TY - GEN
T1 - A Recursive Algorithm for Computing Inferences in Imprecise Markov Chains
AU - T'Joens, Natan
AU - Krak, Thomas
AU - De Bock, Jasper
AU - de Cooman, Gert
PY - 2019
Y1 - 2019
N2 - We present an algorithm that can efficiently compute a broad class of inferences for discrete-time imprecise Markov chains, a generalised type of Markov chains that allows one to take into account partially specified probabilities and other types of model uncertainty. The class of inferences that we consider contains, as special cases, tight lower and upper bounds on expected hitting times, on hitting probabilities and on expectations of functions that are a sum or product of simpler ones. Our algorithm exploits the specific structure that is inherent in all these inferences: they admit a general recursive decomposition. This allows us to achieve a computational complexity that scales linearly in the number of time points on which the inference depends, instead of the exponential scaling that is typical for a naive approach.
AB - We present an algorithm that can efficiently compute a broad class of inferences for discrete-time imprecise Markov chains, a generalised type of Markov chains that allows one to take into account partially specified probabilities and other types of model uncertainty. The class of inferences that we consider contains, as special cases, tight lower and upper bounds on expected hitting times, on hitting probabilities and on expectations of functions that are a sum or product of simpler ones. Our algorithm exploits the specific structure that is inherent in all these inferences: they admit a general recursive decomposition. This allows us to achieve a computational complexity that scales linearly in the number of time points on which the inference depends, instead of the exponential scaling that is typical for a naive approach.
KW - Imprecise Markov chains
KW - Recursively decomposable inferences
KW - Upper and lower expectations
UR - https://www.scopus.com/pages/publications/85072862291
U2 - 10.1007/978-3-030-29765-7_38
DO - 10.1007/978-3-030-29765-7_38
M3 - Conference contribution
SN - 9783030297640
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 455
EP - 465
BT - Symbolic and Quantitative Approaches to Reasoning with Uncertainty - 15th European Conference, ECSQARU 2019, Proceedings
A2 - Kern-Isberner, Gabriele
A2 - Ognjanović, Zoran
PB - Springer
ER -