TY - GEN
T1 - Markov field types and tilings
AU - Baryshnikov, Yuliy
AU - Duda, Jaroslaw
AU - Szpankowski, Wojciech
PY - 2014/1/1
Y1 - 2014/1/1
N2 - The method of types is one of the most popular technique in information theory and combinatorics. However, it was never thoroughly studied for Markov fields. Markov fields can be viewed as models for systems involving a large number of variables with local dependencies and interactions. These local dependencies can be captured by a shape of interactions (locations that contribute the next probability transition). Shapes marked by symbols from a finite alphabet are called tiles. Two assignments in a Markov filed have the same type if they have the same empirical distribution or they can be tiled by the same number of tile types. Our goal is to study the growth of the number of Markov field types or the number of tile types. This intricate and important problem was left open for too long.
AB - The method of types is one of the most popular technique in information theory and combinatorics. However, it was never thoroughly studied for Markov fields. Markov fields can be viewed as models for systems involving a large number of variables with local dependencies and interactions. These local dependencies can be captured by a shape of interactions (locations that contribute the next probability transition). Shapes marked by symbols from a finite alphabet are called tiles. Two assignments in a Markov filed have the same type if they have the same empirical distribution or they can be tiled by the same number of tile types. Our goal is to study the growth of the number of Markov field types or the number of tile types. This intricate and important problem was left open for too long.
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U2 - 10.1109/ISIT.2014.6875312
DO - 10.1109/ISIT.2014.6875312
M3 - Conference contribution
AN - SCOPUS:84906536029
SN - 9781479951864
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2639
EP - 2643
BT - 2014 IEEE International Symposium on Information Theory, ISIT 2014
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2014 IEEE International Symposium on Information Theory, ISIT 2014
Y2 - 29 June 2014 through 4 July 2014
ER -