<div dir="ltr"><div dir="ltr"><div class="gmail_default" style="font-size:small"><div style="color:rgb(80,0,80)"><font style="font-family:arial,sans-serif;color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><b>When:</b>    </font></font><font style="color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><font face="arial, sans-serif">    Monday</font><span class="gmail_default" style="font-family:arial,sans-serif">, November 14th</span><font face="arial, sans-serif"> at</font><b><font face="arial, sans-serif"> </font><span style="background-color:rgb(255,255,0)"><font face="verdana, sans-serif">11:30 am CT</font></span></b></font></font></div><div style="color:rgb(80,0,80)"><font style="color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><b><span style="background-color:rgb(255,255,0)"><font face="verdana, sans-serif"><br></font></span></b></font></font></div><div style="color:rgb(80,0,80)"><span style="font-family:arial,sans-serif;color:rgb(34,34,34)"><font color="#500050"><b>Where:     </b> T</font></span><span style="font-family:arial,sans-serif;color:rgb(34,34,34)"><font color="#000000">alk will be </font><font color="#0000ff"><u><b>live, in-person</b></u></font><font color="#000000"> at</font></span><br></div><div class="gmail_default"><span style="color:rgb(0,0,0);font-family:arial,sans-serif">                   TTIC, 6045 S. Kenwood Avenue</span><br></div><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="#000000">                   </font><font color="#000000">5th Floor, Room 530 </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"><b><font color="#000000"><br></font></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 style="color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><font face="arial, sans-serif"><b>Virtually:</b> </font><font face="verdana, sans-serif">  Via Panopto </font></font></font><font color="#000000" style="font-family:arial,sans-serif">(<b><a href="https://uchicago.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=a6540580-fb4e-4402-b1a9-af460182dc1f" target="_blank">livestream</a></b></font><font color="#000000" style="font-family:arial,sans-serif">)</font><b style="color:rgb(0,0,0);font-family:arial,sans-serif"> </b><span style="font-family:verdana,sans-serif;color:rgb(0,0,0)">  </span><font face="arial, sans-serif"><b><font color="#000000"><br></font></b></font></p><p class="MsoNormal" style="margin:0in;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"><font style="vertical-align:inherit"><font style="vertical-align:inherit"><font style="color:rgb(80,0,80)"><b>Who: </b> </font><font color="#500050" style="color:rgb(80,0,80)">    </font><font color="#000000"><font color="#500050">    </font></font></font></font></font>Paul Valiant, Purdue University</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><div class="MsoNormal" align="center" style="margin:0in 0in 8pt;font-size:11pt;text-align:center;line-height:15.6933px;font-family:Calibri,sans-serif"><hr size="2" width="100%" align="center"></div><div><p style="letter-spacing:0.2px;white-space:pre-wrap"><font face="arial, sans-serif"><b style="letter-spacing:normal"><font color="#000000">Title:</font></b><b style="color:rgb(0,0,255);letter-spacing:normal">          </b><span style="letter-spacing:normal">Mean Estimation in Low and High Dimensions</span></font></p><div><font face="arial, sans-serif"><b><font color="#000000">Abstract:</font><font color="#0000ff"> </font></b><span style="color:rgb(33,37,41)">This talk will discuss the fundamental statistical problem of estimating the mean of a distribution, as accurately as possible given samples from it. This problem arises both as a subcomponent of many algorithms, and also in practice as one of the most important data primitives when dealing with real-world data. While many variants and extensions of this problem have been proposed and analyzed, in this talk I will discuss two of the most iconic: 1) when the data comes from a real-valued distribution, and 2) when the data comes from a high-dimensional vector-valued distribution. In both cases, we achieve the first estimators whose accuracy is optimal to 1+o(1) factors, optimal in its dependence on the unknown (co-) variance of the underlying distribution, the number of samples n, and the desired confidence delta. I will highlight some of the crucial and novel analytical tools used in the analysis, and in particular, draw attention to a new "vector Bernstein inequality" which makes precise the intuition that sums of bounded independent random variables in increasingly high dimensions increasingly "adhere to a spherical shell". These results suggest several possible extensions in this large and active area of statistical estimation research. This talk is based on joint work with Jasper C.H. Lee.