The Viterbi process, decay-convexity and parallelized maximum a-posteriori estimation.
Year: 2018
Type: preprint
Abstract: The Viterbi process is the limiting maximum a-posteriori estimate of the unobserved path in a hidden Markov model as the length of the time horizon grows. The existence of such a process suggests that approximate estimation using optimization algorithms which process data segments in parallel may be accurate. For models on state-space $\mathbb{R}^{d}$ satisfying a new decay-convexity condition, we develop an approach to existence of the Viterbi process via fixed points of ordinary differential equations in a certain infinite dimensional Hilbert space. Bounds on the distance to the Viterbi process show that approximate estimation via parallelization can indeed be accurate and scaleable to high-dimensional problems because the rate of convergence to the Viterbi process does not necessarily depend on $d$. The results are applied to a factor model with stochastic volatility and a model of neural population activity.
Source: arXiv (Cornell University)
Author: Nick Whiteley
Institution: University of Bristol
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2896895261