Related papers: Branch-and-bound method for calculating Viterbi pa…
We consider the problem of estimating the maximum posterior probability (MAP) state sequence for a finite state and finite emission alphabet hidden Markov model (HMM) in the Bayesian setup, where both emission and transition matrices have…
Hidden Markov models (HMMs) are characterized by an unobservable Markov chain and an observable process -- a noisy version of the hidden chain. Decoding the original signal from the noisy observations is one of the main goals in nearly all…
We present a novel algorithm to solve a non-linear system of equations, whose solution can be interpreted as a tight lower bound on the vector of expected hitting times of a Markov chain whose transition probabilities are only partially…
Time-homogeneous Markov chains are often used as disease progression models in studies of cost-effectiveness and optimal decision-making. Maximum likelihood estimation of these models can be challenging when data are collected at a time…
Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. Some of the most…
In this paper we introduce a new network reachability problem where the goal is to find the most reliable path between two nodes in a network, represented as a directed acyclic graph. Individual edges within this network may fail according…
This paper considers the average complexity of maximum likelihood (ML) decoding of convolutional codes. ML decoding can be modeled as finding the most probable path taken through a Markov graph. Integrated with the Viterbi algorithm (VA),…
Background: Hidden Markov models are widely employed by numerous bioinformatics programs used today. Applications range widely from comparative gene prediction to time-series analyses of micro-array data. The parameters of the underlying…
This paper deals with convergence of the maximum a posterior probability path estimator in hidden Markov models. We show that when the state space of the hidden process is continuous, the optimal path may stabilize in a way which is…
We propose a simple tractable pair hidden Markov model for pairwise sequence alignment that accounts for the presence of short tandem repeats. Using the framework of gain functions, we design several optimization criteria for decoding this…
We develop and analyze methods for computing provably optimal {\em maximum a posteriori} (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex…
Computing optimal conditional reachability probabilities in Markov decision processes (MDPs) is tractable by a reduction to reachability probabilities. Yet, this reduction yields cyclic, challenging MDPs that are often notoriously hard to…
In this work we present a flexible, probabilistic and reference-free method of error correction for high throughput DNA sequencing data. The key is to exploit the high coverage of sequencing data and model short sequence outputs as…
The dynamics of mechanical systems such as turbomachinery with multiple blades are often modeled by arrays of periodically driven coupled nonlinear oscillators. It is known that such systems may have multiple stable vibrational modes, and…
Inter-symbol interference (ISI) channels with data dependent Gauss Markov noise have been used to model read channels in magnetic recording and other data storage systems. The Viterbi algorithm can be adapted for performing maximum…
This paper is concerned with determining the shortest path for a pursuer aiming to intercept a moving target travelling at a constant speed. To address this challenge, we introduce an efficient mathematical model outlined as an optimal…
Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product…
We study the computation of lower and upper probabilities of hitting a target set of states for imprecise Markov chains, where transition uncertainty is modelled by a convex set of transition matrices. In the precise case, hitting…
We present a novel method for computing reachability probabilities of parametric discrete-time Markov chains whose transition probabilities are fractions of polynomials over a set of parameters. Our algorithm is based on two key…
The Viterbi algorithm, presented in 1967, allows a maximum likelihood decoding of partial response codes. This study focuses on the duobinary code which is the first member of this family and has been specified for the digital part of…