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"></span><span style='font-family:"Microsoft YaHei Light",sans-serif;color:#073763;mso-fareast-language:JA'> <a href="https://statistics.yale.edu/" target="_blank" title=Home><span style='font-size:22.0pt;color:#0563C1'>Department of Statistics and Data Science </span></a></span><i><span style='font-size:22.0pt;font-family:"Microsoft YaHei Light",sans-serif;color:#073763;mso-fareast-language:JA'> </span></i><span style='font-family:"Microsoft YaHei Light",sans-serif;mso-fareast-language:JA'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><u><span style='font-size:16.0pt;color:#073763;mso-fareast-language:JA'>You are invited to a scheduled Zoom Seminar</span></u><u><span style='mso-fareast-language:JA'><o:p></o:p></span></u></p><h1 style='mso-margin-top-alt:.1in;margin-right:0in;margin-bottom:0in;margin-left:0in;background:white'><span style='font-size:23.0pt;font-family:Mallory;color:black;text-transform:uppercase;font-weight:normal'>ANDRE WIBISONO</span><span style='font-size:13.0pt;font-family:Mallory;color:black'>, </span><span class=odd><span style='font-size:13.0pt;font-family:Mallory;color:black'>Yale University</span></span><span style='font-size:23.0pt;font-family:Mallory;text-transform:uppercase;font-weight:normal'><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=124 height=149 style='width:1.2916in;height:1.552in' src="cid:image003.jpg@01D7D09F.65179220" align=left hspace=12 v:shapes="Picture_x0020_3"><![endif]><span class=date-display-single><span style='font-size:13.5pt;font-family:Mallory;color:black'>Monday, November 08, 2021</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-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:13.0pt;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'>Zoom</span><span style='font-size:13.0pt;font-family:Mallory;color:#222222'>: <a href="https://yale.zoom.us/j/99169700816?pwd=SWEvWHI5d3dPNVdHMkZMZURMWWJPUT09">https://yale.zoom.us/j/99169700816?pwd=SWEvWHI5d3dPNVdHMkZMZURMWWJPUT09</a> <o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:13.0pt;font-family:Mallory;color:#222222'>Password: 24<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="http://www.cs.yale.edu/homes/wibisono/"><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'><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'><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'>Title: On Bias and Discretization: Sampling under Isoperimetry via Langevin Algorithm<o:p></o:p></span></b></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:13.0pt;font-family:Mallory;color:#222222'>Information and Abstract: <o:p></o:p></span></b></p><p style='margin:0in;background:white;box-sizing: inherit'><span style='font-size:13.0pt;font-family:Mallory;color:#222222'>Sampling is a fundamental algorithmic task. Many applications require sampling from probability distributions in high-dimensional spaces, and in modern problems the distributions are complicated and non-logconcave. While the setting of logconcave functions is well-studied, it is important to have efficient sampling algorithms with good convergence guarantees beyond logconcavity. In this talk we study sampling from the perspective of optimization in the space of distributions. We focus on the Langevin dynamics and the Unadjusted Langevin Algorithm (ULA) as a case study. We prove a biased convergence guarantee of ULA in KL divergence assuming the target distribution satisfies Log-Sobolev Inequality (LSI) and the log-density has bounded Hessian; notably, we do not assume convexity nor bounds on higher derivatives. We also show convergence guarantees in Rényi divergence assuming the biased limit satisfies LSI or Poincaré inequality. We investigate the source of the bias of ULA and consider how to remove the bias. We point out the difficulty is that the heat flow is exactly solvable, but neither its forward nor backward method is implementable in general.<o:p></o:p></span></p><p style='margin:0in;background:white;box-sizing: inherit'><span style='font-size:13.0pt;font-family:Mallory;color:#222222'><o:p> </o:p></span></p><p style='margin:0in;background:white'><span style='font-size:13.0pt;font-family:Mallory;color:#222222'>Zoom is Yale’s audio and visual conferencing platform.<o:p></o:p></span></p><p style='margin:0in;background:white;box-sizing: inherit'><span style='font-size:13.0pt;font-family:Mallory;color:#222222'>Topic: Yale S&DS Department Seminar<o:p></o:p></span></p><p style='margin:0in;background:white;box-sizing: inherit'><span style='font-size:13.0pt;font-family:Mallory;color:#222222'>Time: 4:00pm - 5:00pm<o:p></o:p></span></p><p style='margin:0in;background:white;box-sizing: inherit'><span style='font-size:13.0pt;font-family:Mallory;color:#222222'>Join from PC, Mac, Linux, iOS or Android: <a href="https://yale.zoom.us/j/99169700816?pwd=SWEvWHI5d3dPNVdHMkZMZURMWWJPUT09" target="_blank"><span style='color:#286DC0'>https://yale.zoom.us/j/99169700816?pwd=SWEvWHI5d3dPNVdHMkZMZURMWWJPUT09</span></a><o:p></o:p></span></p><p style='margin:0in;background:white;box-sizing: inherit'><span style='font-size:13.0pt;font-family:Mallory;color:#222222'>Password: 24<o:p></o:p></span></p><p style='margin:0in;background:white;box-sizing: inherit'><span style='font-size:13.0pt;font-family:Mallory;color:#222222'>Or Telephone</span><span style='font-size:13.0pt;font-family:"MS Gothic";color:#222222'>：</span><span style='font-size:13.0pt;font-family:Mallory;color:#222222'>203-432-9666 (2-ZOOM if on-campus) or 646 568 7788<o:p></o:p></span></p><p style='margin:0in;background:white;box-sizing: inherit'><span style='font-size:13.0pt;font-family:Mallory;color:#222222'>Meeting ID: 991 6970 0816<o:p></o:p></span></p><p style='margin:0in;background:white;box-sizing: inherit'><span style='font-size:13.0pt;font-family:Mallory;color:#222222'>International numbers available: <a href="https://yale.zoom.us/u/acBOaD1ic6" target="_blank"><span style='color:#286DC0'>https://yale.zoom.us/u/acBOaD1ic6</span></a><o:p></o:p></span></p><p style='margin:0in;background:white;box-sizing: inherit'><span style='font-size:13.0pt;font-family:Mallory;color:#222222'>For H.323 and SIP information for video conferencing units please click here: <a href="https://yale.service-now.com/it?id=support_article&sys_id=434b72d3db9e8fc83514b1c0ef961924" target="_blank"><span style='color:#286DC0'>https://yale.service-now.com/it?id=support_article&sys_id=434b72d3db9e8fc83514b1c0ef961924</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><span style='mso-fareast-language:JA'><o:p> </o:p></span></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>