
On Computing the Total Variation Distance of Hidden Markov Models
We prove results on the decidability and complexity of computing the tot...
read it

Nonasymptotic control of the MLE for misspecified nonparametric hidden Markov models
We study the problem of estimating an unknown time process distribution ...
read it

A Lagged Particle Filter for Stable Filtering of certain HighDimensional StateSpace Models
We consider the problem of highdimensional filtering of statespace mod...
read it

On approximation of smoothing probabilities for hidden Markov models
We consider the smoothing probabilities of hidden Markov model (HMM). We...
read it

Exact inference for a class of nonlinear hidden Markov models
Exact inference for hidden Markov models requires the evaluation of all ...
read it

Exact inference for a class of nonlinear hidden Markov models on general state spaces
Exact inference for hidden Markov models requires the evaluation of all ...
read it

Efficient Bayesian model selection for coupled hidden Markov models with application to infectious diseases
Performing model selection for coupled hidden Markov models (CHMMs) is h...
read it
Exploiting locality in highdimensional factorial hidden Markov models
We propose algorithms for approximate filtering and smoothing in highdimensional factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according a notion of locality in a factor graph associated with the emission distribution. This allows the exponentialindimension cost of exact filtering and smoothing to be avoided. We prove that the approximation accuracy, measured in a local total variation norm, is `dimensionfree' in the sense that as the overall dimension of the model increases the error bounds we derive do not necessarily degrade. A key step in the analysis is to quantify the error introduced by localizing the likelihood function in a Bayes' rule update. The factorial structure of the likelihood function which we exploit arises naturally when data have known spatial or network structure. We demonstrate the new algorithms on synthetic examples and a London Underground passenger flow problem, where the factor graph is effectively given by the train network.
READ FULL TEXT
Comments
There are no comments yet.