<div dir="ltr"><div class="gmail-group-header" style="box-sizing:inherit;font-family:Mallory,Verdana,Arial,Helvetica,sans-serif;font-size:17px"><span class="gmail-field gmail-field-name-title gmail-field-type-ds gmail-field-label-hidden" style="box-sizing:inherit"><span style="box-sizing:inherit"><span class="gmail-odd gmail-first gmail-last" style="box-sizing:inherit"><h1 class="gmail-title" style="box-sizing:inherit;font-weight:300;padding:0px;font-feature-settings:"kern","liga","dlig";font-size:1.76471em;line-height:normal;font-stretch:normal;color:rgb(0,60,118);text-transform:uppercase;display:inline-block">PRAGYA SUR</h1></span></span></span>, <span class="gmail-field gmail-field-name-field-university gmail-field-type-text gmail-field-label-hidden" style="box-sizing:inherit;margin-left:5px"><span style="box-sizing:inherit"><span class="gmail-odd gmail-first gmail-last" style="box-sizing:inherit">Stanford University</span></span></span><div class="gmail-field gmail-field-name-field-abstract-title gmail-field-type-text gmail-field-label-hidden" style="box-sizing:inherit"><div class="gmail-field-items" style="box-sizing:inherit"><div class="gmail-field-item even" style="box-sizing:inherit;font-size:20px;font-weight:600;line-height:1.2;margin-bottom:1em;margin-top:0.5em">A modern maximum-likelihood approach for high-dimensional logistic regression</div></div></div></div><div class="gmail-group-left" style="box-sizing:inherit;float:left;width:auto;padding-right:15.3125px;max-width:30%;font-family:Mallory,Verdana,Arial,Helvetica,sans-serif;font-size:17px"><div class="gmail-field gmail-field-name-field-image gmail-field-type-image gmail-field-label-hidden" style="box-sizing:inherit"><div class="gmail-field-items" style="box-sizing:inherit"><div class="gmail-field-item even" style="box-sizing:inherit"><img src="https://statistics.yale.edu/sites/default/files/styles/user_picture_node/public/photo_7.jpg?itok=fIXdW_WA" width="400" height="480" alt="" style="box-sizing: inherit; border: 0px; max-width: 100%; height: auto; vertical-align: bottom;"></div></div></div></div><div class="gmail-group-right" style="box-sizing:inherit;float:left;width:auto;max-width:65%;padding-left:22.9688px;font-family:Mallory,Verdana,Arial,Helvetica,sans-serif;font-size:17px"><div class="gmail-field gmail-field-name-field-event-time gmail-field-type-datetime gmail-field-label-hidden" style="box-sizing:inherit"><div class="gmail-field-items" style="box-sizing:inherit"><div class="gmail-field-item even" style="box-sizing:inherit;color:rgb(0,60,118);font-size:18px;line-height:1.4"><span class="gmail-date-display-single" style="box-sizing:inherit">Wednesday, February 27, 2019<span class="gmail-date-display-range" style="box-sizing:inherit;float:left;width:416.203px"><span class="gmail-date-display-start" style="box-sizing:inherit">4:00PM</span> to <span class="gmail-date-display-end" style="box-sizing:inherit">5:15PM</span></span></span></div></div></div><div class="gmail-field gmail-field-name-field-location gmail-field-type-location gmail-field-label-hidden" style="box-sizing:inherit"><div class="gmail-field-items" style="box-sizing:inherit"><div class="gmail-field-item even" style="box-sizing:inherit"><div class="gmail-location gmail-vcard" style="box-sizing:inherit"><div class="gmail-adr" style="box-sizing:inherit"><span class="gmail-fn" style="box-sizing:inherit">Dunham Lab.</span> <span class="gmail-map-icon" style="box-sizing:inherit;margin-left:0.25em;font-size:0.925em;line-height:1.55;letter-spacing:0.05em;word-spacing:0.05em;text-transform:lowercase;font-feature-settings:"smcp""><a href="http://maps.google.com/?q=10+Hillhouse+Avenue%2C+Room+220%2C+New+Haven%2C+CT%2C+%2C+us" style="box-sizing:inherit;outline:none;line-height:inherit;color:rgb(40,109,192)">see map</a> </span><div class="gmail-street-address" style="box-sizing:inherit">10 Hillhouse Avenue, Room 220</div><span class="gmail-locality" style="box-sizing:inherit">New Haven</span>, <span class="gmail-region" style="box-sizing:inherit">CT</span></div></div></div></div></div><div class="gmail-field gmail-field-name-field-website gmail-field-type-link-field gmail-field-label-hidden" style="box-sizing:inherit"><div class="gmail-field-items" style="box-sizing:inherit"><div class="gmail-field-item even" style="box-sizing:inherit"><a href="https://web.stanford.edu/~pragya/index.html" style="box-sizing:inherit;text-decoration-line:none;outline:none;line-height:1.5;color:rgb(0,60,118);font-size:16px">Website</a></div></div></div></div><div class="gmail-group-footer" style="box-sizing:inherit;clear:both;padding-top:15px;font-family:Mallory,Verdana,Arial,Helvetica,sans-serif;font-size:17px"><div class="gmail-field gmail-field-name-body gmail-field-type-text-with-summary gmail-field-label-above" style="box-sizing:inherit"><div class="gmail-field-label" style="box-sizing:inherit;font-weight:bold">Information and Abstract: </div><div class="gmail-field-items" style="box-sizing:inherit"><div class="gmail-field-item even" style="box-sizing:inherit"><p style="box-sizing:inherit;margin:0px 0px 1em;padding:0px">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.</p></div></div></div><div class="gmail-field gmail-field-name-field-event-description gmail-field-type-text-with-summary gmail-field-label-hidden" style="box-sizing:inherit"><div class="gmail-field-items" style="box-sizing:inherit"><div class="gmail-field-item even" style="box-sizing:inherit"><p style="box-sizing:inherit;margin:0px 0px 1em;padding:0px">Pre-talk tea, Dunham Lab., Suite 222, Room 228</p><p style="box-sizing:inherit;margin:0px 0px 1em;padding:0px"><br></p></div></div></div></div></div>