3 research outputs found
Statistical Physics Analysis of Maximum a Posteriori Estimation for Multi-channel Hidden Markov Models
The performance of Maximum a posteriori (MAP) estimation is studied
analytically for binary symmetric multi-channel Hidden Markov processes. We
reduce the estimation problem to a 1D Ising spin model and define order
parameters that correspond to different characteristics of the MAP-estimated
sequence. The solution to the MAP estimation problem has different operational
regimes separated by first order phase transitions. The transition points for
-channel system with identical noise levels, are uniquely determined by
being odd or even, irrespective of the actual number of channels. We
demonstrate that for lower noise intensities, the number of solutions is
uniquely determined for odd , whereas for even there are exponentially
many solutions. We also develop a semi analytical approach to calculate the
estimation error without resorting to brute force simulations. Finally, we
examine the tradeoff between a system with single low-noise channel and one
with multiple noisy channels.Comment: The paper has been submitted to Journal of Statistical Physics with
submission number JOSS-S-12-0039