<div dir="ltr"><div dir="ltr"><div class="gmail_default" style="font-size:small"><div class="gmail_default"><div class="gmail_default"><p style="color:rgb(80,0,80);font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;margin:0px"><font face="arial, sans-serif" color="#000000"><font style="vertical-align:inherit"><font style="vertical-align:inherit"><b>When:</b>    </font></font><font style="vertical-align:inherit"><font style="vertical-align:inherit">  Thursday, January 27th at<b> <span style="background-color:rgb(255,255,0)">11:00 am CT</span></b></font></font><br></font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif" color="#000000"> </font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font style="color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><b>Where:</b>     </font></font><font color="#000000">Zoom Virtual Talk (</font><font color="#0000ff"><b><a href="https://uchicagogroup.zoom.us/webinar/register/WN_icenSqi8T-yFoYN942KgjA" target="_blank">register in advance here</a></b></font><font color="#000000">)</font></font></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;color:rgb(80,0,80);line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><br></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif" style="color:rgb(80,0,80)"><font style="vertical-align:inherit"><font style="vertical-align:inherit"><font color="#000000"><b>Who: </b> </font><font color="#500050">    </font><font color="#000000">  </font></font></font></font><font color="#000000">Jason Altschuler, MIT</font></p></div><div class="gmail_default" style="color:rgb(80,0,80)"><b style="font-size:13px;font-family:arial,sans-serif;color:rgb(0,0,0)"><br></b></div><div class="gmail_default" style="color:rgb(80,0,80)"><b style="font-size:13px;font-family:arial,sans-serif;color:rgb(0,0,0)"><br></b></div><div class="gmail_default" style="color:rgb(80,0,80)"><font face="arial, sans-serif"><b style="color:rgb(34,34,34)">Title:        </b><span style="color:rgb(34,34,34)">Transport and Beyond: Efficient Optimization Over Probability Distributions</span><br style="color:rgb(34,34,34)"><br style="color:rgb(34,34,34)"><b style="color:rgb(34,34,34)">Abstract:</b><br style="color:rgb(34,34,34)"><span style="color:rgb(34,34,34)">The core of classical optimization focuses on the setting where decision variables are vectors in R^d. However, modern applications throughout machine learning, data science, and engineering demand high-dimensional optimization problems where decision variables are probability distributions. Can such optimization problems be solved efficiently? This talk presents two vignettes in this direction.</span><br style="color:rgb(34,34,34)"><br style="color:rgb(34,34,34)"><span style="color:rgb(34,34,34)">The first vignette concerns entropic optimal transport and related problems including Min-Mean-Cycle and Matrix Preconditioning. We present approximation algorithms that are faster in both theory and practice, yielding near-linear runtimes in general, and even faster runtimes in commonly arising geometric settings. The second vignette concerns Wasserstein barycenters and more generally, multimarginal optimal transport problems. Despite considerable attention, even in dimension as low as 2, it remained unknown whether Wasserstein barycenters can be computed in polynomial time. We uncover the subtle dependence of the answer on the dimension: yes in fixed dimension and no in general. Taken together, these two vignettes illustrate the growing interface of optimization, probability, and efficient algorithms.</span><br style="color:rgb(34,34,34)"></font></div><div class="gmail_default" style="color:rgb(80,0,80)"><br></div><div class="gmail_default" style="color:rgb(80,0,80)"><font face="arial, sans-serif"><b>Host:</b> <b><font color="#0000ff"><a href="mailto:nati@ttic.edu" target="_blank">Nathan Srebro</a></font></b></font></div><br></div><div class="gmail_default"><br></div><div class="gmail_default"><br></div><div class="gmail_default"><br></div></div><div><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><span style="font-family:arial,helvetica,sans-serif;font-size:x-small">Mary C. Marre</span><br></div><div><div><font face="arial, helvetica, sans-serif" size="1">Faculty Administrative Support</font></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6" size="1"><b>Toyota Technological Institute</b></font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6" size="1">6045 S. Kenwood Avenue</font></i></div><div><font size="1"><i><font face="arial, helvetica, sans-serif" color="#3d85c6">Chicago, IL  60637</font></i><br></font></div><div><b><i><a href="mailto:mmarre@ttic.edu" target="_blank"><font face="arial, helvetica, sans-serif" size="1">mmarre@ttic.edu</font></a></i></b></div></div></div></div></div><br></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Jan 20, 2022 at 5:57 PM Mary Marre <<a