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

Supervised Classification Using Finite Mixture Copula

Use of copula for statistical classification is recent and gaining popularity. For example, statistical classification using copula has been proposed for automatic character recognition, medical diagnostic and most recently in data mining. Classical discrimination rules assume normality. But in this data age time, this assumption is often questionable. In fact features of data could be a mixture of discrete and continues random variables. In this paper, mixture copula densities are used to model class conditional distributions. Such types of densities are useful when the marginal densities of the vector of features are not normally distributed and are of a mixed kind of variables. Authors have shown that such mixture models are very useful for uncovering hidden structures in the data, and used them for clustering in data mining. Under such mixture models, maximum likelihood estimation methods are not suitable and regular expectation maximization algorithm is inefficient and may not converge. A new estimation method is proposed to estimate such densities and build the classifier based on mixture finite Gaussian densities. Simulations are used to compare the performance of the copula based classifier with classical normal distribution based models, logistic regression based model and independent model cases. The method is also applied to a real data

Probabilistic Inference from Arbitrary Uncertainty using Mixtures of Factorized Generalized Gaussians

This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both the joint probability density of the variables and the likelihood function of the (objective or subjective) observation are approximated by a special mixture model, in such a way that any desired conditional distribution can be directly obtained without numerical integration. We have developed an extended version of the expectation maximization (EM) algorithm to estimate the parameters of mixture models from uncertain training examples (indirect observations). As a consequence, any piece of exact or uncertain information about both input and output values is consistently handled in the inference and learning stages. This ability, extremely useful in certain situations, is not found in most alternative methods. The proposed framework is formally justified from standard probabilistic principles and illustrative examples are provided in the fields of nonparametric pattern classification, nonlinear regression and pattern completion. Finally, experiments on a real application and comparative results over standard databases provide empirical evidence of the utility of the method in a wide range of applications

Semi-supervised source localization in reverberant environments with deep generative modeling

We propose a semi-supervised approach to acoustic source localization in reverberant environments based on deep generative modeling. Localization in reverberant environments remains an open challenge. Even with large data volumes, the number of labels available for supervised learning in reverberant environments is usually small. We address this issue by performing semi-supervised learning (SSL) with convolutional variational autoencoders (VAEs) on reverberant speech signals recorded with microphone arrays. The VAE is trained to generate the phase of relative transfer functions (RTFs) between microphones, in parallel with a direction of arrival (DOA) classifier based on RTF-phase. These models are trained using both labeled and unlabeled RTF-phase sequences. In learning to perform these tasks, the VAE-SSL explicitly learns to separate the physical causes of the RTF-phase (i.e., source location) from distracting signal characteristics such as noise and speech activity. Relative to existing semi-supervised localization methods in acoustics, VAE-SSL is effectively an end-to-end processing approach which relies on minimal preprocessing of RTF-phase features. As far as we are aware, our paper presents the first approach to modeling the physics of acoustic propagation using deep generative modeling. The VAE-SSL approach is compared with two signal processing-based approaches, steered response power with phase transform (SRP-PHAT) and MUltiple SIgnal Classification (MUSIC), as well as fully supervised CNNs. We find that VAE-SSL can outperform the conventional approaches and the CNN in label-limited scenarios. Further, the trained VAE-SSL system can generate new RTF-phase samples, which shows the VAE-SSL approach learns the physics of the acoustic environment. The generative modeling in VAE-SSL thus provides a means of interpreting the learned representations.Comment: Revision, submitted to IEEE Acces

Modern considerations for the use of naive Bayes in the supervised classification of genetic sequence data

