<div dir="ltr"><div class="gmail_quote"><br><br><div dir="ltr"><p class="MsoNormal" style="margin:0cm 0cm 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="font-size:16px">Prezados colegas, </span></font></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:12pt;font-family:Arial,"sans-serif""> </span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:12pt">O <b>COLMEA
- Colóquio Interinstitucional Modelos Estocásticos e Aplicações </b>- tem
mais um encontro no próximo dia 22 de novembro de 2023, a partir das 14:00h, na
PUC-Rio. Nesta ocasião teremos palestras de </span><span style="font-size:12pt">Philip Thompson (FGV EMAp)</span><span style="font-size:12pt">  e </span><span style="font-size:12pt">Oliver Riordan (Oxford). </span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:12pt"><br>
</span><b><span lang="EN-US" style="font-size:12pt">Programa:<br>
</span></b><span lang="EN-US" style="font-size:12pt"><br>
14:00 h - 15:20h  </span><span lang="EN-US" style="font-size:12pt">Philip
Thompson (FGV EMAp)</span><span lang="EN-US" style="font-size:12pt;font-family:Arial,"sans-serif"">  </span><span lang="EN-US" style="font-size:12pt"><br>
<b>Outlier-robust additive matrix decomposition and robust matrix completion</b></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><b><span lang="EN-US" style="font-size:12pt"> </span></b></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt">15:40h - 17:00h   Oliver Riordan (Oxford)<br>
<b>The chromatic number of random graphs</b></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:12pt"><br>
17:00h Discussão e lanche<br>
<br>
<b>Local:</b><br>
Sala de reuniões do Decanato do CTC,</span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:12pt">12
º andar do prédio Cardeal Leme,<br>
PUC-Rio</span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:12pt"> </span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:12pt">Informações
mais completas sobre o COLMEA podem ser encontradas aqui:<br>
</span><a href="http://www.im.ufrj.br/~coloquiomea/" target="_blank"><span style="font-size:12pt">http://www.im.ufrj.br/~coloquiomea/</span></a><span style="font-size:12pt"><br>
<br>
Todos são muito bem-vindos. Agradecemos também pela divulgação em suas
instituições. Resumos das palestras no final da mensagem.<br>
<br>
Atenciosamente,<br>
<br>
O comitê organizador:<br>
Americo Cunha (UERJ)<br>
Evaldo M.F. Curado (CBPF)<br>
João Batista M. Pereira (UFRJ)<br>
Leandro P. R. Pimentel (UFRJ)<br>
Maria Eulalia Vares (UFRJ)<br>
Nuno Crokidakis (UFF)<br>
Roberto I. Oliveira (IMPA)<br>
Simon Griffiths (PUC-Rio)<br>
Yuri F. Saporito (FGV-EMAp)</span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:12pt"> </span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:12pt;color:black"> </span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""> </p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><b><span lang="EN-US" style="font-size:12pt;color:black">Outlier-robust
additive matrix decomposition and robust matrix completion</span></b></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt;color:black">Philip Thompson (FGV EMAp)  <br>
<br>
We study least-squares trace regression when the parameter is the sum of a
$r$-low-rank matrix with a $s$-sparse matrix and a fraction $\epsilon$ of the
labels is corrupted. For subgaussian distributions, we highlight three needed
design properties, each one derived from a different process inequality: the
``product process inequality'', ``Chevet's inequality'' and the ``multiplier
process inequality''. Jointly, these properties entail the near-optimality of a
tractable estimator with respect to the effective dimensions
 $d_{\textrm{eff},r}$ and $d_{\textrm{eff},s}$ for the low-rank and sparse
components,  $\epsilon$ and the failure probability $\delta$. The
near-optimal rate has the form $\mathsf{r}(n,d_{\textrm{eff},r}) +
\mathsf{r}(n,d_{\textrm{eff},s}) + \sqrt{(1+\log(1/\delta))/n}+
\epsilon\log(1/\epsilon).$  Here,
$\mathsf{r}(n,d_{\textrm{eff},r})+\mathsf{r}(n,d_{\textrm{eff},s})$ is the
optimal rate in average when there is no contamination. Our estimator is
adaptive to $(s,r,\epsilon,\delta)$ and, for fixed absolute constant $c>0$,
it attains the mentioned rate with probability $1-\delta$ uniformly over all
 $\delta\ge\exp(-cn)$. Disconsidering matrix decomposition, our analysis
also entails optimal bounds for a robust estimator adapted to the noise
variance. Finally, we consider robust matrix completion. We highlight a new
property for this problem: one can robustly and optimally estimate the
incomplete matrix regardless of the magnitude of the corruption. Our estimators
are based on ``sorted'' versions of Huber's loss. We present simulations
matching the theory. In particular, it reveals the superiority of ``sorted''
Huber's losses over the classical Huber's loss.</span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt"> </span><span lang="EN-US"></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><b><span lang="EN-US" style="font-size:12pt;color:black">The chromatic
number of random graphs</span></b></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:12pt;color:black">Oliver
Riordan (Oxford)</span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt;color:black"><br>
The chromatic number of a graph is the minimum number of colours needed to
colour the vertices so that adjacent vertices receive distinct colours. While
this sounds like a game, in applications it is a very important property,
corresponding to the minimum number of groups a set must be divided into to
avoid any incompatible pairs within each group. The chromatic number is also
studied purely theoretically, which will be the point of view here.</span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt;color:black">A basic question is: considering all possible
graphs on $n$ vertices, what do their chromatic numbers look like? How often
does each possible value occur? Or, rephrasing, what is the distribution of the
chromatic number of a graph chosen uniformly at random? Writing $X$ for this
random variable, we can look for reasonable upper and lower bounds on the mean
of $X$, and upper and lower bounds on the variance of $X$. For the last
combination, nothing was known until a recent breakthrough of Annika Heckel. In
this talk I will discuss some of the history of the problem, and try to
describe some of the ideas Annika used, which she and I have since taken
further. </span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><span lang="EN-US" style="font-size:12pt;color:black"> </span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-size:11pt;font-family:Calibri,"sans-serif""><span style="font-size:12pt;font-family:Arial,"sans-serif""> </span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""> </p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,"sans-serif""> </p></div>
</div></div>