Variational Inference and Learning of Piecewise-linear Dynamical Systems

06/02/2020
by   Xavier Alameda-Pineda, et al.
0

Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. The baseline method assumes that both the dynamic and observation models follow linear-Gaussian models. Non-linear extensions lead to intractable solvers. It is also possible to consider several linear models, or a piecewise linear model, and to combine them with a switching mechanism, which is also intractable because of the exponential explosion of the number of Gaussian components. In this paper, we propose a variational approximation of piecewise linear dynamic systems. We provide full details of the derivation of a variational expectation-maximization algorithm that can be used either as a filter or as a smoother. We show that the model parameters can be split into two sets, a set of static (or observation parameters) and a set of dynamic parameters. The immediate consequences are that the former set can be estimated off-line and that the number of linear models (or the number of states of the switching variable) can be learned based on model selection. We apply the proposed method to the problem of visual tracking and we thoroughly compare our algorithm with several visual trackers applied to the problem of head-pose estimation.

READ FULL TEXT

page 1

page 8

research
09/29/2021

Variational Inference for Continuous-Time Switching Dynamical Systems

Switching dynamical systems provide a powerful, interpretable modeling f...
research
09/25/2014

Identification of jump Markov linear models using particle filters

Jump Markov linear models consists of a finite number of linear state sp...
research
06/03/2023

Variational Gaussian Process Diffusion Processes

Diffusion processes are a class of stochastic differential equations (SD...
research
11/20/2022

Approximate Uncertainty Propagation for Continuous Gaussian Process Dynamical Systems

When learning continuous dynamical systems with Gaussian Processes, comp...
research
11/07/2017

Distributed Bayesian Piecewise Sparse Linear Models

The importance of interpretability of machine learning models has been i...
research
01/13/2019

A Fully Bayesian Infinite Generative Model for Dynamic Texture Segmentation

Generative dynamic texture models (GDTMs) are widely used for dynamic te...
research
09/29/2020

Estimation of Switched Markov Polynomial NARX models

This work targets the identification of a class of models for hybrid dyn...

Please sign up or login with your details

Forgot password? Click here to reset