through the Poisson process while random functions captures the rest complexities of the object. Thus the title: composing deep learning and Bayesian nonparametric methods. This conclusion is not a conjecture. In spacial cases such as latent feature models , we can prove this claim by working on infinite dimensional spaces, and that is how Bayesian nonparametric kicks in. Moreover, we will assume some regularity assumptions on random objects such as exchangeability. Then the representations will show up magically using representation theorems. We will see this two times throughout this thesis. One may ask: when a random object is too simple, such as a non-negative random vector in the case of latent feature models, how can we exploit exchangeability? The answer is to aggregate infinite random objects and map them altogether onto an infinite dimensional space. And then assume exchangeability on the infinite dimensional space. We demonstrate two examples of latent feature models by (1) concatenating them as an infinite sequence (Section 2,3) and (2) stacking them as a 2d array (Section 4). Besides, we will see that Bayesian nonparametric methods are useful to model discrete patterns in time series data. We will showcase two examples: (1) using variance Gamma processes to model change points (Section 5), and (2) using Chinese restaurant processes to model speech with switching speakers (Section 6). We also aware that the inference problem can be non-trivial in popular Bayesian nonparametric models. In Section 7, we find a novel solution of online inference for the popular HDP-HMM model.

Abstract not available

This thesis advances understanding of the forensic value of the automatic speech parameters by addressing the following question: what is the potentiality of the speech cepstrum as a forensic-acoustic parameter? Despite many advances in automatic speech and speaker recognition, robust and unconstrained progress in technical forensic speaker identification has been partly impeded by our incomplete understanding of the interaction and relation between forensic phonetics and the techniques employed in state-of-the-art automatic speech and speaker recognition. The posed question underlies the recurrent and longstanding issue of acoustic parameterisation in the area of forensic phonetics, where 1) speaker identification often must be carried out under less than optimal conditions, and 2) views differ on the usefulness and trustworthiness of the formant frequency measurements. To this end, a new formulation for the forensic evaluation of speech data was derived which is effectively a spectral likelihood ratio with enhanced sensitivity to the local peaks of the formant structure of the speech spectrum of vowel sounds, while retaining the characteristics of the Bayesian framework. This new hybrid formula was used together with a novel approach, which is founded on a statistically-based matched-pairs technique to account for various levels of variation inherent in speech recordings, thereby providing a spectrally meaningful measure of variations between two speech spectra and hence the true worth of speech samples as forensic evidence. The experimental results are obtained based on a forensically-realistic database of a relatively large population of 297 native speakers of Japanese. In sum, the research conducted in this thesis is a major step forward in advancing the forensic-phonetic field which broadens the objective basis of the forensic speaker identification. Beyond advancing knowledge in the field, the semi data-independent nature of the new formula ultimately has great implications in technical forensic speaker identification. It also provides us with a valuable biometric tool with both academic and commercial potential in crime investigation in a field which is already suffering from the lack of adequate data.

