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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><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:.5104in' id=logo src="cid:image001.jpg@01D8DFAB.0A9E5560" alt="Department of Statistics and Data Science
"></span></a><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><span class=locality><b><span style='font-size:16.0pt;font-family:"Arial",sans-serif'><a href="https://statistics.yale.edu/seminars/mengdi-wang"><span style='color:windowtext;text-decoration:none'>Mengdi Wang</span></a>, Princeton University</span></b></span><b><span style='font-size:16.0pt;font-family:Mallory;color:#222222'><o:p></o:p></span></b></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=126 height=151 style='width:1.3125in;height:1.5729in' src="cid:image003.jpg@01D8E207.D86F9770" align=left hspace=12 v:shapes="Picture_x0020_2"><![endif]><span style='font-family:"Arial",sans-serif'><o:p></o:p></span></p><p class=MsoNormal><span class=fn><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Date: </span></b></span><span class=fn><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Monday</span></span><span class=date-display-single><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>, October 17, 2022</span></span><span class=date-display-single><span style='font-size:12.0pt'><o:p></o:p></span></span></p><p class=MsoNormal><span class=fn><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif'>Talk Time:</span></b></span><span class=date-display-single><span style='font-size:12.0pt;font-family:"Arial",sans-serif'> </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><o:p></o:p></p><p class=MsoNormal style='background:white'><span class=fn><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>Zoom meeting link:</span></b></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'> <a href="https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09">https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09</a> / Password: 24</span><o:p></o:p></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-family:"Arial",sans-serif'><o:p> </o:p></span></b></p><p class=MsoNormal><b><span style='font-family:"Arial",sans-serif'><o:p> </o:p></span></b></p><p class=MsoNormal><b><span style='font-family:"Arial",sans-serif'><o:p> </o:p></span></b></p><p class=MsoNormal><b><span style='font-family:"Arial",sans-serif'><o:p> </o:p></span></b></p><p class=MsoNormal><b><span style='font-size:15.0pt;font-family:Mallory;color:#222222;background:white'>Title: Thompson Sampling-Guided Directed Evolution for Sequence Optimization</span></b><b><span style='font-size:15.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></b></p><p class=MsoNormal><b><span style='font-size:15.0pt;font-family:"Arial",sans-serif'><o:p> </o:p></span></b></p><p class=MsoNormal style='text-align:justify;text-justify:inter-ideograph;line-height:150%'><b><span style='font-family:"Arial",sans-serif'>Information and Abstract:<o:p></o:p></span></b></p><p class=MsoNormal style='text-align:justify;text-justify:inter-ideograph;line-height:150%'><span style='font-size:12.0pt;line-height:150%;font-family:"Arial",sans-serif;color:#222222;background:white'>Directed Evolution (DE), a landmark wet-lab method originated in 1960s, enables discovery of novel protein designs via evolving a population of candidate sequences. Recent advances in biotechnology has made it possible to collect high-throughput data, allowing the use of machine learning to map out a protein’s sequence-to-function relation. There is a growing interest in machine learning-assisted DE for accelerating protein optimization. Yet the theoretical understanding of DE, as well as the use of machine learning in DE, remains limited.</span><span style='font-size:12.0pt;line-height:150%;font-family:"Arial",sans-serif;color:#222222'><br><span style='background:white'>In this paper, we connect DE with the bandit learning theory and make a first attempt to study regret minimization in DE. We propose a Thompson Sampling-guided Directed Evolution (TS-DE) framework for sequence optimization, where the sequence-to-function mapping is unknown and querying a single value is subject to costly and noisy measurements. TS-DE updates a posterior of the function based on collected measurements. It uses a posterior-sampled function estimate to guide the crossover recombination and mutation steps in DE. In the case of a linear model, we show that TS-DE enjoys a Bayesian regret of order $\tilde O(d^{2}\sqrt{MT})$\footnote{$\tilde O(\cdot)$ ignores the logarithmic terms.}, where $d$ is feature dimension, $M$ is population size and $T$ is number of rounds. This regret bound is nearly optimal, confirming that bandit learning can provably accelerate DE. It may have implications for more general sequence optimization and evolutionary algorithms. </span></span><b><span style='font-size:12.0pt;line-height:150%;font-family:"Arial",sans-serif'><o:p></o:p></span></b></p><p class=MsoNormal><b><span style='font-family:"Arial",sans-serif'><o:p> </o:p></span></b></p><p class=MsoNormal style='margin-bottom:14.0pt'><b><i><span style='font-size:14.0pt'>3:30pm - Pre-talk meet & greet Zoom Link: </span></i></b><span style='font-family:"Arial",sans-serif'>: <a href="https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09"><span style='color:#286DC0'>https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09</span></a><br>Password: 24</span><b><i><span style='font-size:14.0pt'><o:p></o:p></span></i></b></p><p class=MsoNormal><span style='font-family:"Arial",sans-serif'>Join from PC, Mac, Linux, iOS or Android: <a href="https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09"><span style='color:#286DC0'>https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09</span></a><br>Password: 24<br>Or Telephone</span><span lang=JA style='font-family:"MS Gothic"'>：</span><span style='font-family:"Arial",sans-serif'>203-432-9666 (2-ZOOM if on-campus) or 646 568 7788<br>Meeting ID: 924 1107 7917<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Arial",sans-serif'><o:p> </o:p></span></p><h2 style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:6.0pt;margin-left:0in;box-sizing: inherit;font-feature-settings: "kern", "liga", "dlig"'><span style='font-family:"Arial",sans-serif;font-weight:normal'><o:p> </o:p></span></h2><h2 style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:6.0pt;margin-left:0in'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black;font-weight:normal'>For more details and upcoming events visit our website at <a href="http://statistics.yale.edu/"><span style='color:black;text-decoration:none'>http://statistics.yale.edu/</span></a>. </span><span style='font-family:"Arial",sans-serif;font-weight:normal'><o:p></o:p></span></h2><h2 style='margin:0in'><span style='font-family:"Arial",sans-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;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 style='margin:0in;box-sizing: inherit'><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 style='line-height:18.0pt;background:white'><span style='font-family:"Arial",sans-serif'><o:p> </o:p></span></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>