</span></font></div><div><font face="arial, sans-serif"><span style="color:rgb(33,37,41)"><br></span></font></div>Host: <a href="mailto:madhurt@ttic.edu" target="_blank"><b>Madhur Tulsiani</b></a><div><b style="color:rgb(0,0,255)"><div><br></div></b></div><p style="color:rgb(60,64,67);letter-spacing:0.2px;white-space:pre-wrap"><span style="letter-spacing:normal;color:rgb(34,34,34);font-family:arial,sans-serif">For more information on the <i>C</i></span><span style="letter-spacing:normal;color:rgb(34,34,34);font-family:arial,sans-serif"><i>olloquium</i></span><span style="letter-spacing:normal;color:rgb(34,34,34);font-family:arial,sans-serif"><i> Series</i> or to subscribe to the mailing list, please see </span><a href="http://www.ttic.edu/colloquium.php" target="_blank" style="letter-spacing:normal;font-family:arial,sans-serif">http://www.ttic.edu/colloquium.php</a><span style="letter-spacing:normal;color:rgb(34,34,34);font-family:arial,sans-serif"> </span></p></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 Mon, Nov 14, 2022 at 10:30 AM 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 dir="ltr"><div style="font-size:small"><div><div style="color:rgb(80,0,80)"><font style="font-family:arial,sans-serif;color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><b>When:</b>    </font></font><font style="color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><font face="arial, sans-serif">    Monday</font><span class="gmail_default" style="font-family:arial,sans-serif">, November 14th</span><font face="arial, sans-serif"> at</font><b><font face="arial, sans-serif"> </font><span style="background-color:rgb(255,255,0)"><font face="verdana, sans-serif">11:30 am CT</font></span></b></font></font></div><div style="color:rgb(80,0,80)"><font style="color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><b><span style="background-color:rgb(255,255,0)"><font face="verdana, sans-serif"><br></font></span></b></font></font></div><div style="color:rgb(80,0,80)"><span style="font-family:arial,sans-serif;color:rgb(34,34,34)"><font color="#500050"><b>Where:     </b> T</font></span><span style="font-family:arial,sans-serif;color:rgb(34,34,34)"><font color="#000000">alk will be </font><font color="#0000ff"><u><b>live, in-person</b></u></font><font color="#000000"> at</font></span><br></div><div><span style="color:rgb(0,0,0);font-family:arial,sans-serif">                   TTIC, 6045 S. Kenwood Avenue</span><br></div><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="#000000">                   </font><font color="#000000">5th Floor, Room 530 </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"><b><font color="#000000"><br></font></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 style="color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><font face="arial, sans-serif"><b>Virtually:</b> </font><font face="verdana, sans-serif">  Via Panopto </font></font></font><font color="#000000" style="font-family:arial,sans-serif">(<b><a href="https://uchicago.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=a6540580-fb4e-4402-b1a9-af460182dc1f" target="_blank">livestream</a></b></font><font color="#000000" style="font-family:arial,sans-serif">)</font><b style="color:rgb(0,0,0);font-family:arial,sans-serif"> </b><span style="font-family:verdana,sans-serif;color:rgb(0,0,0)">  </span><font face="arial, sans-serif"><b><font color="#000000"><br></font></b></font></p><p class="MsoNormal" style="margin:0in;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"><font style="vertical-align:inherit"><font style="vertical-align:inherit"><font style="color:rgb(80,0,80)"><b>Who: </b> </font><font color="#500050" style="color:rgb(80,0,80)">    </font><font color="#000000"><font color="#500050">    </font></font></font></font></font>Paul Valiant, Purdue University</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><div class="MsoNormal" align="center" style="margin:0in 0in 8pt;font-size:11pt;text-align:center;line-height:15.6933px;font-family:Calibri,sans-serif"><hr size="2" width="100%" align="center"></div><div><p style="letter-spacing:0.2px;white-space:pre-wrap"><font face="arial, sans-serif"><b style="letter-spacing:normal"><font color="#000000">Title:</font></b><b style="color:rgb(0,0,255);letter-spacing:normal">          </b><span style="letter-spacing:normal">Mean Estimation in Low and High Dimensions</span></font></p><div><font face="arial, sans-serif"><b><font color="#000000">Abstract:</font><font color="#0000ff"> </font></b><span style="color:rgb(33,37,41)">This talk will discuss the fundamental statistical problem of estimating the mean of a distribution, as accurately as possible given samples from it. This problem arises both as a subcomponent of many algorithms, and also in practice as one of the most important data primitives when dealing with real-world data. While many