[HTML][HTML] Context tree selection: A unifying view
A Garivier, F Leonardi - Stochastic processes and their applications, 2011 - Elsevier
Context tree models have been introduced by Rissanen in [25] as a parsimonious
generalization of Markov models. Since then, they have been widely used in applied …
generalization of Markov models. Since then, they have been widely used in applied …
Stochastic chains with memory of variable length
A Galves, E Löcherbach - arXiv preprint arXiv:0804.2050, 2008 - arxiv.org
Stochastic chains with memory of variable length constitute an interesting family of
stochastic chains of infinite order on a finite alphabet. The idea is that for each past, only a …
stochastic chains of infinite order on a finite alphabet. The idea is that for each past, only a …
Exponential inequalities for empirical unbounded context trees
A Galves, F Leonardi - In and out of equilibrium 2, 2008 - Springer
In this paper we obtain non-uniform exponential upper bounds for the rate of convergence of
a version of the algorithm Context, when the underlying tree is not necessarily bounded. The …
a version of the algorithm Context, when the underlying tree is not necessarily bounded. The …
Stationary and transition probabilities in slow mixing, long memory markov processes
M Asadi, RP Torghabeh… - IEEE Transactions on …, 2014 - ieeexplore.ieee.org
We observe a length-n sample generated by an unknown, stationary ergodic Markov
process (model) over a finite alphabet A. Given any string w of symbols from A we want …
process (model) over a finite alphabet A. Given any string w of symbols from A we want …
Probabilistic Context Neighborhood model for lattices
D Duarte, DF Magalhães, AM Piroutek, C Alves - Spatial Statistics, 2024 - Elsevier
Abstract We present the Probabilistic Context Neighborhood model designed for two-
dimensional lattices as a variation of a Markov random field assuming discrete values. In this …
dimensional lattices as a variation of a Markov random field assuming discrete values. In this …
Optimal Gaussian concentration bounds for stochastic chains of unbounded memory
JR Chazottes, S Gallo, D Takahashi - arXiv preprint arXiv:2001.06633, 2020 - arxiv.org
We obtain optimal Gaussian concentration bounds (GCBs) for stochastic chains of
unbounded memory (SCUMs) on countable alphabets. These stochastic processes are also …
unbounded memory (SCUMs) on countable alphabets. These stochastic processes are also …
Markov approximation of chains of infinite order in the -metric
S Gallo, M Lerasle, DY Takahashi - Markov Processes and Related …, 2013 - hal.science
We derive explicit upper bounds for the d-distance between a chain of in nite order and its
canonical k-steps Markov approximation. Our proof is entirely construc-tive and involves …
canonical k-steps Markov approximation. Our proof is entirely construc-tive and involves …
On rate of convergence of statistical estimation of stationary ergodic processes
I Csiszár, Z Talata - IEEE Transactions on Information theory, 2010 - ieeexplore.ieee.org
Stationary ergodic processes with finite alphabets are approximated by finite memory
processes based on an n-length realization of the process. Under the assumptions of …
processes based on an n-length realization of the process. Under the assumptions of …
[PDF][PDF] Statistical model selection for stochastic systems with applications to bioinformatics, linguistics and neurobiology
These lecture notes present new results on statistical model selection for stochastic systems.
The majority of the results are original and first appeared in several recent papers co …
The majority of the results are original and first appeared in several recent papers co …
Random perturbations of stochastic processes with unbounded variable length memory
P Collet, A Galves, F Leonardi - 2008 - projecteuclid.org
We consider binary infinite order stochastic chains perturbed by a random noise. This
means that at each time step, the value assumed by the chain can be randomly and …
means that at each time step, the value assumed by the chain can be randomly and …