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"><span style='font-size:22.0pt;font-family:"Arial",sans-serif;color:#286DC0;mso-ligatures:none;text-decoration:none'><img border=0 width=150 height=49 style='width:1.5625in;height:.5104in' id=logo src="cid:image001.jpg@01DA583B.8647D420" alt="Department of Statistics and Data Science
"></span></a></span><span style='font-family:"Arial",sans-serif;color:black'> <a href="https://statistics.yale.edu/" title=Home><b><span style='font-size:22.0pt;color:#286DC0'>Department of Statistics and Data Science </span></b></a></span><b><i><u><span style='font-size:22.0pt;font-family:"Arial",sans-serif;color:#286DC0'> </span></u></i></b><b><i><u><span style='font-size:22.0pt;font-family:"Arial",sans-serif;color:#286DC0;mso-ligatures:none'><o:p></o:p></span></u></i></b></p><p class=MsoNormal><b><span style='font-family:"Times New Roman",serif'><o:p> </o:p></span></b></p><p class=MsoNormal style='background:white'><span style='font-size:16.0pt;font-family:"Times New Roman",serif;color:#00356B'><a href="https://statistics.yale.edu/seminars/alex-wein-0"><span style='color:black;text-decoration:none'>Alex Wein</span></a>, </span><span style='font-size:16.0pt;font-family:"Times New Roman",serif;color:#222222'>University of California, Davis<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><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=141 height=169 style='width:1.4687in;height:1.7604in' src="cid:image003.jpg@01DA5D8C.F4E25850" align=left hspace=12 v:shapes="Picture_x0020_3"><![endif]><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black'>Date: <span class=date-display-single>Monday, February 12, 2024</span></span><span class=date-display-single><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span class=date-display-single><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black'>Time: </span></span><span class=date-display-start><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black'>4:00PM</span></span><span class=date-display-range><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black'> to </span></span><span class=date-display-end><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black'>5:00PM</span></span><o:p></o:p></p><p class=MsoNormal style='background:white'><span class=fn><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black'>Location: Kline Tower</span></span><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black'> <span class=map-icon><span style='letter-spacing:.6pt'><a href="http://maps.google.com/?q=219+Prospect+Street%2C+13+Floor%2C+Rm+1327%2C+New+Haven%2C+CT%2C+06511%2C+us"><span style='color:black'>see map</span></a> </span></span></span><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black'>219 Prospect Street, 13 Floor, Rm 1327</span><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span class=locality><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black'>New Haven</span></span><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:black'>, <span class=region>CT</span> <span class=postal-code>06511</span></span><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:#222222'>Zoom Link: <a href="https://yale.zoom.us/j/94223816617">https://yale.zoom.us/j/94223816617</a> Meeting ID: 942 2381 6617<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:#222222'><a href="https://www.alex-wein.com/"><span style='color:#003C76'>Website</span></a><o:p></o:p></span></p><p class=MsoNormal style='background:white'><b><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:#222222'><o:p> </o:p></span></b></p><p class=MsoNormal style='background:white'><b><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:#222222'><o:p> </o:p></span></b></p><p class=MsoNormal style='background:white'><b><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:#222222'>Fine-Grained Extensions of the Low-Degree Testing Framework<o:p></o:p></span></b></p><p class=MsoNormal style='background:white'><b><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:#222222'><o:p> </o:p></span></b></p><p class=MsoNormal style='background:white'><b><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:#222222'>Information and Abstract: </span></b><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:#222222'>The low-degree polynomial framework has emerged as a versatile tool for probing the computational complexity of statistical problems by studying the power and limitations of a restricted class of algorithms: low-degree polynomials. Focusing on the setting of hypothesis testing, I will discuss some extensions of this method that allow us to tackle finer-grained questions than the standard approach.<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:#222222'><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:12.0pt;font-family:"Times New Roman",serif;color:#222222'>First, for the task of detecting a planted clique in a random graph, we ask not merely when this can be done in polynomial time O(n^c), but seek the optimal exponent c as a function of the clique size. To this end, we consider algorithms that make non-adaptive edge queries and then apply a low-degree test, and we determine the number of queries required. This is joint work with Jay Mardia and Kabir Verchand.<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:12.0pt;font-family:"Times New Roman",serif;color:#222222'>Second, in the spiked Wigner model with any iid spike prior, we seek the precise optimal tradeoff curve between type I and type II error rates. Conditional on an appropriate strengthening of the “low-degree conjecture,” we show that tests based on the spectrum achieve the best possible tradeoff curve among poly-time algorithms, while exponential-time non-spectral tests can do better. This is joint work with Ankur Moitra.<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'><strong><span style='font-size:12.0pt;font-family:"Calibri",sans-serif;color:#222222'>3:30pm - Pre-talk meet and greet teatime - 219 Prospect Street, 13 floor, there will be light snacks and beverages in the kitchen area.</span></strong><span style='font-size:12.0pt;font-family:"Times New Roman",serif;color:#222222'><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman",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><span style='font-size:12.0pt;font-family:"Times New Roman",serif'><o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Arial",sans-serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:18.0pt;font-family:"Arial",sans-serif'>Department of Statistics and Data Science<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:black'>Yale University<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:black'>Kline Tower<br>219 Prospect Street<br>New Haven, CT 06511<o:p></o:p></span></p><p class=MsoNormal><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><o:p> </o:p></p></div></body></html>