href="mailto:mmarre@ttic.edu">mmarre@ttic.edu</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div><div style="font-size:small"><p style="color:rgb(80,0,80);font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;margin:0px"><font face="arial, sans-serif" color="#000000"><font style="vertical-align:inherit"><font style="vertical-align:inherit"><b>When:</b>    </font></font><font style="vertical-align:inherit"><font style="vertical-align:inherit">  Thursday, January 27th at<b> <span style="background-color:rgb(255,255,0)">11:00 am CT</span></b></font></font><br></font></p><p class="MsoNormal" style="color:rgb(80,0,80);margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif" color="#000000"> </font></p><p class="MsoNormal" style="color:rgb(80,0,80);margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif"><font style="color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><b>Where:</b>     </font></font><font color="#000000">Zoom Virtual Talk (</font><font color="#0000ff"><b><a href="https://uchicagogroup.zoom.us/webinar/register/WN_icenSqi8T-yFoYN942KgjA" target="_blank">register in advance here</a></b></font><font color="#000000">)</font></font></p><p class="MsoNormal" style="color:rgb(80,0,80);margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><br></p><p class="MsoNormal" style="margin:0in 0in 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font face="arial, sans-serif" style="color:rgb(80,0,80)"><font style="vertical-align:inherit"><font style="vertical-align:inherit"><font color="#000000"><b>Who: </b> </font><font color="#500050">    </font><font color="#000000">  </font></font></font></font><font color="#000000">Jason Altschuler, MIT</font></p></div><div style="font-size:small;color:rgb(80,0,80)"><b style="font-size:13px;font-family:arial,sans-serif;color:rgb(0,0,0)"><br></b></div><div style="font-size:small;color:rgb(80,0,80)"><b style="font-size:13px;font-family:arial,sans-serif;color:rgb(0,0,0)"><br></b></div><div style="color:rgb(80,0,80)"><font face="arial, sans-serif"><b style="color:rgb(34,34,34)">Title:        </b><span style="color:rgb(34,34,34)">Transport and Beyond: Efficient Optimization Over Probability Distributions</span><br style="color:rgb(34,34,34)"><br style="color:rgb(34,34,34)"><b style="color:rgb(34,34,34)">Abstract:</b><br style="color:rgb(34,34,34)"><span style="color:rgb(34,34,34)">The core of classical optimization focuses on the setting where decision variables are vectors in R^d. However, modern applications throughout machine learning, data science, and engineering demand high-dimensional optimization problems where decision variables are probability distributions. Can such optimization problems be solved efficiently? This talk presents two vignettes in this direction.</span><br style="color:rgb(34,34,34)"><br style="color:rgb(34,34,34)"><span style="color:rgb(34,34,34)">The first vignette concerns entropic optimal transport and related problems including Min-Mean-Cycle and Matrix Preconditioning. We present approximation algorithms that are faster in both theory and practice, yielding near-linear runtimes in general, and even faster runtimes in commonly arising geometric settings. The second vignette concerns Wasserstein barycenters and more generally, multimarginal optimal transport problems. Despite considerable attention, even in dimension as low as 2, it remained unknown whether Wasserstein barycenters can be computed in polynomial time. We uncover the subtle dependence of the answer on the dimension: yes in fixed dimension and no in general. Taken together, these two vignettes illustrate the growing interface of optimization, probability, and efficient algorithms.</span><br style="color:rgb(34,34,34)"></font></div><div style="color:rgb(80,0,80)"><br></div><div style="color:rgb(80,0,80)"><font face="arial, sans-serif"><b>Host:</b> <b><font color="#0000ff"><a href="mailto:nati@ttic.edu" target="_blank">Nathan Srebro</a></font></b></font></div><br></div><div style="font-size:small"><br></div><div style="font-size:small"><br></div><div style="font-size:small"><br></div><div><div dir="ltr"><div dir="ltr"><div><span style="font-family:arial,helvetica,sans-serif;font-size:x-small">Mary C. Marre</span><br></div><div><div><font face="arial, helvetica, sans-serif" size="1">Faculty Administrative Support</font></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6" size="1"><b>Toyota Technological Institute</b></font></i></div><div><i><font face="arial, helvetica, sans-serif" color="#3d85c6" size="1">6045 S. Kenwood Avenue</font></i></div><div><font size="1"><i><font face="arial, helvetica, sans-serif" color="#3d85c6">Chicago, IL  60637</font></i><br></font></div><div><b><i><a href="mailto:mmarre@ttic.edu" target="_blank"><font face="arial, helvetica, sans-serif" size="1">mmarre@ttic.edu</font></a></i></b></div></div></div></div></div></div>
</blockquote></div></div>