2021 Spring.Includes bibliographical references.Genetic sequence classification is the task of assigning a known genetic label to an unknown genetic sequence. Often, this is the first step in genetic sequence analysis and is critical to understanding data produced by molecular techniques like high throughput sequencing. Here, we explore an algorithm called naive Bayes that was historically successful in classifying 16S ribosomal gene sequences for microbiome analysis. We extend the naive Bayes classifier to perform the task of general sequence classification by leveraging advancements in computational parallelism and the statistical distributions that underlie naive Bayes. In Chapter 2, we show that our implementation of naive Bayes, called WarpNL, performs within a margin of error of modern classifiers like Kraken2 and local alignment. We discuss five crucial aspects of genetic sequence classification and show how these areas affect classifier performance: the query data, the reference sequence database, the feature encoding method, the classification algorithm, and access to computational resources. In Chapter 3, we cover the critical computational advancements introduced in WarpNL that make it efficient in a modern computing framework. This includes efficient feature encoding, introduction of a log-odds ratio for comparison of naive Bayes posterior estimates, description of schema for parallel and distributed naive Bayes architectures, and use of machine learning classifiers to perform outgroup sequence classification. Finally in Chapter 4, we explore a variant of the Dirichlet multinomial distribution that underlies the naive Bayes likelihood, called the beta-Liouville multinomial. We show that the beta-Liouville multinomial can be used to enhance classifier performance, and we provide mathematical proofs regarding its convergence during maximum likelihood estimation. Overall, this work explores the naive Bayes algorithm in a modern context and shows that it is competitive for genetic sequence classification

On Practical machine Learning and Data Analysis

This thesis discusses and addresses some of the difficulties associated with practical machine learning and data analysis. Introducing data driven methods in e.g industrial and business applications can lead to large gains in productivity and efficiency, but the cost and complexity are often overwhelming. Creating machine learning applications in practise often involves a large amount of manual labour, which often needs to be performed by an experienced analyst without significant experience with the application area. We will here discuss some of the hurdles faced in a typical analysis project and suggest measures and methods to simplify the process. One of the most important issues when applying machine learning methods to complex data, such as e.g. industrial applications, is that the processes generating the data are modelled in an appropriate way. Relevant aspects have to be formalised and represented in a way that allow us to perform our calculations in an efficient manner. We present a statistical modelling framework, Hierarchical Graph Mixtures, based on a combination of graphical models and mixture models. It allows us to create consistent, expressive statistical models that simplify the modelling of complex systems. Using a Bayesian approach, we allow for encoding of prior knowledge and make the models applicable in situations when relatively little data are available. Detecting structures in data, such as clusters and dependency structure, is very important both for understanding an application area and for specifying the structure of e.g. a hierarchical graph mixture. We will discuss how this structure can be extracted for sequential data. By using the inherent dependency structure of sequential data we construct an information theoretical measure of correlation that does not suffer from the problems most common correlation measures have with this type of data. In many diagnosis situations it is desirable to perform a classification in an iterative and interactive manner. The matter is often complicated by very limited amounts of knowledge and examples when a new system to be diagnosed is initially brought into use. We describe how to create an incremental classification system based on a statistical model that is trained from empirical data, and show how the limited available background information can still be used initially for a functioning diagnosis system. To minimise the effort with which results are achieved within data analysis projects, we need to address not only the models used, but also the methodology and applications that can help simplify the process. We present a methodology for data preparation and a software library intended for rapid analysis, prototyping, and deployment. Finally, we will study a few example applications, presenting tasks within classification, prediction and anomaly detection. The examples include demand prediction for supply chain management, approximating complex simulators for increased speed in parameter optimisation, and fraud detection and classification within a media-on-demand system

On adaptive decision rules and decision parameter adaptation for automatic speech recognition

Recent advances in automatic speech recognition are accomplished by designing a plug-in maximum a posteriori decision rule such that the forms of the acoustic and language model distributions are specified and the parameters of the assumed distributions are estimated from a collection of speech and language training corpora. Maximum-likelihood point estimation is by far the most prevailing training method. However, due to the problems of unknown speech distributions, sparse training data, high spectral and temporal variabilities in speech, and possible mismatch between training and testing conditions, a dynamic training strategy is needed. To cope with the changing speakers and speaking conditions in real operational conditions for high-performance speech recognition, such paradigms incorporate a small amount of speaker and environment specific adaptation data into the training process. Bayesian adaptive learning is an optimal way to combine prior knowledge in an existing collection of general models with a new set of condition-specific adaptation data. In this paper, the mathematical framework for Bayesian adaptation of acoustic and language model parameters is first described. Maximum a posteriori point estimation is then developed for hidden Markov models and a number of useful parameters densities commonly used in automatic speech recognition and natural language processing.published_or_final_versio