Bayesian approaches to prediction and the assessment of predictive uncertainty in generalized linear models are often based on averaging predictions over different models, and this requires methods for accounting for model uncertainty. In this thesis we describe computational methods for Bayesian inference and model selection for generalized linear models, which improve on existing techniques. These methods are applied to the building of flexible models for gamma ray count data (data measuring the natural radioactivity of rocks) at the Castlereagh Waste Management Centre, which served as a hazardous waste disposal facility for the Sydney region between March 1978 and August 1998. Bayesian model selection methods for generalized linear models enable us to approach problems of smoothing, change point detection and spatial prediction for these data within a common methodological and computational framework, by considering appropriate basis expansions of a mean function. The data at Castlereagh were collected in the following way. A number of boreholes were drilled at the site, and for each borehole a gamma ray detector recorded gamma ray emissions at different depths as the detector was raised gradually from the bottom of the borehole to ground level. The profile of intensity of gamma counts can be informative about the geology at each location, and estimation of intensity profiles raises problems of smoothing and change point detection for count data. The gamma count profiles can also be modelled spatially, to inform the geological profile across the site. Understanding the geological structure of the site is important for modelling the transport of chemical contaminants beneath the waste disposal area. The structure of the thesis is as follows. Chapter 1 describes the Castlereagh hazardous waste site and the geophysical data, which motivated the methodology developed in this research. We summarise the principles of Gamma Ray (GR) logging, a method routinely employed by geophysicists and environmental engineers in the detailed evaluation of hazardous site geology, and detail the use of the Castlereagh data in this research. In Chapter 2 we review some fundamental ideas of Bayesian inference and computation and discuss them in the context of generalised linear models. Chapter 3 details the theoretical basis of our work. Here we give a new Markov chain Monte Carlo sampling scheme for Bayesian variable selection in generalized linear models, which is analogous to the well-known Swendsen-Wang algorithm for the Ising model. Special cases of this sampling scheme are used throughout the rest of the thesis. In Chapter 4 we discuss the use of methods for Bayesian model selection in generalized linear models in two specific applications, which we implement on the Castlereagh data. First, we consider smoothing problems where we flexibly estimate the dependence of a response variable on one or more predictors, and we apply these ideas to locally adaptive smoothing of gamma ray count data. Second, we discuss how the problem of multiple change point detection can be cast as one of model selection in a generalized linear model, and consider application to change point detection for gamma ray count data. In Chapter 5 we consider spatial models based on partitioning a spatial region of interest into cells via a Voronoi tessellation, where the number of cells and the positions of their centres is unknown, and show how these models can be formulated in the framework of established methods for Bayesian model selection in generalized linear models. We implement the spatial partition modelling approach to the spatial analysis of gamma ray data, showing how the posterior distribution of the number of cells, cell centres and cell means provides us with an estimate of the mean response function describing spatial variability across the site. Chapter 6 presents some conclusions and suggests directions for future research. A paper based on the work of Chapter 3 has been accepted for publication in the Journal of Computational and Graphical Statistics, and a paper based on the work in Chapter 4 has been accepted for publication in Mathematical Geology. A paper based on the spatial modelling of Chapter 5 is in preparation and will be submitted for publication shortly. The work in this thesis was collaborative, to a smaller or larger extent in its various components. I authored Chapters 1 and 2 entirely, including definition of the problem in the context of the CWMC site, data gathering and preparation for analysis, review of the literature on computational methods for Bayesian inference and model selection for generalized linear models. I also authored Chapters 4 and 5 and benefited from some of Dr Nott's assistance in developing the algorithms. In Chapter 3, Dr Nott led the development of sampling scheme B (corresponding to having non-zero interaction parameters in our Swendsen-Wang type algorithm). I developed the algorithm for sampling scheme A (corresponding to setting all algorithm interaction parameters to zero in our Swendsen-Wang type algorithm), and performed the comparison of the performance of the two sampling schemes. The final discussion in Chapter 6 and the direction for further research in the case study context is also my work.

Thesis (Ph.D.)--McMaster University, 2005. / Supervisor: Simon Haykin. Includes bibliographical references (leaves [126]-135).

