[Sds-seminars] Pragya Sur talking today at 4pm!

[Dan Spielman]

PRAGYA SUR, Stanford University
A modern maximum-likelihood approach for high-dimensional logistic
regression
Wednesday, February 27, 20194:00PM to 5:15PM
Dunham Lab. see map
<http://maps.google.com/?q=10+Hillhouse+Avenue%2C+Room+220%2C+New+Haven%2C+CT%2C+%2C+us>

10 Hillhouse Avenue, Room 220
New Haven, CT
Website <https://web.stanford.edu/~pragya/index.html>
Information and Abstract:

Logistic regression is arguably the most widely used and studied non-linear
model in statistics. Classical maximum-likelihood theory based statistical
inference is ubiquitous in this context. This theory hinges on well-known
fundamental results: (1) the maximum-likelihood-estimate (MLE) is
asymptotically unbiased and normally distributed, (2) its variability can
be quantified via the inverse Fisher information, and (3) the
likelihood-ratio-test (LRT) is asymptotically a Chi-Squared. In this talk,
I will show that in the common modern setting where the number of features
and the sample size are both large and comparable, classical results are
far from accurate. In fact,  (1) the MLE is biased, (2) its variability is
far greater than classical results, and (3) the LRT is not distributed as a
Chi-Square. Consequently, p-values obtained based on classical theory are
completely invalid in high dimensions. In turn, I will propose a new theory
that characterizes the asymptotic behavior of both the MLE and the LRT
under some assumptions on the covariate distribution, in a high-dimensional
setting. Empirical evidence demonstrates that this asymptotic theory
provides accurate inference in finite samples. Practical implementation of
these results necessitates the estimation of a single scalar, the overall
signal strength, and I will propose a procedure for estimating this
parameter precisely. This is based on joint work with Emmanuel Candes and
Yuxin Chen.

Pre-talk tea, Dunham Lab., Suite 222, Room 228
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