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Nonlinear state-space models are ubiquitous in modeling real-world dynamical systems. Sequential Monte Carlo (SMC) techniques, also known as particle methods, are a well-known class of parameter estimation methods for this general class of state-space models. Existing SMC-based techniques rely on excessive sampling of the parameter space, which makes their computation intractable for large systems or tall data sets. Bayesian optimization techniques have been used for fast inference in state-space models with intractable likelihoods. These techniques aim to find the maximum of the likelihood function by sequential sampling of the parameter space through a single SMC approximator. Various SMC approximators with different fidelities and computational costs are often available for sample- based likelihood approximation. In this paper, we propose a multi-fidelity Bayesian optimization algorithm for the inference of general nonlinear state-space models (MFBO-SSM), which enables simultaneous sequential selection of parameters and approximators. The accuracy and speed of the algorithm are demonstrated by numerical experiments using synthetic gene expression data from a gene regulatory network model and real data from the VIX stock price index.
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Computing exact nonlinear reductions of dynamical models
Dynamical systems are commonly used to represent real-world processes. Model reduction techniques are among the core tools for studying dynamical systems models, they allow to reduce the study of a model to a simpler one. In this poster, we present an algorithm for computing exact nonlinear reductions, that is, a set of new rational function macro-variables which satisfy a self-consistent ODE system with the dynamics defined by algebraic functions. We report reductions found by the algorithm in models from the literature.
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- Award ID(s):
- 1853482
- PAR ID:
- 10396285
- Date Published:
- Journal Name:
- ACM Communications in Computer Algebra
- Volume:
- 56
- Issue:
- 2
- ISSN:
- 1932-2240
- Page Range / eLocation ID:
- 25 to 31
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1145/3572867.3572869
