82,601 research outputs found

    Bayesian Aspects of Classification Procedures

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    We consider several statistical approaches to binary classification and multiple hypothesis testing problems. Situations in which a binary choice must be made are common in science. Usually, there is uncertainty involved in making the choice and a great number of statistical techniques have been put forth to help researchers deal with this uncertainty in separating signal from noise in reasonable ways. For example, in genetic studies, one may want to identify genes that affect a certain biological process from among a larger set of genes. In such examples, costs are attached to making incorrect choices and many choices must be made at the same time. Reasonable ways of modeling the cost structure and choosing the appropriate criteria for evaluating the performance of statistical techniques are needed. The following three chapters have proposals of some Bayesian methods for these issues. In the first chapter, we focus on an empirical Bayes approach to a popular binary classification problem formulation. In this framework, observations are treated as independent draws from a hierarchical model with a mixture prior distribution. The mixture prior combines prior distributions for the ``noise\u27\u27 and for the ``signal\u27\u27 observations. In the literature, parametric assumptions are usually made about the prior distribution from which the ``signal\u27\u27 observations come. We suggest a Bayes classification rule which minimizes the expectation of a flexible and easily interpretable mixture loss function which brings together constant penalties for false positive misclassifications and L2L_2 penalties for false negative misclassifications. Due in part to the form of the loss function, empirical Bayes techniques can then be used to construct the Bayes classification rule without specifying the ``signal\u27\u27 part of the mixture prior distribution. The proposed classification technique builds directly on the nonparametric mixture prior approach proposed by Raykar and Zhao (2010, 2011). Many different criteria can be used to judge the success of a classification procedure. A very useful criterion called the False Discovery Rate (FDR) was introduced by Benjamini and Hochberg in a 1995 paper. For many applications, the FDR, which is defined as the expected proportion of false positive results among the observations declared to be ``signal\u27\u27, is a reasonable criterion to target. Bayesian versions of the false discovery rate, the so-called positive false discovery rate (pFDR) and local false discovery rate, were proposed by Storey (2002, 2003) and Efron and coauthors (2001), respectively. There is an interesting connection between the local false discovery rate and the nonparametric mixture prior approach for binary classification problems. The second part of the dissertation is focused on this link and provides a comparison of various approaches for estimating Bayesian false discovery rates. The third chapter is an account of a connection between the celebrated Neyman-Pearson lemma and the area (AUC) under the receiver operating characteristic (ROC) curve when the observations that need to be classified come from a pair of normal distributions. Using this connection, it is possible to derive a classification rule which maximizes the AUC for binormal data

    Modulation Classification for MIMO-OFDM Signals via Approximate Bayesian Inference

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    The problem of modulation classification for a multiple-antenna (MIMO) system employing orthogonal frequency division multiplexing (OFDM) is investigated under the assumption of unknown frequency-selective fading channels and signal-to-noise ratio (SNR). The classification problem is formulated as a Bayesian inference task, and solutions are proposed based on Gibbs sampling and mean field variational inference. The proposed methods rely on a selection of the prior distributions that adopts a latent Dirichlet model for the modulation type and on the Bayesian network formalism. The Gibbs sampling method converges to the optimal Bayesian solution and, using numerical results, its accuracy is seen to improve for small sample sizes when switching to the mean field variational inference technique after a number of iterations. The speed of convergence is shown to improve via annealing and random restarts. While most of the literature on modulation classification assume that the channels are flat fading, that the number of receive antennas is no less than that of transmit antennas, and that a large number of observed data symbols are available, the proposed methods perform well under more general conditions. Finally, the proposed Bayesian methods are demonstrated to improve over existing non-Bayesian approaches based on independent component analysis and on prior Bayesian methods based on the `superconstellation' method.Comment: To be appear in IEEE Trans. Veh. Technolog

    Classification of chirp signals using hierarchical bayesian learning and MCMC methods

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    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

    Multivariate Bayesian semiparametric models for authentication of food and beverages

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    Food and beverage authentication is the process by which foods or beverages are verified as complying with its label description, for example, verifying if the denomination of origin of an olive oil bottle is correct or if the variety of a certain bottle of wine matches its label description. The common way to deal with an authentication process is to measure a number of attributes on samples of food and then use these as input for a classification problem. Our motivation stems from data consisting of measurements of nine chemical compounds denominated Anthocyanins, obtained from samples of Chilean red wines of grape varieties Cabernet Sauvignon, Merlot and Carm\'{e}n\`{e}re. We consider a model-based approach to authentication through a semiparametric multivariate hierarchical linear mixed model for the mean responses, and covariance matrices that are specific to the classification categories. Specifically, we propose a model of the ANOVA-DDP type, which takes advantage of the fact that the available covariates are discrete in nature. The results suggest that the model performs well compared to other parametric alternatives. This is also corroborated by application to simulated data.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS492 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Nonlinear Models Using Dirichlet Process Mixtures

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    We introduce a new nonlinear model for classification, in which we model the joint distribution of response variable, y, and covariates, x, non-parametrically using Dirichlet process mixtures. We keep the relationship between y and x linear within each component of the mixture. The overall relationship becomes nonlinear if the mixture contains more than one component. We use simulated data to compare the performance of this new approach to a simple multinomial logit (MNL) model, an MNL model with quadratic terms, and a decision tree model. We also evaluate our approach on a protein fold classification problem, and find that our model provides substantial improvement over previous methods, which were based on Neural Networks (NN) and Support Vector Machines (SVM). Folding classes of protein have a hierarchical structure. We extend our method to classification problems where a class hierarchy is available. We find that using the prior information regarding the hierarchical structure of protein folds can result in higher predictive accuracy
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