Browsing by Subject "Variable selection"

Now showing 1 - 4 of 4
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    Data supporting "Predicting total phosphorus levels as indicators for shallow lake management"
    (2018-07-18) Vitense, Kelsey; Hanson, Mark A; Herwig, Brian R; Zimmer, Kyle D; Fieberg, John R; kelsey.vitense@gmail.com; Vitense, Kelsey
    This repository contains data supporting "Predicting total phosphorus levels as indicators for shallow lake management" in Ecological Indicators.
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    Statistical Methods for Variable Selection in Causal Inference
    (2018-07) Koch, Brandon Lee
    Estimating the causal effect of a binary intervention or action (referred to as a "treatment") on a continuous outcome is often an investigator's primary goal. Randomized trials are ideal for estimating causal effects because randomization eliminates selection bias in treatment assignment. However, randomized trials are not always ethically or practically possible, and observational data must be used to estimate the causal effect of treatment. Unbiased estimation of causal effects with observational data requires adjustment for confounding variables that are related to both the outcome and treatment assignment. Adjusting for all measured covariates in a study protects against bias, but including covariates unrelated to outcome may increase the variability of the estimated causal effect. Standard variable selection techniques aim to maximize predictive ability of a model for the outcome and are used to decrease variability of the estimated causal effect, but they ignore covariate associations with treatment and may not adjust for important confounders weakly associated to outcome. We propose two approaches for estimating causal effects that simultaneously consider models for both outcome and treatment assignment. The first approach is a variable selection technique for identifying confounders and predictors of outcome using an adaptive group lasso approach that simultaneously performs coefficient selection, regularization, and estimation across the treatment and outcome models. In the second approach, two methods are proposed that simultaneously model outcome and treatment assignment using a Bayesian formulation with spike and slab priors on each covariate coefficient; the Spike and Slab Causal Estimator (SSCE) aims to achieve minimum bias of the causal effect estimator while Bilevel SSCE (BSSCE) aims to minimize its mean squared error. We also propose TEHTrees, a new method that combines matching and conditional inference trees to characterize treatment effect heterogeneity. One of its main virtues is that, by employing formal hypothesis testing procedures in constructing the tree, TEHTrees preserves the Type I error rate.
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    Sufficient dimension reduction and variable selection.
    (2010-12) Chen, Xin
    Sufficient dimension reduction (SDR) in regression was first introduced by Cook (2004). It reduces the dimension of the predictor space without loss of information and it is very helpful when the number of predictors is large. It alleviates the “curse of dimensionality” for many statistical methods. In this thesis, we study the properties of a dimension reduction method named “continuum regression”; we propose a unified method – coordinate-independent sparse estimation (CISE) – that can simultaneously achieve sparse sufficient dimension reduction and screen out irrelevant and redundant variables efficiently; we also introduce a new dimension reduction method called “principal envelope models”.
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    Variable selection in high-dimensional classification
    (2013-06) Mai, Qing
    Classification has long been an important research topic for statisticians. Nowadays, scientists are further challenged by classification problems for high-dimensional datasets in various fields, ranging from genomics, economics to machine learning. For such massive datasets, classical classification techniques may be inefficient or even infeasible, while new techniques are highly sought-after. My dissertation work tackles high-dimensional classification problems by utilizing variable selection. In particular, three methods are proposed and studied: direct sparse discriminant analysis, semiparametric sparse discriminant analysis and the Kolmogorov filter. In the proposal of direct sparse discriminant analysis (DSDA), I first point out the disadvantage in many current methods that they ignore the correlation structure between predictors. Then DSDA is proposed to extend the well-known linear discriminant analysis to high dimensions, fully respecting the correlation structure. The proposal is efficient and consistent, with excellent numerical performance. In addition to the proposal of DSDA, I also study its connection to many popular proposals of linear discriminant analysis in high dimensions, including the L1-Fisher's discriminant analysis and the sparse optimal scoring. Semiparametric sparse discriminant analysis (SeSDA) extends DSDA by relaxing the normality assumption, which is fundamental for any method requiring the linear discriminant analysis model. SeSDA is more robust than DSDA, while it preserves the good properties of DSDA. Along with the development of SeSDA, a new concentration inequality is obtained that can provide theoretical justifications for methods based on Gaussian copulas. Moreover, the Kolmogorov filter is proposed as a fully nonparametric method that performs variable selection for high-dimensional classification. It requires minimal assumptions on the distribution of the predictors, and is supported by both theoretical and numerical examples. Also, some potential future work is discussed on variable selection in classification.