{"615776":{"#nid":"615776","#data":{"type":"event","title":"ISyE Seminar - Pragya Sur","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003ETitle:\u0026nbsp;\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003EA modern maximum-likelihood approach for high-dimensional logistic regression\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EAbstract\u003C\/strong\u003E\u003Cstrong\u003E:\u0026nbsp;\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003ELogistic regression is arguably the most widely used and studied non-linear model in statistics.\u0026nbsp;Classical maximum-likelihood theory based statistical inference is ubiquitous in this context. This theory\u0026nbsp;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, \u0026nbsp;(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.\u0026nbsp;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.\u0026nbsp;This is based on joint work with Emmanuel Candes and Yuxin Chen.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EBio:\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003EPragya Sur is a fifth year Ph.D. student in the \u003Ca href=\u0022http:\/\/www-stat.stanford.edu\/\u0022\u003EDepartment of Statistics\u003C\/a\u003E at Stanford University. She is fortunate to be advised by \u003Ca href=\u0022http:\/\/statweb.stanford.edu\/~candes\/\u0022\u003EProf. Emmanuel Cand\u0026egrave;s\u003C\/a\u003E, and is supported by a generous \u003Ca href=\u0022https:\/\/humsci.stanford.edu\/current-students\/fellowships-and-funding\u0022\u003ERic Weiland Graduate Fellowship\u003C\/a\u003E in the \u003Ca href=\u0022https:\/\/humsci.stanford.edu\/\u0022\u003EStanford School of Humanities and Sciences\u003C\/a\u003E. In 2017, she spent a wonderful summer as a research intern in \u003Ca href=\u0022https:\/\/www.microsoft.com\/en-us\/research\/\u0022\u003EMicrosoft Research\u003C\/a\u003E, mentored by \u003Ca href=\u0022https:\/\/www.seas.harvard.edu\/directory\/dwork\u0022\u003EProf. Cynthia Dwork\u003C\/a\u003E.\u003C\/p\u003E\r\n\r\n\u003Cp\u003EHer research spectrum broadly spans high-dimensional statistical inference, controlled variable selection and connections to causality, and fairness in machine learning algorithms.\u003C\/p\u003E\r\n\r\n\u003Cp\u003EPrior to joining Stanford, she received a Bachelor of Statistics in 2012 and a Master of Statistics in 2014 from the \u003Ca href=\u0022http:\/\/www.isical.ac.in\/\u0022\u003EIndian Statistical Institute, Kolkata\u003C\/a\u003E.\u003C\/p\u003E\r\n","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":[{"value":"\u003Cp\u003E\u003Cstrong\u003EAbstract\u003C\/strong\u003E\u003Cstrong\u003E:\u0026nbsp;\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003ELogistic regression is arguably the most widely used and studied non-linear model in statistics.\u0026nbsp;Classical maximum-likelihood theory based statistical inference is ubiquitous in this context. This theory\u0026nbsp;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, \u0026nbsp;(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.\u0026nbsp;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.\u0026nbsp;This is based on joint work with Emmanuel Candes and Yuxin Chen.\u003C\/p\u003E\r\n","format":"limited_html"}],"field_summary_sentence":[{"value":"A modern maximum-likelihood approach for high-dimensional logistic regression"}],"uid":"34868","created_gmt":"2019-01-02 15:52:44","changed_gmt":"2019-01-02 15:52:44","author":"sbryantturner3","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2019-01-07T11:00:00-05:00","event_time_end":"2019-01-07T12:00:00-05:00","event_time_end_last":"2019-01-07T12:00:00-05:00","gmt_time_start":"2019-01-07 16:00:00","gmt_time_end":"2019-01-07 17:00:00","gmt_time_end_last":"2019-01-07 17:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"1242","name":"School of Industrial and Systems Engineering (ISYE)"}],"categories":[],"keywords":[],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1795","name":"Seminar\/Lecture\/Colloquium"}],"invited_audience":[{"id":"78761","name":"Faculty\/Staff"},{"id":"177814","name":"Postdoc"},{"id":"78771","name":"Public"},{"id":"174045","name":"Graduate students"},{"id":"78751","name":"Undergraduate students"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}