Approximation of Markov Processes by Lower Dimensional Processes via Total Variation Metrics
Journal article, 2017

The aim of this paper is to approximate a Finite-State Markov (FSM) process by another process defined on a lower dimensional state space, called the approximating process, with respect to a total variation distance fidelity criterion. The approximation problem is formulated as an optimization problem using two different approaches. The first approach is based on approximating the transition probability matrix of the FSM process by a lower-dimensional transition probability matrix, resulting in an approximating process which is a Finite-State Hidden Markov (FSHM) process. The second approach is based on approximating the invariant probability vector of the original FSM process by another invariant probability vector defined on a lower-dimensional state space. Going a step further, a method is proposed based on optimizing a Kullback-Leibler divergence to approximate the FSHM processes by FSM processes. The solutions of these optimization problems are described by optimal partition functions which aggregate the states of the FSM process via a corresponding water-filling solution, resulting in lower-dimensional approximating processes which are FSHM or FSM processes. Throughout the paper, the theoretical results are justified by illustrative examples that demonstrate our proposed methodology.

Markov process

aggregation

total variation distance

Engineering

model-reduction

Approximating process

Automation & Control Systems

water-filling

Author

I. Tzortzis

University of Cyprus

C. D. Charalambous

University of Cyprus

Themistoklis Charalambous

Chalmers, Signals and Systems, Communication and Antenna Systems, Communication Systems

C. N. Hadjicostis

University of Cyprus

Mikael Johansson

Royal Institute of Technology (KTH)

IEEE Transactions on Automatic Control

0018-9286 (ISSN)

Vol. 62 3 1030-1045

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis

DOI

10.1109/tac.2016.2578299

More information

Latest update

3/5/2018 7