Abstract
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.
Original language  Undefined/Unknown 

Journal  arXiv 
Publication status  Submitted  5 Feb 2019 
Bibliographical note
30 pages, 50 pages of appendix, 16 figuresKeywords
 stat.ML
 cs.LG
 68T10, 62M05, 60J20
Student theses

Highdimensional hidden Markov models: methodology, computational issues, solutions and applications
Author: Rimella, L., 28 Sept 2021Supervisor: Whiteley, N. (Supervisor)
Student thesis: Doctoral Thesis › Doctor of Philosophy (PhD)
File