<div dir="ltr"><div class="gmail_default" style="font-family:georgia,serif;font-size:small"><div class="gmail_default" style="font-family:Arial,Helvetica,sans-serif"><div class="gmail_default"><font color="#000000" face="georgia, serif"><b>When:</b>         April 19th<b> at <span style="background-color:rgb(255,255,0)">12:30pm CT  </span></b></font><div dir="ltr"><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif"> <br><b>Where:</b><b>  </b>      <span class="gmail-il">Talk</span> will be given<span style="background-color:rgb(255,255,0)"> </span><span style="background-color:rgb(255,255,0)"><font style="font-weight:bold"><u>live, in-person</u></font><font style="font-weight:bold"> </font></span>at</font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif">                       TTIC, 6045 S. Kenwood Avenue</font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif">                        5th Floor, Room 530<b>              </b>   </font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif"><br></font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="georgia, serif" color="#000000"><b><span class="gmail_default"></span>Virtually:</b>    via Panopto (<a href="https://uchicago.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=479b1837-8c4c-40b5-b6ef-b09a00fef8c7" target="_blank">Livestream</a>) </font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif"> </font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="georgia, serif" color="#000000"><b>Who:</b><b> </b>          Theodor Misiakiewicz , TTIC</font></p><table border="0" cellspacing="0" cellpadding="0" width="0" style="width:0in;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;border-collapse:collapse"><tbody><tr><td style="padding:0in"></td></tr></tbody></table><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif"> <span class="gmail_default"></span></font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="georgia, serif" color="#000000"><b>Title</b>:            Deterministic equivalents for kernel regression</font></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="georgia, serif" color="#000000"><br></font></p><div><font face="georgia, serif" color="#000000"><b>Abstract:</b>   In this talk, we revisit kernel ridge regression (KRR) which has attracted renewed interest recently due to its connections to deep learning. A large body of work has sought to precisely characterize the performance of KRR in toy settings, either through novel uniform convergence bounds or by leveraging RMT in asymptotic regimes. In a parallel—and mostly disjoint—line of work dating back 20 years, physicists have derived closed-form estimates for the risk of KRR using statistical physics heuristics.  These estimates show remarkably good agreement with the learning curves obtained numerically for both synthetic and real data, and complex kernels, including pre-trained neural networks.</font></div><font face="georgia, serif" color="#000000"><br>In this talk, we prove that these deterministic estimates hold for a general class of problems satisfying some spectral properties. Our proofs rely on a careful derivation of deterministic equivalents for random matrix functionals in the dimension-free regime pioneered by Cheng and Montanari (2022).<br><br>If time permits, we will discuss the case of kernel methods with general loss functions. Gaussian universality no longer holds. We show instead that the model belongs to another universality class defined in terms of a Gaussian model to which we append a low-dimensional non-gaussian part.</font></div></div><div><font face="georgia, serif" color="#000000"><br></font></div><div><div class="gmail_default"><b><font color="#000000" face="georgia, serif">*********************************************************************************************</font></b></div><p class="MsoNormal" style="margin:0in 0in 8pt;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;line-height:15.6933px"><font face="georgia, serif" color="#000000"><b>Masks are optional in all common areas. </b><b>Full visitor guidance is available at <a href="http://ttic.edu/visitors" target="_blank">ttic.edu/visitors</a>.</b></font></p><p class="MsoNormal" style="margin:0in 0in 12pt;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;line-height:15.6933px"><b><font color="#000000" face="georgia, serif">*********************************************************************************************</font></b></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b><i><font color="#000000" face="georgia, serif"><span class="gmail-il">Research</span> at TTIC Seminar Series</font></i></b></p><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="georgia, serif"> </font></p><div class="gmail_default"><div dir="ltr"><div class="gmail_default"><div dir="ltr"><p class="MsoNormal" style="margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="georgia, serif" color="#000000">TTIC is hosting a weekly seminar series presenting the <span class="gmail-il">research</span> currently underway at the Institute. Every week a different TTIC faculty member will present their <span class="gmail-il">research</span>.  The lectures are intended for students seeking <span class="gmail-il">research</span> topics and advisors and for the general TTIC and University of Chicago communities interested in hearing what their colleagues are up to.</font></p></div></div></div></div></div></div><div style="font-family:Arial,Helvetica,sans-serif"><br></div><span class="gmail_signature_prefix" style="font-family:Arial,Helvetica,sans-serif">--</span><br style="font-family:Arial,Helvetica,sans-serif"><div dir="ltr" class="gmail_signature" style="font-family:Arial,Helvetica,sans-serif"><div dir="ltr"><b><font color="#3d85c6">Brandie Jones </font></b><div><div><div><font color="#3d85c6"><b><i>Executive </i></b></font><b style="color:rgb(61,133,198)"><i>Administrative Assistant</i></b></div></div><div><font color="#3d85c6">Toyota Technological Institute</font></div><div><font color="#3d85c6">6045 S. Kenwood Avenue</font></div><div><font color="#3d85c6">Chicago, IL  60637</font></div></div><div><font color="#3d85c6"><a href="http://www.ttic.edu/" target="_blank">www.ttic.edu</a> </font></div></div></div></div></div>