How can an agent generalize its knowledge to new circumstances? To learn effectively an agent acting in a sequential decision problem must make intelligent action selection choices based on its available knowledge. This dissertation focuses on Bayesian methods of representing learned knowledge and develops novel algorithms that exploit the represented knowledge when selecting actions. Our first contribution introduces the multi-task Reinforcement Learning setting in which an agent solves a sequence of tasks. An agent equipped with knowledge of the relationship between tasks can transfer knowledge between them. We propose the transfer of two distinct types of knowledge: knowledge of domain models and knowledge of policies. To represent the transferable knowledge, we propose hierarchical Bayesian priors on domain models and policies respectively. To transfer domain model knowledge, we introduce a new algorithm for model-based Bayesian Reinforcement Learning in the multi-task setting which exploits the learned hierarchical Bayesian model to improve exploration in related tasks. To transfer policy knowledge, we introduce a new policy search algorithm that accepts a policy prior as input and uses the prior to bias policy search. A specific implementation of this algorithm is developed that accepts a hierarchical policy prior. The algorithm learns the hierarchical structure and reuses components of the structure in related tasks. Our second contribution addresses the basic problem of generalizing knowledge gained from previously-executed policies. Bayesian Optimization is a method of exploiting a prior model of an objective function to quickly identify the point maximizing the modeled objective. Successful use of Bayesian Optimization in Reinforcement Learning requires a model relating policies and their performance. Given such a model, Bayesian Optimization can be applied to search for an optimal policy. Early work using Bayesian Optimization in the Reinforcement Learning setting ignored the sequential nature of the underlying decision problem. The work presented in this thesis explicitly addresses this problem. We construct new Bayesian models that take advantage of sequence information to better generalize knowledge across policies. We empirically evaluate the value of this approach in a variety of Reinforcement Learning benchmark problems. Experiments show that our method significantly reduces the amount of exploration required to identify the optimal policy. Our final contribution is a new framework for learning parametric policies from queries presented to an expert. In many domains it is difficult to provide expert demonstrations of desired policies. However, it may still be a simple matter for an expert to identify good and bad performance. To take advantage of this limited expert knowledge, our agent presents experts with pairs of demonstrations and asks which of the demonstrations best represents a latent target behavior. The goal is to use a small number of queries to elicit the latent behavior from the expert. We formulate a Bayesian model of the querying process, an inference procedure that estimates the posterior distribution over the latent policy space, and an active procedure for selecting new queries for presentation to the expert. We show, in multiple domains, that the algorithm successfully learns the target policy and that the active learning strategy generally improves the speed of learning. / Graduation date: 2013

[by] Adrianus J.M. Houtsma and Julius L. Goldstein. / Based on a Ph.D. thesis in the Dept. of Electrical Engineering, 1971, by A.J.M. Houtsma. / Bibliography: p. 71-75.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 215-219).

Ph.D. / Electrical and Computer Engineering / Probabilistic inference is the problem of estimating the hidden variables (states or parameters) of a system in an optimal and consistent fashion as a set of noisy or incomplete observations of the system becomes available online. The optimal solution to this problem is given by the recursive Bayesian estimation algorithm which recursively updates the posterior density of the system state as new observations arrive. This posterior density constitutes the complete solution to the probabilistic inference problem, and allows us to calculate any "optimal" estimate of the state. Unfortunately, for most real-world problems, the optimal Bayesian recursion is intractable and approximate solutions must be used. Within the space of approximate solutions, the extended Kalman filter (EKF) has become one of the most widely used algorithms with applications in state, parameter and dual estimation. Unfortunately, the EKF is based on a sub-optimal implementation of the recursive Bayesian estimation framework applied to Gaussian random variables. This can seriously affect the accuracy or even lead to divergence of any inference system that is based on the EKF or that uses the EKF as a component part. Recently a number of related novel, more accurate and theoretically better motivated algorithmic alternatives to the EKF have surfaced in the literature, with specific application to state estimation for automatic control. We have extended these algorithms, all based on derivativeless deterministic sampling based approximations of the relevant Gaussian statistics, to a family of algorithms called Sigma-Point Kalman Filters (SPKF). Furthermore, we successfully expanded the use of this group of algorithms (SPKFs) within the general field of probabilistic inference and machine learning, both as stand-alone filters and as subcomponents of more powerful sequential Monte Carlo methods (particle filters). We have consistently shown that there are large performance benefits to be gained by applying Sigma-Point Kalman filters to areas where EKFs have been used as the de facto standard in the past, as well as in new areas where the use of the EKF is impossible.

