Some hierarchical and group regularization methods and applications

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We analyze methods to model data with group effects that may be hierarchical. We begin by introducing a problem inferring human results from experiments done on mice in Chapter 2. Since we have paired experimental results across many genes and diseases, this suggests a hierarchical random effects model. Alternatively, we can also simplify the generative assumptions and consider a fixed effect model with regularization. While these basic models can outperform the baseline estimate of using the results on mice directly, they do not take full advantage of the two factors in the data. We impose either a hierarchical model or an additive model to account for the two effects. In Chapter 3, we propose a two factor random effects model with a more general covariance structure, which captures correlation across related genes and diseases and thus, allows interactions between the factors. The benefit of this model extends to general linear regression problems with networked data. Finally, in Chapter 4, we analyze pliable lasso, which extends the lasso, for regularizing two factor fixed effects with potential interactions between them. While the lasso can be used for all terms, including interactions, the large amount of coefficients introduces variance into the estimator. Pliable lasso imposes a hierarchical structure, that allows variance reduction. Since pliable lasso is a more general method for estimating interaction effects and not just fixed effects, our analysis is done with general main and interaction effects.


Type of resource text
Form electronic resource; remote; computer; online resource
Extent 1 online resource.
Place California
Place [Stanford, California]
Publisher [Stanford University]
Copyright date 2019; ©2019
Publication date 2019; 2019
Issuance monographic
Language English


Author Du, Wenfei
Degree supervisor Tibshirani, Robert
Thesis advisor Tibshirani, Robert
Thesis advisor Imbens, Guido
Thesis advisor Taylor, Jonathan E
Degree committee member Imbens, Guido
Degree committee member Taylor, Jonathan E
Associated with Stanford University, Department of Statistics.


Genre Theses
Genre Text

Bibliographic information

Statement of responsibility Wenfei Du.
Note Submitted to the Department of Statistics.
Thesis Thesis Ph.D. Stanford University 2019.
Location electronic resource

Access conditions

© 2019 by Wenfei Du
This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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