Selective inference and learning mixed graphical models
Abstract/Contents
- Abstract
- This thesis studies two problems in modern statistics. First, we study selective inference, or inference for hypothesis that are chosen after looking at the data. The motiving application is inference for regression coefficients selected by the lasso. We present the Condition-on-Selection method that allows for valid selective inference, and study its application to the lasso, and several other selection algorithms. In the second part, we consider the problem of learning the structure of a pairwise graphical model over continuous and discrete variables. We present a new pairwise model for graphical models with both continuous and discrete variables that is amenable to structure learning. In previous work, authors have considered structure learning of Gaussian graphical models and structure learning of discrete models. Our approach is a natural generalization of these two lines of work to the mixed case. The penalization scheme involves a novel symmetric use of the group-lasso norm and follows naturally from a particular parametrization of the model. We provide conditions under which our estimator is model selection consistent in the high-dimensional regime.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2015 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Lee, Jason Dean |
|---|---|
| Associated with | Stanford University, Department of Computational and Mathematical Engineering. |
| Primary advisor | Hastie, Trevor |
| Primary advisor | Taylor, Jonathan |
| Thesis advisor | Hastie, Trevor |
| Thesis advisor | Taylor, Jonathan |
| Thesis advisor | Mackey, Lester |
| Advisor | Mackey, Lester |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Jason Dean Lee. |
|---|---|
| Note | Submitted to the Department of Computational and Mathematical Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2015. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2015 by Jason Dean Lee
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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