Probabilistic learning of nonlinear dynamical systems using sequential Monte Carlo

Abstract

Probabilistic modeling provides the capability to represent and manipulate uncertainty in data, models, predictions and decisions. We are concerned with the problem of learning probabilistic models of dynamical systems from measured data. Specifically, we consider learning of probabilistic nonlinear state-space models. There is no closed-form solution available for this problem, implying that we are forced to use approximations. In this tutorial we will provide a self-contained introduction to one of the state-of-the-art methods---the particle Metropolis--Hastings algorithm---which has proven to offer a practical approximation. This is a Monte Carlo based method, where the particle filter is used to guide a Markov chain Monte Carlo method through the parameter space. One of the key merits of the particle Metropolis--Hastings algorithm is that it is guaranteed to converge to the "true solution" under mild assumptions, despite being based on a particle filter with only a finite number of particles. We will also provide a motivating numerical example illustrating the method using a modeling language tailored for sequential Monte Carlo methods. The intention of modeling languages of this kind is to open up the power of sophisticated Monte Carlo methods---including particle Metropolis--Hastings---to a large group of users without requiring them to know all the underlying mathematical details.

Thomas B. Schön, Andreas Svensson, Lawrence Murray and Fredrik Lindsten, 2018. Probabilistic learning of nonlinear dynamical systems using sequential Monte Carlo. In Mechanical Systems and Signal Processing, Volume 104, pp. 866-883

References in corpus (5)

• The pseudo-marginal approach for efficient Monte Carlo computations
• Nested Sequential Monte Carlo Methods
• Learning of state-space models with highly informative observations: a tempered Sequential Monte Carlo solution
• Delayed Sampling and Automatic Rao-Blackwellization of Probabilistic Programs
• Smoothing with Couplings of Conditional Particle Filters

Cited by in corpus (5)

• Nonlinear System Identification: Learning while respecting physical models using a sequential Monte Carlo method
• Extending the Best Linear Approximation Framework to the Process Noise Case
• Learning of state-space models with highly informative observations: a tempered Sequential Monte Carlo solution
• Sequentially guided MCMC proposals for synthetic likelihoods and correlated synthetic likelihoods
• Inference of population-level disease transmissibility from household-structured symptom onset data