<div dir="ltr"><div dir="ltr"><div class="gmail_default" style="font-size:small"><div class="gmail_default"><div class="gmail_default" style="color:rgb(80,0,80)"><font face="arial, sans-serif"><font style="color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><b>When:</b> </font></font><font style="vertical-align:inherit"><font style="vertical-align:inherit"><font style="color:rgb(0,0,0)"> Friday, October 27</font><span class="gmail_default" style="color:rgb(0,0,0)">, 2023</span><font style="color:rgb(0,0,0)"> at</font><b style="color:rgb(0,0,0)"> <u style="background-color:rgb(255,255,0)">10:30</u></b><span style="background-color:rgb(255,255,0)"><b><u><font color="#000000"> a</font></u></b><b><u><font color="#000000">m CT</font></u><font color="#000000"> </font></b></span></font></font><br></font></div><div class="gmail_default" style="color:rgb(80,0,80)"><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;margin:0px"><b style="font-family:arial,sans-serif"><font color="#500050"><br></font></b></p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;margin:0px"><b style="font-family:arial,sans-serif"><font color="#500050">Where: </font></b><font color="#000000" style="font-family:arial,sans-serif">Talk will be given </font><font color="#000000" style="font-family:arial,sans-serif;font-weight:bold"><u>live, in-person</u></font><font style="font-family:arial,sans-serif;font-weight:bold"> </font><span style="font-family:arial,sans-serif">at</span><br></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="arial, sans-serif"><font color="#500050"> </font><font color="#000000"> TTIC, 6045 S. Kenwood Avenue</font></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="arial, sans-serif" color="#000000"> 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 face="arial, sans-serif"><b><span style="color:black"><br></span></b></font></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"><b style="color:rgb(60,64,67);letter-spacing:0.2px">Virtually:</b><span style="color:rgb(60,64,67);letter-spacing:0.2px"> <i>via </i>Panopto </span>(<b><a href="https://uchicago.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=ae4322fa-9067-4b60-821e-b0a2001ab975" target="_blank">livestream</a></b><span style="color:rgb(60,64,67);letter-spacing:0.2px">)</span><br></font></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"><span style="color:rgb(60,64,67);letter-spacing:0.2px"><font face="arial, sans-serif"></font><font face="georgia, serif"><b><font size="1">*limited access: see info below</font></b></font></span></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"><span style="color:rgb(60,64,67);letter-spacing:0.2px"><br></span></font></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 style="font-family:arial,sans-serif;vertical-align:inherit"><font style="vertical-align:inherit"><b>Who: </b> <font color="#500050"> </font><font color="#000000"><font color="#500050"> </font></font></font></font>Tselil Schramm, Stanford University</p></div></div><div class="gmail_default"><br></div><div class="gmail_default"><div dir="ltr"><div><div class="MsoNormal" align="center" style="margin:0in 0in 8pt;text-align:center;line-height:15.6933px;font-size:11pt;font-family:Calibri,sans-serif"><hr size="3" width="100%" noshade align="center" style="color:rgb(46,116,181)"></div><font size="2"><b>Title: </b>Spectral Clustering in High-Dimensional Gaussian Mixture Block Models<br><b><br></b></font></div><div><font size="2"><b>Abstract: </b>The Gaussian mixture block model is a simple generative model for networks: to generate a sample, we associate each node with a latent feature vector sampled from a mixture of Gaussians, and we add an edge between nodes if and only if their feature vectors are sufficiently similar. The different components of the Gaussian mixture represent the fact that there may be several types of nodes with different distributions over features -- for example, in a social network each component represents the different attributes of a distinct community. In this talk I will discuss recent results on the performance of spectral clustering algorithms on networks sampled from high-dimensional Gaussian mixture block models, where the dimension of the latent feature vectors grows as the size of the network goes to infinity. Our results merely begin to sketch out the information-computation landscape for clustering in these models, and I will make an effort to emphasize open questions. </font></div><div><br></div><div>Based on joint work with Shuangping Li.<br></div></div><div><div id="m_3983419646637522536m_-7220900540036838011gmail-:qg" role="button" aria-label="Show trimmed content" aria-expanded="false"><img src="https://ssl.gstatic.com/ui/v1/icons/mail/images/cleardot.gif" class="gmail-CToWUd"></div></div></div><div class="gmail_default">Host: <a href="mailto:madhurt@ttic.edu" target="_blank"><b>Madhur Tulsiani</b></a></div><div class="gmail_default"><br></div><div class="gmail_default"><font color="#0000ff" face="arial black, sans-serif">*</font><font face="tahoma, sans-serif">Access to this livestream is limited to TTIC / UChicago (press panopto link and sign in to your UChicago account with </font><span style="font-family:tahoma,sans-serif;color:rgb(29,29,33);font-weight:600">CNetID</span><font face="tahoma, sans-serif">). </font><br></div><div class="gmail_default"><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"><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, Rm 517</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><font size="1"><i><font face="arial, helvetica, sans-serif" color="#3d85c6">773-834-1757</font></i></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 