Critical scaling in hidden state inference for linear Langevin dynamics
File(s)
Accepted version
Author(s)
Bravi, B
Sollich, P
Type
Journal Article
Abstract
We consider the problem of inferring the dynamics of unknown (i.e. hidden) nodes from a set of observed trajectories and study analytically the average prediction error and the typical relaxation time of correlations between errors. We focus on a stochastic linear dynamics of continuous degrees of freedom interacting via random Gaussian couplings in the infinite network size limit. The expected error on the hidden time courses can be found as the equal-time hidden-to-hidden covariance of the probability distribution conditioned on observations. In the stationary regime, we analyze the phase diagram in the space of relevant parameters, namely the ratio between the numbers of observed and hidden nodes, the degree of symmetry of the interactions and the amplitudes of the hidden-to-hidden and hidden-to-observed couplings relative to the decay constant of the internal hidden dynamics. In particular, we identify critical regions in parameter space where the relaxation time and the inference error diverge, and determine the corresponding scaling behaviour.
Date Issued
2017-06-22
Date Acceptance
2017-04-03
Citation
Journal of Statistical Mechanics: Theory and Experiment, 2017, 2017 (6), pp.1-31
ISSN
1742-5468
Publisher
IOP Publishing
Start Page
1
End Page
31
Journal / Book Title
Journal of Statistical Mechanics: Theory and Experiment
Volume
2017
Issue
6
Copyright Statement
© 2017 IOP Publishing Ltd and SISSA Medialab srl
Identifier
https://iopscience.iop.org/article/10.1088/1742-5468/aa6bc4
Subjects
Fluids & Plasmas
0105 Mathematical Physics
0203 Classical Physics
Publication Status
Published
Date Publish Online
2017-06-22