8,378 research outputs found
Distinguishing Hidden Markov Chains
Hidden Markov Chains (HMCs) are commonly used mathematical models of
probabilistic systems. They are employed in various fields such as speech
recognition, signal processing, and biological sequence analysis. We consider
the problem of distinguishing two given HMCs based on an observation sequence
that one of the HMCs generates. More precisely, given two HMCs and an
observation sequence, a distinguishing algorithm is expected to identify the
HMC that generates the observation sequence. Two HMCs are called
distinguishable if for every there is a distinguishing
algorithm whose error probability is less than . We show that one
can decide in polynomial time whether two HMCs are distinguishable. Further, we
present and analyze two distinguishing algorithms for distinguishable HMCs. The
first algorithm makes a decision after processing a fixed number of
observations, and it exhibits two-sided error. The second algorithm processes
an unbounded number of observations, but the algorithm has only one-sided
error. The error probability, for both algorithms, decays exponentially with
the number of processed observations. We also provide an algorithm for
distinguishing multiple HMCs. Finally, we discuss an application in stochastic
runtime verification.Comment: This is the full version of a LICS'16 pape
Distinguishing regional from within-codon rate heterogeneity in DNA sequence alignments
We present an improved phylogenetic factorial hidden Markov model (FHMM) for detecting two types of mosaic structures in DNA sequence alignments, related to (1) recombination and (2) rate heterogeneity. The focus of the present work is on improving the modelling of the latter aspect. Earlier papers have modelled different degrees of rate heterogeneity with separate hidden states of the FHMM. This approach fails to appreciate the intrinsic difference between two types of rate heterogeneity: long-range regional effects, which are potentially related to differences in the selective pressure, and the short-term periodic patterns within the codons, which merely capture the signature of the genetic code. We propose an improved model that explicitly distinguishes between these two effects, and we assess its performance on a set of simulated DNA sequence alignments
Active Classification for POMDPs: a Kalman-like State Estimator
The problem of state tracking with active observation control is considered
for a system modeled by a discrete-time, finite-state Markov chain observed
through conditionally Gaussian measurement vectors. The measurement model
statistics are shaped by the underlying state and an exogenous control input,
which influence the observations' quality. Exploiting an innovations approach,
an approximate minimum mean-squared error (MMSE) filter is derived to estimate
the Markov chain system state. To optimize the control strategy, the associated
mean-squared error is used as an optimization criterion in a partially
observable Markov decision process formulation. A stochastic dynamic
programming algorithm is proposed to solve for the optimal solution. To enhance
the quality of system state estimates, approximate MMSE smoothing estimators
are also derived. Finally, the performance of the proposed framework is
illustrated on the problem of physical activity detection in wireless body
sensing networks. The power of the proposed framework lies within its ability
to accommodate a broad spectrum of active classification applications including
sensor management for object classification and tracking, estimation of sparse
signals and radar scheduling.Comment: 38 pages, 6 figure
TIPPtool: Compositional Specification and Analysis of Markovian Performance Models
In this short paper we briefly describe a tool which is based on a Markovian stochastic process algebra. The tool offers both model specification and quantitative model analysis in a compositional fashion, wrapped in a userfriendly graphical front-end
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