[ABE-L] INSPER - Data Science Academic Seminar

[Hedibert Lopes]

Boa tarde a todos,


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.


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).


March 03, 2022

12:00 p.m. de São Paulo, Brasil (UTC/GMT -03:00)

Zoom link: https://zoom.us/j/97410173464


Title:Sparse Markov Models for High-dimensional Inference


Speaker:Guilherme Ost


University:Universidade Federal do Rio de Janeiro -UFRJ


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).



Abs a todos,

Hedibert
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