- Main
Detection and Localization of a Submatrix: Theory, Methods and Algorithms
- Liu, Yuchao
- Advisor(s): Arias-Castro, Ery
Abstract
We consider the problem of detecting and localizing an submatrix with larger-than-usual
entries inside a large, noisy matrix. This problem arises from analysis of data in
genetics, bioinformatics, and social sciences. We consider that entries of the data matrix are
independently following distributions from a natural exponential family, which generalizes
the common Gaussian assumptions in the literature. In Chapter 2 a permutation test for
testing the existence of the elevated submatrix is studied. The test's asymptotic power is
illustrated, and its robust variation (rank method) is also studied. In The latter part of
Chapter 2 and Chapter 3 we remove the prior knowledge of the submatrix size, aiming
to develop adaptive methods for detection and localization. Latter part of Chapter 2
proposes a Bonferroni testing framework based on the permutation scan test, to solve
the detection problem. An accelerating framework is also developed without sacricing
asymptotic power. In Chapter 3, a new size-adaptive estimator is proposed to solve the
localization problem. Its asymptotic performance is studied, and two fast algorithms to
approximate the estimator are developed.
Main Content
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