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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><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:"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@01D90FB6.F86F79A0" alt="Department of Statistics and Data Science
"></span></a> <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><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><i><span style='font-size:14.0pt'><o:p></o:p></span></i></p><h1 style='margin:0in'><i><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black;font-weight:normal'><a href="x-apple-data-detectors://10/"><span style='color:black;text-decoration:none'>3:30pm</span></a> - Pre-talk meet and greet, DL Suite 222, Room 228</span></i><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black;font-weight:normal'><o:p></o:p></span></h1><p class=MsoNormal><span class=date-display-single><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></span></p><p class=MsoNormal><span class=date-display-single><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>JIAOYANG HUANG, University of Pennsylvania</span></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><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=135 height=162 style='width:1.4027in;height:1.6875in' src="cid:image004.jpg@01D90FB9.2C843AD0" align=left hspace=12 v:shapes="Picture_x0020_3"><![endif]><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></p><p class=MsoNormal><span class=date-display-single><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Date: Monday, December 19, 2022<o:p></o:p></span></span></p><p class=MsoNormal><span class=date-display-single><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Time: </span></span><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'>Location: Dunham Lab. </span></span><span class=map-icon><span style='font-size:12.0pt;font-family:"Arial",sans-serif;letter-spacing:.6pt'><a href="http://maps.google.com/?q=10+Hillhouse+Avenue%2C+Rm.+220%2C+New+Haven%2C+CT%2C+06511%2C+us"><span style='color:windowtext'>see map</span></a> </span></span><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'>10 Hillhouse Avenue, Rm. 220<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><a href="https://statistics.wharton.upenn.edu/profile/huangjy/"><span style='font-size:12.0pt;font-family:Mallory;color:#003C76;background:white;text-decoration:none'>Website</span></a> <span style='font-size:12.0pt;font-family:"Arial",sans-serif'><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><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></b></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><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Title: Efficient derivative-free Bayesian inference for large-scale inverse problems<o:p></o:p></span></b></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><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>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;box-sizing: inherit'><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>We consider Bayesian inference for large-scale inverse problems, where computational challenges arise from the need for the repeated evaluations of an expensive forward model, which is often given as a black box or is impractical to differentiate. In this talk I will propose a new derivative-free algorithm Unscented Kalman Inversion, which utilizes the ideas from Kalman filter, to efficiently solve these inverse problems. First, I will explain some basics about Variational Inference under general metric tensors. In particular, under the Fisher-Rao metric, the Gaussian Variational Inference leads to the natural gradient descent. Next, I will discuss two different views of our algorithm. It can be obtained from a Gaussian approximation of the filtering distribution of a novel mean field dynamical system. And it can also be viewed as a derivative-free approximation of the natural gradient descent. I will also discuss theoretical properties for linear inverse problems. Finally, I will discuss an extension of our algorithm using Gaussian mixture approximation, which leads to the Gaussian Mixture Kalman Inversion, an efficient derivative-free Bayesian inference approach capable of capturing multiple modes. I will demonstrate the effectiveness of this approach in several numerical experiments with multimodal posterior distributions, which typically converge within O(10) iterations. <o:p></o:p></span></p><p style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:0in'><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>This is based on joint works with Yifan Chen, Daniel Zhengyu Huang, Sebastian Reich and Andrew Stuart.<o:p></o:p></span></p><p class=MsoNormal><em><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Zoom Option: </span></b></em><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Link: Join from PC, Mac, Linux, iOS or Android: <a href="https://yale.zoom.us/j/92411077917?"><span style='color:#286DC0'>https://yale.zoom.us/j/92411077917?</span></a>pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09 <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: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'><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'><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><h2 style='margin:0in;box-sizing: inherit;font-feature-settings: "kern", "liga", "dlig"'><span style='font-family:YaleNew;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><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><o:p> </o:p></p></div></body></html>