Variable Selection and Decision Trees: The DiVaS and ALoVaS Methods
In this thesis we propose a novel modification to Bayesian decision tree methods. We provide a historical survey of the statistics and computer science research in decision trees. Our approach facilitates covariate selection explicitly in the model, something not present in previous research. We def...
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ndltd-VTETD-oai-vtechworks.lib.vt.edu-10919-708782021-04-24T05:40:06Z Variable Selection and Decision Trees: The DiVaS and ALoVaS Methods Roberts, Lucas R. Statistics Leman, Scotland C. House, Leanna L. North, Christopher L. Smith, Eric P. Statistics Decision Trees Variable selection Additive Logistic Normal In this thesis we propose a novel modification to Bayesian decision tree methods. We provide a historical survey of the statistics and computer science research in decision trees. Our approach facilitates covariate selection explicitly in the model, something not present in previous research. We define a transformation that allows us to use priors from linear models to facilitate covariate selection in decision trees. Using this transform, we modify many common approaches to variable selection in the linear model and bring these methods to bear on the problem of explicit covariate selection in decision tree models. We also provide theoretical guidelines, including a theorem, which gives necessary and sufficient conditions for consistency of decision trees in infinite dimensional spaces. Our examples and case studies use both simulated and real data cases with moderate to large numbers of covariates. The examples support the claim that our approach is to be preferred in large dimensional datasets. Moreover, our approach shown here has, as a special case, the model known as Bayesian CART. Ph. D. 2016-04-30T06:00:56Z 2016-04-30T06:00:56Z 2014-11-06 Dissertation vt_gsexam:3973 http://hdl.handle.net/10919/70878 In Copyright http://rightsstatements.org/vocab/InC/1.0/ ETD application/pdf Virginia Tech |
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Statistics Decision Trees Variable selection Additive Logistic Normal |
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Statistics Decision Trees Variable selection Additive Logistic Normal Roberts, Lucas R. Variable Selection and Decision Trees: The DiVaS and ALoVaS Methods |
description |
In this thesis we propose a novel modification to Bayesian decision tree methods. We provide a
historical survey of the statistics and computer science research in decision trees. Our approach
facilitates covariate selection explicitly in the model, something not present in previous research.
We define a transformation that allows us to use priors from linear models to facilitate covariate
selection in decision trees. Using this transform, we modify many common approaches to variable
selection in the linear model and bring these methods to bear on the problem of explicit covariate
selection in decision tree models. We also provide theoretical guidelines, including a theorem,
which gives necessary and sufficient conditions for consistency of decision trees in infinite dimensional
spaces. Our examples and case studies use both simulated and real data cases with moderate
to large numbers of covariates. The examples support the claim that our approach is to be preferred
in large dimensional datasets. Moreover, our approach shown here has, as a special case, the model
known as Bayesian CART. === Ph. D. |
author2 |
Statistics |
author_facet |
Statistics Roberts, Lucas R. |
author |
Roberts, Lucas R. |
author_sort |
Roberts, Lucas R. |
title |
Variable Selection and Decision Trees: The DiVaS and ALoVaS Methods |
title_short |
Variable Selection and Decision Trees: The DiVaS and ALoVaS Methods |
title_full |
Variable Selection and Decision Trees: The DiVaS and ALoVaS Methods |
title_fullStr |
Variable Selection and Decision Trees: The DiVaS and ALoVaS Methods |
title_full_unstemmed |
Variable Selection and Decision Trees: The DiVaS and ALoVaS Methods |
title_sort |
variable selection and decision trees: the divas and alovas methods |
publisher |
Virginia Tech |
publishDate |
2016 |
url |
http://hdl.handle.net/10919/70878 |
work_keys_str_mv |
AT robertslucasr variableselectionanddecisiontreesthedivasandalovasmethods |
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1719399155423510528 |