variants and extensions of this problem have been proposed and analyzed, in this talk I will discuss two of the most iconic: 1) when the data comes from a real-valued distribution, and 2) when the data comes from a high-dimensional vector-valued distribution. In both cases, we achieve the first estimators whose accuracy is optimal to 1+o(1) factors, optimal in its dependence on the unknown (co-) variance of the underlying distribution, the number of samples n, and the desired confidence delta. I will highlight some of the crucial and novel analytical tools used in the analysis, and in particular, draw attention to a new "vector Bernstein inequality" which makes precise the intuition that sums of bounded independent random variables in increasingly high dimensions increasingly "adhere to a spherical shell". These results suggest several possible extensions in this large and active area of statistical estimation research. This talk is based on joint work with Jasper C.H. Lee.</span></font></div><div><font face="arial, sans-serif"><span style="color:rgb(33,37,41)"><br></span></font></div>Host: <a href="mailto:madhurt@ttic.edu" target="_blank"><b>Madhur Tulsiani</b></a><div><b style="color:rgb(0,0,255)"><div><br></div></b></div><p style="color:rgb(60,64,67);letter-spacing:0.2px;white-space:pre-wrap"><span style="letter-spacing:normal;color:rgb(34,34,34);font-family:arial,sans-serif">For more information on the <i>C</i></span><span style="letter-spacing:normal;color:rgb(34,34,34);font-family:arial,sans-serif"><i>olloquium</i></span><span style="letter-spacing:normal;color:rgb(34,34,34);font-family:arial,sans-serif"><i> Series</i> or to subscribe to the mailing list, please see </span><a href="http://www.ttic.edu/colloquium.php" style="letter-spacing:normal;font-family:arial,sans-serif" target="_blank">http://www.ttic.edu/colloquium.php</a><span style="letter-spacing:normal;color:rgb(34,34,34);font-family:arial,sans-serif"> </span><br></p></div><br></div><div><br></div></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, 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 Sun, Nov 13, 2022 at 2:48 PM Mary Marre <<a href="mailto:mmarre@ttic.edu" target="_blank">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 dir="ltr"><div style="font-size:small"><div><div style="color:rgb(80,0,80)"><font style="font-family:arial,sans-serif;color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><b>When:</b>    </font></font><font style="color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><font face="arial, sans-serif">    Monday</font><span class="gmail_default" style="font-family:arial,sans-serif">, November 14th</span><font face="arial, sans-serif"> at</font><b><font face="arial, sans-serif"> </font><span style="background-color:rgb(255,255,0)"><font face="verdana, sans-serif">11:30 am CT</font></span></b></font></font></div><div style="color:rgb(80,0,80)"><font style="color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><b><span style="background-color:rgb(255,255,0)"><font face="verdana, sans-serif"><br></font></span></b></font></font></div><div style="color:rgb(80,0,80)"><span style="font-family:arial,sans-serif;color:rgb(34,34,34)"><font color="#500050"><b>Where:     </b> T</font></span><span style="font-family:arial,sans-serif;color:rgb(34,34,34)"><font color="#000000">alk will be </font><font color="#0000ff"><u><b>live, in-person</b></u></font><font color="#000000"> at</font></span><br></div><div><span style="color:rgb(0,0,0);font-family:arial,sans-serif">                   TTIC, 6045 S. Kenwood Avenue</span><br></div><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="#000000">                   </font><font color="#000000">5th Floor, Room 530 </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"><b><font color="#000000"><br></font></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 style="color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><font face="arial, sans-serif"><b>Virtually:</b> </font><font face="verdana, sans-serif">  Via Panopto </font></font></font><font color="#000000" style="font-family:arial,sans-serif">(<b><a href="https://uchicago.