Transposable regularized covariance models with applications to high-dimensional data

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High-dimensional data is becoming more prevalent with new technologies in biomedical sciences, imaging and the Internet. Many examples of this data often contain complex relationships between and among sets of variables. When arranged in the form of a matrix, this data is transposable, meaning that either the rows, columns or both can be treated as features. To model transposable data, we present a modification of the matrix-variate normal, the mean-restricted matrix-variate normal, and introduce transposable regularized covariance models by placing penalties on inverse covariance matrices. We give theoretical results exploiting the structure of our transposable models that give computationally feasible algorithms for parameter estimation and calculation of conditional expectations. These contributions make the matrix-variate normal accessible for application to high-dimensional data. We apply our model to two applications: missing data imputation and large-scale inference with the matrix-variate normal distribution. Examples, simulations and results are given using the Netflix movie-rating data and microarrays, demonstrating the flexibility and functionality of our transposable models.


Type of resource text
Form electronic; electronic resource; remote
Extent 1 online resource.
Publication date 2010
Issuance monographic
Language English


Associated with Allen, Genevera Irene
Associated with Stanford University, Department of Statistics
Primary advisor Tibshirani, Robert
Thesis advisor Tibshirani, Robert
Thesis advisor Owen, Art B
Thesis advisor Taylor, Jonathan E
Advisor Owen, Art B
Advisor Taylor, Jonathan E


Genre Theses

Bibliographic information

Statement of responsibility Genevera Irene Allen.
Note Submitted to the Department of Statistics.
Thesis Thesis (Ph. D.)--Stanford University, 2010.
Location electronic resource

Access conditions

© 2010 by Genevera Irene Allen
This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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