Large-Scale System Identification Using a Randomized SVD
- URL: http://arxiv.org/abs/2109.02703v1
- Date: Mon, 6 Sep 2021 19:25:15 GMT
- Title: Large-Scale System Identification Using a Randomized SVD
- Authors: Han Wang and James Anderson
- Abstract summary: We show that an approximate matrix factorization can replace the standard SVD in the realization algorithm.
This is the only method capable of producing a model.
- Score: 4.567810220723372
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Learning a dynamical system from input/output data is a fundamental task in
the control design pipeline. In the partially observed setting there are two
components to identification: parameter estimation to learn the Markov
parameters, and system realization to obtain a state space model. In both
sub-problems it is implicitly assumed that standard numerical algorithms such
as the singular value decomposition (SVD) can be easily and reliably computed.
When trying to fit a high-dimensional model to data, for example in the
cyber-physical system setting, even computing an SVD is intractable. In this
work we show that an approximate matrix factorization obtained using randomized
methods can replace the standard SVD in the realization algorithm while
maintaining the non-asymptotic (in data-set size) performance and robustness
guarantees of classical methods. Numerical examples illustrate that for large
system models, this is the only method capable of producing a model.
Related papers
- Balanced Neural ODEs: nonlinear model order reduction and Koopman operator approximations [0.0]
Variational Autoencoders (VAEs) are a powerful framework for learning compact latent representations.
NeuralODEs excel in learning transient system dynamics.
This work combines the strengths of both to create fast surrogate models with adjustable complexity.
arXiv Detail & Related papers (2024-10-14T05:45:52Z) - Latent Semantic Consensus For Deterministic Geometric Model Fitting [109.44565542031384]
We propose an effective method called Latent Semantic Consensus (LSC)
LSC formulates the model fitting problem into two latent semantic spaces based on data points and model hypotheses.
LSC is able to provide consistent and reliable solutions within only a few milliseconds for general multi-structural model fitting.
arXiv Detail & Related papers (2024-03-11T05:35:38Z) - Online Variational Sequential Monte Carlo [49.97673761305336]
We build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference.
Online VSMC is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation.
arXiv Detail & Related papers (2023-12-19T21:45:38Z) - Cost-sensitive probabilistic predictions for support vector machines [1.743685428161914]
Support vector machines (SVMs) are widely used and constitute one of the best examined and used machine learning models.
We propose a novel approach to generate probabilistic outputs for the SVM.
arXiv Detail & Related papers (2023-10-09T11:00:17Z) - Numerical Optimizations for Weighted Low-rank Estimation on Language
Model [73.12941276331316]
Singular value decomposition (SVD) is one of the most popular compression methods that approximates a target matrix with smaller matrices.
Standard SVD treats the parameters within the matrix with equal importance, which is a simple but unrealistic assumption.
We show that our method can perform better than current SOTA methods in neural-based language models.
arXiv Detail & Related papers (2022-11-02T00:58:02Z) - Numerically Stable Sparse Gaussian Processes via Minimum Separation
using Cover Trees [57.67528738886731]
We study the numerical stability of scalable sparse approximations based on inducing points.
For low-dimensional tasks such as geospatial modeling, we propose an automated method for computing inducing points satisfying these conditions.
arXiv Detail & Related papers (2022-10-14T15:20:17Z) - Deep learning-enhanced ensemble-based data assimilation for
high-dimensional nonlinear dynamical systems [0.0]
Ensemble Kalman filter (EnKF) is a DA algorithm widely used in applications involving high-dimensional nonlinear dynamical systems.
In this work, we propose hybrid ensemble Kalman filter (H-EnKF), which is applied to a two-layer quasi-geostrophic flow system as a test case.
arXiv Detail & Related papers (2022-06-09T23:34:49Z) - Distributed Dynamic Safe Screening Algorithms for Sparse Regularization [73.85961005970222]
We propose a new distributed dynamic safe screening (DDSS) method for sparsity regularized models and apply it on shared-memory and distributed-memory architecture respectively.
We prove that the proposed method achieves the linear convergence rate with lower overall complexity and can eliminate almost all the inactive features in a finite number of iterations almost surely.
arXiv Detail & Related papers (2022-04-23T02:45:55Z) - Tensor Network Kalman Filtering for Large-Scale LS-SVMs [17.36231167296782]
Least squares support vector machines are used for nonlinear regression and classification.
A framework based on tensor networks and the Kalman filter is presented to alleviate the demanding memory and computational complexities.
Results show that our method can achieve high performance and is particularly useful when alternative methods are computationally infeasible.
arXiv Detail & Related papers (2021-10-26T08:54:03Z) - A Novel Anomaly Detection Algorithm for Hybrid Production Systems based
on Deep Learning and Timed Automata [73.38551379469533]
DAD:DeepAnomalyDetection is a new approach for automatic model learning and anomaly detection in hybrid production systems.
It combines deep learning and timed automata for creating behavioral model from observations.
The algorithm has been applied to few data sets including two from real systems and has shown promising results.
arXiv Detail & Related papers (2020-10-29T08:27:43Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.