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=a6540580-fb4e-4402-b1a9-af460182dc1f" target="_blank">livestream</a></b></font><font color="#000000" style="font-family:arial,sans-serif">)</font><b style="color:rgb(0,0,0);font-family:arial,sans-serif"> </b><span style="font-family:verdana,sans-serif;color:rgb(0,0,0)">  </span><font face="arial, sans-serif"><b><font color="#000000"><br></font></b></font></p><p class="MsoNormal" style="margin:0in;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"><font style="vertical-align:inherit"><font style="vertical-align:inherit"><font style="color:rgb(80,0,80)"><b>Who: </b> </font><font color="#500050" style="color:rgb(80,0,80)">    </font><font color="#000000"><font color="#500050">    </font></font></font></font></font>Paul Valiant, Purdue University</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><div class="MsoNormal" align="center" style="margin:0in 0in 8pt;font-size:11pt;text-align:center;line-height:15.6933px;font-family:Calibri,sans-serif"><hr size="2" width="100%" align="center"></div><div><p style="letter-spacing:0.2px;white-space:pre-wrap"><font face="arial, sans-serif"><b style="letter-spacing:normal"><font color="#000000">Title:</font></b><b style="color:rgb(0,0,255);letter-spacing:normal">          </b><span style="letter-spacing:normal">Mean Estimation in Low and High Dimensions</span></font></p><div><font face="arial, sans-serif"><b><font color="#000000">Abstract:</font><font color="#0000ff"> </font></b><span style="color:rgb(33,37,41)">This talk will discuss the fundamental statistical problem of estimating the mean of a distribution, as accurately as possible given samples from it. This problem arises both as a subcomponent of many algorithms, and also in practice as one of the most important data primitives when dealing with real-world data. While many variants and extensions of this problem have been proposed and analyzed, in this talk I will discuss two of the most iconic: 1) when the data comes from a real-valued distribution, and 2) when the data comes from a high-dimensional vector-valued distribution. In both cases, we achieve the first estimators whose accuracy is optimal to 1+o(1) factors, optimal in its dependence on the unknown (co-) variance of the underlying distribution, the number of samples n, and the desired confidence delta. I will highlight some of the crucial and novel analytical tools used in the analysis, and in particular, draw attention to a new "vector Bernstein inequality" which makes precise the intuition that sums of bounded independent random variables in increasingly high dimensions increasingly "adhere to a spherical shell". These results suggest several possible extensions in this large and active area of statistical estimation research. This talk is based on joint work with Jasper C.H. Lee.</span></font></div><div><font face="arial, sans-serif"><span style="color:rgb(33,37,41)"><br></span></font></div>Host: <a href="mailto:madhurt@ttic.edu" target="_blank"><b>Madhur Tulsiani</b></a><div><b style="color:rgb(0,0,255)"><div><br></div></b></div><p style="color:rgb(60,64,67);letter-spacing:0.2px;white-space:pre-wrap"><span style="letter-spacing:normal;color:rgb(34,34,34);font-family:arial,sans-serif">For more information on the <i>C</i></span><span style="letter-spacing:normal;color:rgb(34,34,34);font-family:arial,sans-serif"><i>olloquium</i></span><span style="letter-spacing:normal;color:rgb(34,34,34);font-family:arial,sans-serif"><i> Series</i> or to subscribe to the mailing list, please see </span><a href="http://www.ttic.edu/colloquium.php" style="letter-spacing:normal;font-family:arial,sans-serif" target="_blank">http://www.ttic.edu/colloquium.php</a><span style="letter-spacing:normal;color:rgb(34,34,34);font-family:arial,sans-serif"> </span><br></p></div><br></div><div><br></div></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, 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 Mon, Nov 7, 2022 at 10:03 PM Mary Marre <<a href="mailto:mmarre@ttic.edu" target="_blank">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;color:rgb(80,0,80)"><font style="font-family:arial,sans-serif;color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><b>When:</b>    </font></font><font style="color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><font face="arial, sans-serif">    Monday</font><span class="gmail_default" style="font-family:arial,sans-serif">, November 14th</span><font face="arial, sans-serif"> at</font><b><font face="arial, sans-serif"> </font><span style="background-color:rgb(255,255,0)"><font face="verdana, sans-serif">11:30 am CT</font></span></b></font></font></div><div style="font-size:small;color:rgb(80,0,80)"><font style="color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><b><span style="background-color:rgb(255,255,0)"><font face="verdana, sans-serif"><br></font></span></b></font></font></div><div style="font-size:small;color:rgb(80,0,80)"><span style="font-family:arial,sans-serif;color:rgb(34,34,34)"><font color="#500050"><b>Where:     </b> T</font></span><span style="font-family:arial,sans-serif;color:rgb(34,34,34)"><font color="#000000">alk will be </font><font color="#0000ff"><u><b>live, in-person</b></u></font><font color="#000000"> at</font></span><br></div><div style="font-size:small"><span style="color:rgb(0,0,0);font-family:arial,sans-serif">                   TTIC, 6045 S. Kenwood Avenue</span><br></div><p class="MsoNormal" style="font-size:small;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="#000000">                   </font><font color="#000000">5th Floor, Room 530 </font></font></p><p class="MsoNormal" style="font-size:small;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><font color="#000000"><br></font></b></font></p><p class="MsoNormal" style="font-size:small;margin:0in;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font style="color:rgb(0,0,0);vertical-align:inherit"><font style="vertical-align:inherit"><font face="arial, sans-serif"><b>Virtually:</b> </font><font face="verdana, sans-serif">  Via Panopto </font></font></font><font color="#000000" style="font-family:arial,sans-serif">(<b><a href="https://uchicago.