Browsing by Subject "feature selection"
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Item Application of Bayesian Hierarchical Models in Genetic Data Analysis(2012-08-15) Zhang, LinGenetic data analysis has been capturing a lot of attentions for understanding the mechanism of the development and progressing of diseases like cancers, and is crucial in discovering genetic markers and treatment targets in medical research. This dissertation focuses on several important issues in genetic data analysis, graphical network modeling, feature selection, and covariance estimation. First, we develop a gene network modeling method for discrete gene expression data, produced by technologies such as serial analysis of gene expression and RNA sequencing experiment, which generate counts of mRNA transcripts in cell samples. We propose a generalized linear model to fit the discrete gene expression data and assume that the log ratios of the mean expression levels follow a Gaussian distribution. We derive the gene network structures by selecting covariance matrices of the Gaussian distribution with a hyper-inverse Wishart prior. We incorporate prior network models based on Gene Ontology information, which avails existing biological information on the genes of interest. Next, we consider a variable selection problem, where the variables have natural grouping structures, with application to analysis of chromosomal copy number data. The chromosomal copy number data are produced by molecular inversion probes experiments which measure probe-specific copy number changes. We propose a novel Bayesian variable selection method, the hierarchical structured variable se- lection (HSVS) method, which accounts for the natural gene and probe-within-gene architecture to identify important genes and probes associated with clinically relevant outcomes. We propose the HSVS model for grouped variable selection, where simultaneous selection of both groups and within-group variables is of interest. The HSVS model utilizes a discrete mixture prior distribution for group selection and group-specific Bayesian lasso hierarchies for variable selection within groups. We further provide methods for accounting for serial correlations within groups that incorporate Bayesian fused lasso methods for within-group selection. Finally, we propose a Bayesian method of estimating high-dimensional covariance matrices that can be decomposed into a low rank and sparse component. This covariance structure has a wide range of applications including factor analytical model and random effects model. We model the covariance matrices with the decomposition structure by representing the covariance model in the form of a factor analytic model where the number of latent factors is unknown. We introduce binary indicators for estimating the rank of the low rank component combined with a Bayesian graphical lasso method for estimating the sparse component. We further extend our method to a graphical factor analytic model where the graphical model of the residuals is of interest. We achieve sparse estimation of the inverse covariance of the residuals in the graphical factor model by employing a hyper-inverse Wishart prior method for a decomposable graph and a Bayesian graphical lasso method for an unrestricted graph.Item Cost-Sensitive Classification Methods for the Detection of Smuggled Nuclear Material in Cargo Containers(2013-07-09) Webster, Jennifer BClassification problems arise in so many different parts of life ? from sorting machine parts to diagnosing a disease. Humans make these classifications utilizing vast amounts of data, filtering observations for useful information, and then making a decision based on a subjective level of cost/risk of classifying objects incorrectly. This study investigates the translation of the human decision process into a mathematical problem in the context of a border security problem: How does one find special nuclear material being smuggled inside large cargo crates while balancing the cost of invasively searching suspect containers against the risk of al lowing radioactive material to escape detection? This may be phrased as a classification problem in which one classifies cargo containers into two categories ? those containing a smuggled source and those containing only innocuous cargo. This task presents numerous challenges, e.g., the stochastic nature of radiation and the low signal-to-noise ratio caused by background radiation and cargo shielding. In the course of this work, we will break the analysis of this problem into three major sections ? the development of an optimal decision rule, the choice of most useful measurements or features, and the sensitivity of developed algorithms to physical variations. This will include an examination of how accounting for the cost/risk of a decision affects the formulation of our classification problem. Ultimately, a support vector machine (SVM) framework with F -score feature selection will be developed to provide nearly optimal classification given a constraint on the reliability of detection provided by our algorithm. In particular, this can decrease the fraction of false positives by an order of magnitude over current methods. The proposed method also takes into account the relationship between measurements, whereas current methods deal with detectors independently of one another.Item Small sample feature selection(Texas A&M University, 2007-09-17) Sima, ChaoHigh-throughput technologies for rapid measurement of vast numbers of biolog- ical variables offer the potential for highly discriminatory diagnosis and prognosis; however, high dimensionality together with small samples creates the need for fea- ture selection, while at the same time making feature-selection algorithms less reliable. Feature selection is required to avoid overfitting, and the combinatorial nature of the problem demands a suboptimal feature-selection algorithm. In this dissertation, we have found that feature selection is problematic in small- sample settings via three different approaches. First we examined the feature-ranking performance of several kinds of error estimators for different classification rules, by considering all feature subsets and using 2 measures of performance. The results show that their ranking is strongly affected by inaccurate error estimation. Secondly, since enumerating all feature subsets is computationally impossible in practice, a suboptimal feature-selection algorithm is often employed to find from a large set of potential features a small subset with which to classify the samples. If error estimation is required for a feature-selection algorithm, then the impact of error estimation can be greater than the choice of algorithm. Lastly, we took a regression approach by comparing the classification errors for the optimal feature sets and the errors for the feature sets found by feature-selection algorithms. Our study shows that it is unlikely that feature selection will yield a feature set whose error is close to that of the optimal feature set, and the inability to find a good feature set should not lead to the conclusion that good feature sets do not exist.