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Random Weighting in LASSO Regression and in Discrete Mixture Models.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Random Weighting in LASSO Regression and in Discrete Mixture Models./
作者:	Ng, Tun Lee.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2022,
面頁冊數:	179 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-11, Section: B.
Contained By:	Dissertations Abstracts International83-11B.
標題:	Statistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29211262
ISBN:	9798802710739

Random Weighting in LASSO Regression and in Discrete Mixture Models.
Ng, Tun Lee.

Random Weighting in LASSO Regression and in Discrete Mixture Models. - Ann Arbor : ProQuest Dissertations & Theses, 2022 - 179 p.

Source: Dissertations Abstracts International, Volume: 83-11, Section: B.

Thesis (Ph.D.)--The University of Wisconsin - Madison, 2022.

This item must not be sold to any third party vendors.

We consider a general-purpose approximation approach to Bayesian inference in which repeated optimization of a randomized objective function provides surrogate samples from the joint posterior distribution. Our motivation stems from the need for computationally efficient uncertainty quantification in contemporary settings.This thesis consists of two main parts: In the first part, we establish statistical properties of random-weighting methods in LASSO regression under different regularization parameters and suitable regularity conditions. In Chapter 2, we show that existing approaches have conditional model selection consistency and conditional asymptotic normality at different growth rates of regularization parameters as sample size increases. We propose an extension to the available random-weighting methods and establish that the resulting samples attain conditional sparse normality and conditional consistency in a growing-dimension setting. We illustrate the proposed methodology using synthetic and benchmark data sets, and we discuss the relationship of the results to approximate Bayesian analysis and to perturbation bootstrap methods. Relevant technical details for Chapter 2 are collected in Chapter 3.The second part of the thesis concerns with random-weighting discrete mixture models under the Bayesian nonparametric learning (NPL) framework. Specifically, in Chapter 4, we first develop new asymptotics for a Dirichlet Process Mixture (DPM) model -- the DP-rich algorithm. Unlike the DP-means approach that arises as small-variance-asymptotics of the DPM, our DP-rich setup retains the rich-gets-richer property of the DPM. We then apply the random-weighting mechanism under the Bayesian NPL framework on an extended version of the DP-rich setup that leads to our main random-weighting discrete mixture model: the random-weighting scaled DP-rich (RW SDP-rich) approach. We develop a scalable algorithm (which is trivially parallelizable over multiple computing nodes) that ensures local convergence of solutions, and explore various related random-weighting mixture models via simplifications of our RW SDP-rich setup. We illustrate, via various simulations and benchmark data examples, that our RW SDP-rich approach provides reasonable approximation to MCMC posterior clustering for the DPM model. Finally, we establish several appealing theoretical properties of our random-weighting models under the Bayesian NPL framework. Additional details for our random-weighting mixture models are collected as supplementary material in Chapter 5.

ISBN: 9798802710739Subjects--Topical Terms:

517247
Statistics.
Subjects--Index Terms:

Bayesian nonparametrics

Random Weighting in LASSO Regression and in Discrete Mixture Models.
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