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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72" style='word-wrap:break-word'><div class=WordSection1><p class=MsoNormal style='background:white'><span style='color:black'><a href="https://statistics.yale.edu/" title="Department of Statistics and Data Science
"><span style='font-size:22.0pt;font-family:"Arial",sans-serif;color:#286DC0;text-decoration:none'><img border=0 width=150 height=49 style='width:1.5625in;height:.5104in' id=logo src="cid:image001.jpg@01D94ABD.2E8B5D60" alt="Department of Statistics and Data Science
"></span></a></span><span style='font-family:"Arial",sans-serif;color:black'> <a href="https://statistics.yale.edu/" title=Home><b><span style='font-size:22.0pt;color:#286DC0'>Department of Statistics and Data Science </span></b></a></span><b><i><u><span style='font-size:22.0pt;font-family:"Arial",sans-serif;color:#286DC0'> <o:p></o:p></span></u></i></b></p><p class=MsoNormal><span style='font-family:"Arial",sans-serif'>In-Person seminars will be held at Mason Lab 211, 9 Hillhouse Avenue with the option of virtual participation (<a href="https://yale.hosted.panopto.com/Panopto/Pages/Sessions/List.aspx?folderID=f8b73c34-a27b-42a7-a073-af2d00f90ffa"><span style='color:windowtext;text-decoration:none'>https://yale.hosted.panopto.com/Panopto/Pages/Sessions/List.aspx?folderID=f8b73c34-a27b-42a7-a073-af2d00f90ffa</span></a>)<o:p></o:p></span></p><p class=MsoNormal><b><span style='font-family:"Arial",sans-serif'><a href="https://0.0.0.10/"><span style='color:windowtext;text-decoration:none'>3:30pm</span></a> - Pre-talk meet and greet teatime - Dana House, 24 Hillhouse Avenue </span></b><b><o:p></o:p></b></p><h1 style='mso-margin-top-alt:.1in;margin-right:0in;margin-bottom:0in;margin-left:0in;background:white'><span style='font-size:14.0pt;font-family:"Arial",sans-serif;color:black'>Oscar Leong, </span><span class=odd><span style='font-size:14.0pt;font-family:"Arial",sans-serif;color:black'>Caltech</span></span><span style='font-size:14.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></h1><p class=MsoNormal style='background:white'><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
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</v:shape><![endif]--><![if !vml]><img width=113 height=136 style='width:1.177in;height:1.4166in' src="cid:image004.jpg@01D94AC7.7695DAE0" align=left hspace=12 v:shapes="Picture_x0020_2"><![endif]><span class=date-display-single><span style='font-size:13.5pt;font-family:Mallory;color:black'>Date: Wednesday, March 01, 2023</span></span><span class=date-display-single><span style='font-size:13.5pt;font-family:Mallory'><o:p></o:p></span></span></p><p class=MsoNormal style='background:white'><span class=date-display-single><span style='font-size:13.5pt;font-family:Mallory;color:black'>Time: </span></span><span class=date-display-start><span style='font-size:13.5pt;font-family:Mallory;color:black'>4:00PM</span></span><span class=date-display-range><span style='font-size:13.5pt;font-family:Mallory;color:black'> to </span></span><span class=date-display-end><span style='font-size:13.5pt;font-family:Mallory;color:black'>5:00PM</span></span><span style='font-size:13.5pt;font-family:Mallory'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span class=fn><span style='font-size:13.0pt;font-family:Mallory;color:black'>Location: Mason Lab, Rm. 211</span></span><span style='font-size:13.0pt;font-family:Mallory;color:black'> </span><span class=map-icon><span style='font-size:12.0pt;font-family:Mallory;color:black;letter-spacing:.6pt'><a href="http://maps.google.com/?q=9+Hillhouse+Ave%2C+New+Haven%2C+CT%2C+06511%2C+us"><span style='color:black'>see map</span></a> </span></span><span style='font-size:13.0pt;font-family:Mallory'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:13.0pt;font-family:Mallory;color:black'>9 Hillhouse Ave</span><span style='font-size:13.0pt;font-family:Mallory'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span class=locality><span style='font-size:13.0pt;font-family:Mallory;color:#222222'>New Haven</span></span><span style='font-size:13.0pt;font-family:Mallory;color:#222222'>, <span class=region>CT</span> <span class=postal-code>06511</span><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:13.0pt;font-family:Mallory;color:#222222'><a href="https://www.oscarleong.com/"><span style='font-size:12.0pt;color:#003C76'>Website</span></a><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:13.0pt;font-family:Mallory;color:#222222'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><b><span style='font-size:15.0pt;font-family:Mallory;color:#222222'>Title: The Power and Limitations of Convexity in Data Science<o:p></o:p></span></b></p><p class=MsoNormal style='background:white'><b><span style='font-size:15.0pt;font-family:Mallory;color:#222222'><o:p> </o:p></span></b></p><p class=MsoNormal style='background:white'><b><span style='font-size:13.0pt;font-family:Mallory;color:#222222'>Information and Abstract: <o:p></o:p></span></b></p><p style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:0in;background:white;box-sizing: inherit'><span style='font-size:13.0pt;font-family:Mallory;color:#222222'>Optimization is a fundamental pillar of data science. Traditionally, the art and challenge in optimization lay primarily in problem formulation to ensure desirable properties such as convexity. In the context of contemporary data science, however, optimization is practiced differently, with scalable local search methods applied to nonconvex objectives being the dominant paradigm in high-dimensional problems. This has brought a number of foundational mathematical challenges at the interface between optimization and data science pertaining to the dichotomy between convexity and nonconvexity.<o:p></o:p></span></p><p style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:0in;background:white;box-sizing: inherit'><span style='font-size:13.0pt;font-family:Mallory;color:#222222'>In this talk, I will discuss some of my work addressing these challenges in regularization, a technique to encourage structure in solutions to statistical estimation and inverse problems. Even setting aside computational considerations, we currently lack a systematic understanding from a modeling perspective of what types of geometries should be preferred in a regularizer for a given data source. In particular, given a data distribution, what is the optimal regularizer for such data and what are the properties that govern whether it is amenable to convex regularization? Using ideas from star geometry, Brunn-Minkowski theory, and variational analysis, I show that we can characterize the optimal regularizer for a given distribution and establish conditions under which this optimal regularizer is convex. Moreover, I describe results establishing the robustness of our approach, such as convergence of optimal regularizers with increasing sample size and statistical learning guarantees with applications to several classes of regularizers of interest.<o:p></o:p></span></p><p class=MsoNormal><b><i><o:p> </o:p></i></b></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>For more details and upcoming events visit our website at <a href="http://statistics.yale.edu/"><span style='color:black'>http://statistics.yale.edu/</span></a></span><o:p></o:p></p><p class=MsoNormal><span style='font-family:"Arial",sans-serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:18.0pt;font-family:"Arial",sans-serif'>Department of Statistics and Data Science<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:black'>Yale University<br>24 Hillhouse Avenue<br>New Haven, CT 06511<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:black'>t 203.432.0666<br>f 203.432.0633<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>