This thesis provides contributions to research in Bayesian modeling and shrinkage in the wavelet domain. Wavelets are a powerful tool to describe phenomena rapidly changing in time, and wavelet-based modeling has become a standard technique in many areas of statistics, and more broadly, in sciences and engineering. Bayesian modeling and estimation in the wavelet domain have found useful applications in nonparametric regression, image denoising, and many other areas. In this thesis, we build on the existing techniques and propose new methods for applications in nonparametric regression, image denoising, and partially linear models. The thesis consists of an overview chapter and four main topics. In Chapter 1, we provide an overview of recent developments and the current status of Bayesian wavelet shrinkage research. The chapter contains an extensive literature review consisting of almost 100 references. The main focus of the overview chapter is on nonparametric regression, where the observations come from an unknown function contaminated with Gaussian noise. We present many methods which employ model-based and adaptive shrinkage of the wavelet coefficients through Bayes rules. These includes new developments such as dependence models, complex wavelets, and Markov chain Monte Carlo (MCMC) strategies. Some applications of Bayesian wavelet shrinkage, such as curve classification, are discussed. In Chapter 2, we propose the Gibbs Sampling Wavelet Smoother (GSWS), an adaptive wavelet denoising methodology. We use the traditional mixture prior on the wavelet coefficients, but also formulate a fully Bayesian hierarchical model in the wavelet domain accounting for the uncertainty of the prior parameters by placing hyperpriors on them. Since a closed-form solution to the Bayes estimator does not exist, the procedure is computational, in which the posterior mean is computed via MCMC simulations. We show how to efficiently develop a Gibbs sampling algorithm for the proposed model. The developed procedure is fully Bayesian, is adaptive to the underlying signal, and provides good denoising performance compared to state-of-the-art methods. Application of the method is illustrated on a real data set arising from the analysis of metabolic pathways, where an iterative shrinkage procedure is developed to preserve the mass balance of the metabolites in the system. We also show how the methodology can be extended to complex wavelet bases. In Chapter 3, we propose a wavelet-based denoising methodology based on a Bayesian hierarchical model using a double Weibull prior. The interesting feature is that in contrast to the mixture priors traditionally used by some state-of-the-art methods, the wavelet coefficients are modeled by a single density. Two estimators are developed, one based on the posterior mean and the other based on the larger posterior mode; and we show how to calculate these estimators efficiently. The methodology provides good denoising performance, comparable even to state-of-the-art methods that use a mixture prior and an empirical Bayes setting of hyperparameters; this is demonstrated by simulations on standard test functions. An application to a real-word data set is also considered. In Chapter 4, we propose a wavelet shrinkage method based on a neighborhood of wavelet coefficients, which includes two neighboring coefficients and a parental coefficient. The methodology is called Lambda-neighborhood wavelet shrinkage, motivated by the shape of the considered neighborhood. We propose a Bayesian hierarchical model using a contaminated exponential prior on the total mean energy in the Lambda-neighborhood. The hyperparameters in the model are estimated by the empirical Bayes method, and the posterior mean, median, and Bayes factor are obtained and used in the estimation of the total mean energy. Shrinkage of the neighboring coefficients is based on the ratio of the estimated and observed energy. The proposed methodology is comparable and often superior to several established wavelet denoising methods that utilize neighboring information, which is demonstrated by extensive simulations. An application to a real-world data set from inductance plethysmography is considered, and an extension to image denoising is discussed. In Chapter 5, we propose a wavelet-based methodology for estimation and variable selection in partially linear models. The inference is conducted in the wavelet domain, which provides a sparse and localized decomposition appropriate for nonparametric components with various degrees of smoothness. A hierarchical Bayes model is formulated on the parameters of this representation, where the estimation and variable selection is performed by a Gibbs sampling procedure. For both the parametric and nonparametric part of the model we are using point-mass-at-zero contamination priors with a double exponential spread distribution. In this sense we extend the model of Chapter 2 to partially linear models. Only a few papers in the area of partially linear wavelet models exist, and we show that the proposed methodology is often superior to the existing methods with respect to the task of estimating model parameters. Moreover, the method is able to perform Bayesian variable selection by a stochastic search for the parametric part of the model.