[Ml-stat-talks] Fwd: Wilks Statistics Seminar: Weijie Su, , Today, Feb. 24, 2017 12:30 PM, Sherrerd Hall 101
bee at princeton.edu
Fri Feb 24 09:35:27 EST 2017
Talk of interest today.
*** Wilks Statistics Seminar ***
DATE: Today, February 24, 2017
TIME: 12:30 pm
LOCATION: Sherrerd Hall 101
SPEAKER: Weijie Su, University of Pennsylvania
TITLE: False Discovery Rate Control in High-dimensional Linear Regression
ABSTRACT: In many statistical problems, we observe a large number of
potentially explanatory variables of which most may be irrelevant to a
response of interest. For this type of problem, controlling the false
discovery rate (FDR) guarantees that most of the discoveries are truly
explanatory and thus replicable. In this talk, we propose a new method
named SLOPE to control the FDR in sparse high-dimensional linear
regression. This computationally efficient procedure works by regularizing
the fitted coefficients according to their ranks: the higher the rank, the
larger the penalty. This is analogous to the Benjamini-Hochberg procedure,
which compares more significant p-values with more stringent thresholds.
Whenever the columns of the design matrix are not strongly correlated, we
show empirically that SLOPE obtains FDR control at a reasonable level while
offering substantial power. Although SLOPE is developed from a multiple
testing viewpoint, we show the surprising result that it achieves optimal
squared errors under Gaussian random designs over a wide range of sparsity
classes. An appealing feature is that SLOPE does not require any knowledge
of the degree of sparsity. This adaptivity to unknown sparsity has to do
with the FDR control, which strikes the right balance between bias and
variance. The proof of this result presents several elements not found in
the high-dimensional statistics literature.
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