Related papers: Sample Complexity of Sparse System Identification …
The sparse identification of nonlinear dynamics (SINDy) has been established as an effective technique to produce interpretable models of dynamical systems from time-resolved state data via sparse regression. However, to model parameterized…
Block sparsity is an important parameter in many algorithms to successfully recover block sparse signals under the framework of compressive sensing. However, it is often unknown and needs to be estimated. Recently there emerges a few…
This paper details how to parameterize the posterior distribution of state-space systems to generate improved optimization problems for system identification using variational inference. Three different parameterizations of the assumed…
The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables $p_n$ is potentially much larger than the number of samples $n$. However, it was recently…
This note presents a unified analysis of the identification of dynamical systems with low-rank constraints under high-dimensional scaling. This identification problem for dynamic systems are challenging due to the intrinsic dependency of…
Learning governing equations allows for deeper understanding of the structure and dynamics of data. We present a random sampling method for learning structured dynamical systems from under-sampled and possibly noisy state-space…
This paper investigates the idea of designing data-driven partial estimators for nonlinear systems showing parametric uncertainties using sparse multivariate polynomial relationships. A general framework is first presented and then…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
Low complexity of a system model is essential for its use in real-time applications. However, sparse identification methods commonly have stringent requirements that exclude them from being applied in an industrial setting. In this paper,…
Extracting governing equations from dynamic data is an essential task in model selection and parameter estimation. The form of the governing equation is rarely known a priori; however, based on the sparsity-of-effect principle one may…
This paper leverages recent advances in high derivatives reconstruction from noisy-time series and sparse multivariate polynomial identification in order to improve the process of parsimoniously identifying, from a small amount of data,…
This paper proposes a sparse regression strategy for discovery of ordinary differential equations from incomplete and noisy data. Inference is performed over both equation parameters and state variables using a statistically motivated…
This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…
A variety of complex biological, natural and man-made systems exhibit non-Markovian dynamics that can be modeled through fractional order differential equations, yet, we lack sample comlexity aware system identification strategies. Towards…
Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and approximately periodic fast scales are prescribed, while the…
Recent research has shown that performance in signal processing tasks can often be significantly improved by using signal models based on sparse representations, where a signal is approximated using a small number of elements from a fixed…
Sensor selection is an important design problem in large-scale sensor networks. Sensor selection can be interpreted as the problem of selecting the best subset of sensors that guarantees a certain estimation performance. We focus on…
Low-rank tensors are an established framework for high-dimensional least-squares problems. We propose to extend this framework by including the concept of block-sparsity. In the context of polynomial regression each sparsity pattern…
This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…
The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…