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=a6540580-fb4e-4402-b1a9-af460182dc1f" target="_blank">livestream</a></b></font><font color="#000000" style="font-family:arial,sans-serif">)</font><b style="color:rgb(0,0,0);font-family:arial,sans-serif"> </b><span style="font-family:verdana,sans-serif;color:rgb(0,0,0)">  </span><font face="arial, sans-serif"><b><font color="#000000"><br></font></b></font></p><p class="MsoNormal" style="font-size:small;margin:0in;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="font-size:small;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="vertical-align:inherit"><font style="vertical-align:inherit"><font style="color:rgb(80,0,80)"><b>Who: </b> </font><font color="#500050" style="color:rgb(80,0,80)">    </font><font color="#000000"><font color="#500050">    </font></font></font></font></font>Paul Valiant, Purdue University</p><p class="MsoNormal" style="font-size:small;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><div class="MsoNormal" align="center" style="font-size:11pt;margin:0in 0in 8pt;text-align:center;line-height:15.6933px;font-family:Calibri,sans-serif"><hr size="2" width="100%" align="center"></div><div><p style="letter-spacing:0.2px;white-space:pre-wrap"><font face="arial, sans-serif"><b style="letter-spacing:normal"><font color="#000000">Title:</font></b><b style="color:rgb(0,0,255);letter-spacing:normal">          </b><span style="letter-spacing:normal">Mean Estimation in Low and High Dimensions</span></font></p><div><font face="arial, sans-serif"><b><font color="#000000">Abstract:</font><font color="#0000ff"> </font></b><span style="color:rgb(33,37,41)">This talk will discuss the fundamental statistical problem of estimating the mean of a distribution, as accurately as possible given samples from it. This problem arises both as a subcomponent of many algorithms, and also in practice as one of the most important data primitives when dealing with real-world data. While many variants and extensions of this problem have been proposed and analyzed, in this talk I will discuss two of the most iconic: 1) when the data comes from a real-valued distribution, and 2) when the data comes from a high-dimensional vector-valued distribution. In both cases, we achieve the first estimators whose accuracy is optimal to 1+o(1) factors, optimal in its dependence on the unknown (co-) variance of the underlying distribution, the number of samples n, and the desired confidence delta. I will highlight some of the crucial and novel analytical tools used in the analysis, and in particular, draw attention to a new "vector Bernstein inequality" which makes precise the intuition that sums of bounded independent random variables in increasingly high dimensions increasingly "adhere to a spherical shell". These results suggest several possible extensions in this large and active area of statistical estimation research. This talk is based on joint work with Jasper C.H. Lee.</span></font></div><div><font face="arial, sans-serif"><span style="color:rgb(33,37,41)"><br></span></font></div>Host: <a href="mailto:madhurt@ttic.edu" target="_blank"><b>Madhur Tulsiani</b></a><div><b style="color:rgb(0,0,255)"><div style="font-size:small"><br></div></b></div><p style="font-size:small;color:rgb(60,64,67);letter-spacing:0.2px;white-space:pre-wrap"><span style="letter-spacing:normal;color:rgb(34,34,34);font-family:arial,sans-serif">For more information on the <i>C</i></span><span style="letter-spacing:normal;color:rgb(34,34,34);font-family:arial,sans-serif"><span><i>olloquium</i></span></span><span style="letter-spacing:normal;color:rgb(34,34,34);font-family:arial,sans-serif"><i> Series</i> or to subscribe to the mailing list, please see </span><a href="http://www.ttic.edu/colloquium.php" style="letter-spacing:normal;font-family:arial,sans-serif" target="_blank">http://www.ttic.edu/<span>colloquium</span>.php</a><span style="letter-spacing:normal;color:rgb(34,34,34);font-family:arial,sans-serif"> </span><br></p></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, 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>
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