Fri, Oct 20, 2023 at 8:49 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 style="font-size:small"><div style="color:rgb(80,0,80)"><font face="arial, sans-serif"><font style="color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><b>When:</b> </font></font><font style="vertical-align:inherit"><font style="vertical-align:inherit"><font style="color:rgb(0,0,0)"> Friday, October 27</font><span class="gmail_default" style="color:rgb(0,0,0)">, 2023</span><font style="color:rgb(0,0,0)"> at</font><b style="color:rgb(0,0,0)"> <u style="background-color:rgb(255,255,0)">10:30</u></b><span style="background-color:rgb(255,255,0)"><b><u><font color="#000000"> a</font></u></b><b><u><font color="#000000">m CT</font></u><font color="#000000"> </font></b></span></font></font><br></font></div><div style="color:rgb(80,0,80)"><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;margin:0px"><b style="font-family:arial,sans-serif"><font color="#500050"><br></font></b></p><p style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;margin:0px"><b style="font-family:arial,sans-serif"><font color="#500050">Where: </font></b><font color="#000000" style="font-family:arial,sans-serif">Talk will be given </font><font color="#000000" style="font-family:arial,sans-serif;font-weight:bold"><u>live, in-person</u></font><font style="font-family:arial,sans-serif;font-weight:bold"> </font><span style="font-family:arial,sans-serif">at</span><br></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="arial, sans-serif"><font color="#500050"> </font><font color="#000000"> TTIC, 6045 S. Kenwood Avenue</font></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="arial, sans-serif" color="#000000"> 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 face="arial, sans-serif"><b><span style="color:black"><br></span></b></font></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"><b style="color:rgb(60,64,67);letter-spacing:0.2px">Virtually:</b><span style="color:rgb(60,64,67);letter-spacing:0.2px"> <i>via </i>Panopto </span>(<b><a href="https://uchicago.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=ae4322fa-9067-4b60-821e-b0a2001ab975" target="_blank">livestream</a></b><span style="color:rgb(60,64,67);letter-spacing:0.2px">)</span><br></font></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"><span style="color:rgb(60,64,67);letter-spacing:0.2px"><font face="arial, sans-serif"> </font><font face="georgia, serif"><b> <font size="1"> *limited access: see info below</font></b></font></span></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"><span style="color:rgb(60,64,67);letter-spacing:0.2px"><br></span></font></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 style="font-family:arial,sans-serif;vertical-align:inherit"><font style="vertical-align:inherit"><b>Who: </b> <font color="#500050"> </font><font color="#000000"><font color="#500050"> </font></font></font></font>Tselil Schramm, Stanford University</p></div></div><div style="font-size:small"><br></div><div style="font-size:small"><div dir="ltr"><div><div class="MsoNormal" align="center" style="text-align:center;margin:0in 0in 8pt;line-height:107%;font-size:11pt;font-family:Calibri,sans-serif">
<hr size="3" width="100%" noshade style="color:rgb(46,116,181)" align="center">
</div><font size="2"><b>Title: </b>Spectral Clustering in High-Dimensional Gaussian Mixture Block Models<br><b><br></b></font></div><div><font size="2"><b>Abstract: </b>The Gaussian mixture block model is a simple generative model for networks: to generate a sample, we associate each node with a latent feature vector sampled from a mixture of Gaussians, and we add an edge between nodes if and only if their feature vectors are sufficiently similar. The different components of the Gaussian mixture represent the fact that there may be several types of nodes with different distributions over features -- for example, in a social network each component represents the different attributes of a distinct community. In this talk I will discuss recent results on the performance of spectral clustering algorithms on networks sampled from high-dimensional Gaussian mixture block models, where the dimension of the latent feature vectors grows as the size of the network goes to infinity. Our results merely begin to sketch out the information-computation landscape for clustering in these models, and I will make an effort to emphasize open questions. </font></div><div><br></div><div>Based on joint work with Shuangping Li.<br></div></div><div><div id="m_3983419646637522536m_-7220900540036838011gmail-:qg" role="button" aria-label="Show trimmed content" aria-expanded="false"><img src="https://ssl.gstatic.com/ui/v1/icons/mail/images/cleardot.gif"></div></div></div><div style="font-size:small">Host: <a href="mailto:madhurt@ttic.edu" target="_blank"><b>Madhur Tulsiani</b></a></div><div style="font-size:small"><br></div><div><font color="#0000ff" face="arial black, sans-serif">*</font><font face="tahoma, sans-serif">Access to this livestream is limited to TTIC / UChicago (press panopto link and sign in to your UChicago account with </font><span style="font-family:tahoma,sans-serif;color:rgb(29,29,33);font-weight:600">CNetID</span><font face="tahoma, sans-serif">). </font><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" class="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, Rm 517</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><font size="1"><i><font face="arial, helvetica, sans-serif" color="#3d85c6">773-834-1757</font></i></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>