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<p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)">Boa tarde a todos,</p><p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)"><br></p><p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)">Aproveitando o anúncio da Eulália, gostaria de convidá-los também para o seminário do Guilherme Ost da UFRJ.  O tema é de alta relevância para a estatística moderna e o Guilherme é um dos jovens talentos brasileiros da pesquisa estatística.  </p><p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)"><br></p><p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)">Entre os palestrantes do INSPER Data Science Academic Seminar deste semestre estão Helio Migon (UFRJ, 24/3), Guilherme Duarte (UPenn, 07/04) e Paulo Orenstein (IMPA, 02/06).</p><p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)"><br></p><p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)">March 03, 2022</p><p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)">12:00 p.m. de São Paulo, Brasil (UTC/GMT -03:00)</p><p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)">Zoom link: <a href="https://zoom.us/j/97410173464">https://zoom.us/j/97410173464</a></p><p class="gmail-p2" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0);min-height:14px"><br></p><p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)">Title:Sparse Markov Models for High-dimensional Inference<br></p><p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)"><br></p><p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)">Speaker:Guilherme Ost</p>
<p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)"><br></p><p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)">University:Universidade Federal do Rio de Janeiro -UFRJ </p><p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)"><br></p><p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)">Finite order Markov models are theoretically well-studied models for dependent categorical data. Despite their generality, application in empirical work when the order is larger than one is quite rare. Practitioners avoid using higher order Markov models because (1) the number of parameters grows exponentially with the order, (2) the interpretation is often difficult. Mixture of transition distribution models (MTD) were introduced to overcome both limitations. MTD represent higher order Markov models as a convex mixture of single step Markov chains, reducing the number of parameters and increasing the interpretability. Nevertheless, in practice, estimation of MTD models with large orders is still limited because of curse of dimensionality and high algorithm complexity. Here, we prove that if only few lags are relevant we can consistently and efficiently recover the lags and estimate the transition probabilities of high order MTD models. The key innovation is a recursive procedure for the selection of the relevant lags of the model. Our results are based on (1) a new structural result of the MTD and (2) an improved martingale concentration inequality. Our theoretical results are illustrated through simulations. This is a joint work with Daniel Y. Takahashi (Ice/UFRN).</p><p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)"><br></p><p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)"><br></p>
<p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)"><span style="font-family:Calibri,Arial,Helvetica,sans-serif,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols;font-size:small">Abs a todos,</span><br></p><p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)"><span style="font-family:Calibri,Arial,Helvetica,sans-serif,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols;font-size:small">Hedibert</span></p><p class="gmail-p1" style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:12px;line-height:normal;font-family:Helvetica;color:rgb(0,0,0)"><span style="font-family:Calibri,Arial,Helvetica,sans-serif,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols;font-size:small"><br></span></p><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><br></div></div></div>