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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><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'>KUIKUI LIU</span><span style='font-size:13.0pt;font-family:Mallory;color:black;font-weight:normal'>, </span><span class=odd><span style='font-size:13.0pt;font-family:Mallory;color:black;font-weight:normal'>University of Washington</span></span><span style='font-size:13.0pt;font-family:Mallory;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=127 height=152 style='width:1.3229in;height:1.5833in' src="cid:image004.jpg@01D82191.9BC54180" 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'>Wednesday, February 16, 2022</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:13.5pt;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:#222222'>Zoom: <a href="https://yale.zoom.us/j/97960500577">https://yale.zoom.us/j/97960500577</a><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://homes.cs.washington.edu/~liukui17/"><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: Spectral Independence: A New Tool to Analyze Markov Chains<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='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'>Sampling from high-dimensional probability distributions is a fundamental and challenging problem encountered throughout science and engineering. One of the most popular approaches to tackle such problems is the Markov chain Monte Carlo (MCMC) paradigm. While MCMC algorithms are often simple to implement and widely used in practice, analyzing the fidelity of the generated samples remains a difficult problem.<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 describe a new technique called “spectral independence” that my collaborators and I developed over the last couple of years to analyze Markov chains. This technique has allowed us to break long-standing barriers and resolve several decades-old open problems in MCMC theory. Our work has opened up numerous connections with other areas of computer science, mathematics, and statistical physics, leading to dozens of new developments as well as exciting new directions of inquiry. I will then discuss how these connections have allowed us to “unify” nearly all major algorithmic paradigms for approximate counting and sampling. Finally, I will conclude with a wide variety of future directions and open problems at the frontier of this research.<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;background:white;vertical-align:baseline'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black;mso-fareast-language:JA'>For more details and upcoming events visit our website at <a href="http://statistics.yale.edu/" target="_blank"><span style='color:#0563C1'>http://statistics.yale.edu/</span></a> .</span><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-fareast-language:JA'><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-fareast-language:JA'> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;mso-fareast-language:JA'> <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>