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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal style='margin-bottom:12.0pt'><b><i><span style='font-size:14.0pt'>In-Person seminars will be held at Dunham Lab, 10 Hillhouse Ave., Room 220, with an option of remote participation via zoom.</span></i></b><b><i><o:p></o:p></i></b></p><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:"Lucida Sans",sans-serif;color:#286DC0;text-decoration:none'><img border=0 width=150 height=49 style='width:1.5625in;height:.5069in' id=logo src="cid:image001.jpg@01D8CD83.683F0500" alt="Department of Statistics and Data Science
"></span></a></span><span style='color:black'> <a href="https://statistics.yale.edu/" title=Home><b><span style='font-size:22.0pt;font-family:"Lucida Sans",sans-serif;color:#286DC0'>Department of Statistics and Data Science </span></b></a></span><b><i><u><span style='font-size:22.0pt;font-family:"Lucida Sans",sans-serif;color:#286DC0'> <o:p></o:p></span></u></i></b></p><p class=MsoNormal style='margin-top:.1in'><i><u><span style='font-size:16.0pt;font-family:"Arial",sans-serif'>We invite you to attend our in-person seminar.</span></u></i><span style='font-size:13.0pt;font-family:"Arial",sans-serif;background:white'><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:16.0pt;font-family:"Arial",sans-serif'>Jason Altschuler, NYU<o:p></o:p></span></p><p class=MsoNormal><!--[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=171 height=205 style='width:1.7847in;height:2.1388in' src="cid:image004.jpg@01D8CD84.FD95CDE0" align=left hspace=12 v:shapes="Picture_x0020_3"><![endif]><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>In-Person<o:p></o:p></span></b></p><p class=MsoNormal><span class=date-display-single><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Monday, September 26, 2022<o:p></o:p></span></span></p><p class=MsoNormal><span class=date-display-start><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>4:00PM</span></span><span class=date-display-range><span style='font-size:12.0pt;font-family:"Arial",sans-serif'> to </span></span><span class=date-display-end><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>5:00PM</span></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></p><p class=MsoNormal><span class=fn><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Dunham Lab. Room 220</span></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'> <span class=map-icon><span style='letter-spacing:.6pt'><a href="http://maps.google.com/?q=10+Hillhouse+Avenue%2C+New+Haven%2C+CT%2C+06511%2C+us"><span style='color:windowtext'>see map</span></a> </span></span><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>10 Hillhouse Avenue<o:p></o:p></span></p><p class=MsoNormal><span class=locality><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>New Haven</span></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>, <span class=region>CT</span> <span class=postal-code>06511</span><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><a href="https://www.mit.edu/~jasonalt/"><span style='color:#003C76'>Website</span></a><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></p><p class=MsoNormal><strong><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Zoom Link: <o:p></o:p></span></strong></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><a href="https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09">https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09</a> <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Password: 24<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span style='font-size:14.0pt;font-family:"Arial",sans-serif'>Title: Privacy of Noisy SGD<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Information and Abstract: <o:p></o:p></span></p><p style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:0in;box-sizing: inherit'><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>A central issue in machine learning is how to train models on sensitive user data. Industry has widely adopted a simple algorithm: Stochastic Gradient Descent with noise (aka Stochastic Gradient Langevin Dynamics). However, foundational questions about this algorithm’s privacy loss remain open—even in the seemingly simple setting of smooth convex losses over a bounded domain. Our main result resolves these questions by characterizing the differential privacy up to a constant factor. This result reveals that all previous analyses for this setting have the wrong qualitative behavior. Specifically, while previous privacy analyses increase ad infinitum in the number of iterations, we show that after a small burn-in period, running SGD longer leaks no further privacy.<o:p></o:p></span></p><p style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:0in;box-sizing: inherit'><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>In this talk, I will describe this result and our analysis—which departs from previous approaches based on fast mixing, instead using techniques based on optimal transport.<o:p></o:p></span></p><p style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:0in;box-sizing: inherit'><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Joint work with Kunal Talwar<o:p></o:p></span></p><p class=MsoNormal style='line-height:18.0pt;background:white'><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'><a href="x-apple-data-detectors://10/"><span style='color:black;text-decoration:none'>3:30pm</span></a></span></b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'> - Pre-talk meet and greet.</span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></p><p class=MsoNormal><strong><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></strong></p><p class=MsoNormal><strong><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Zoom Link: </span></strong><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Join from PC, Mac, Linux, iOS or Android: <a href="https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09">https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09</a> <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Password: 24<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Or Telephone</span><span style='font-size:12.0pt;font-family:"MS Gothic"'>：</span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>203-432-9666 (2-ZOOM if on-campus) or 646 568 7788<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Meeting ID: 924 1107 7917<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.5pt'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.5pt'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.5pt'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.5pt'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.5pt'><o:p> </o:p></span></p><h2 style='margin:0in;box-sizing: inherit;font-feature-settings: "kern", "liga", "dlig"'><span style='font-family:"Georgia",serif;font-weight:normal'>Department of Statistics and Data Science<o:p></o:p></span></h2><p style='margin:0in;box-sizing: inherit'><span style='font-size:9.0pt;color:black'>Yale University<br>24 Hillhouse Avenue<br>New Haven, CT 06511<o:p></o:p></span></p><p style='margin:0in;box-sizing: inherit'><span style='font-size:9.0pt;color:black'>t 203.432.0666<br>f 203.432.0633<o:p></o:p></span></p><p class=MsoNormal><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></b></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>