Related papers: A joint optimization approach to identifying spars…
We develop a novel framework for sparse multiscale kernel approximation of large scattered data problems based on a samplet representation. Samplets form a multiresolution analysis of localized discrete signed measures and enable…
This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed…
It is now well established that sparse signal models are well suited to restoration tasks and can effectively be learned from audio, image, and video data. Recent research has been aimed at learning discriminative sparse models instead of…
Data-driven methods have recently made great progress in the discovery of partial differential equations (PDEs) from spatial-temporal data. However, several challenges remain to be solved, including sparse noisy data, incomplete candidate…
The reproducing kernel Hilbert space (RKHS) embedding method is a recently introduced estimation approach that seeks to identify the unknown or uncertain function in the governing equations of a nonlinear set of ordinary differential…
In this paper, we study the problem of learning dynamical properties of ensemble systems from their collective behaviors using statistical approaches in reproducing kernel Hilbert space (RKHS). Specifically, we provide a framework to…
Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification of nonlinear dynamics (SINDy) framework, powered by heuristic…
We propose a generic spatiotemporal event forecasting method, which we developed for the National Institute of Justice's (NIJ) Real-Time Crime Forecasting Challenge. Our method is a spatiotemporal forecasting model combining scalable…
We propose a novel framework for discovering Stochastic Partial Differential Equations (SPDEs) from data. The proposed approach combines the concepts of stochastic calculus, variational Bayes theory, and sparse learning. We propose the…
Though the method of least squares has been used for a long time in solving signal processing problems, in the recent field of sparse recovery from compressed measurements, this method has not been given much attention. In this paper we…
We develop an unsupervised machine learning algorithm for the automated discovery and identification of traveling waves in spatio-temporal systems governed by partial differential equations (PDEs). Our method uses sparse regression and…
Compressed sensing is a central topic in signal processing with myriad applications, where the goal is to recover a signal from as few observations as possible. Iterative re-weighting is one of the fundamental tools to achieve this goal.…
The problem of multiple kernel learning based on penalized empirical risk minimization is discussed. The complexity penalty is determined jointly by the empirical $L_2$ norms and the reproducing kernel Hilbert space (RKHS) norms induced by…
Many model selection algorithms rely on sparse dictionary learning to provide interpretable and physics-based governing equations. The optimization algorithms typically use a hard thresholding process to enforce sparse activations in the…
Discovering governing equations from data is important to many scientific and engineering applications. Despite promising successes, existing methods are still challenged by data sparsity and noise issues, both of which are ubiquitous in…
We develop a non-parametric, data-driven, tractable approach for solving multistage stochastic optimization problems in which decisions do not affect the uncertainty. The proposed framework represents the decision variables as elements of a…
Pairwise learning usually refers to a learning task which involves a loss function depending on pairs of examples, among which most notable ones include ranking, metric learning and AUC maximization. In this paper, we study an online…
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…
Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional…
A kernel-based approach for the learning of the solution operator of general nonhomogeneous partial differential equations (PDEs) is proposed. The method incorporates physical priors, typically encoded through the PDE operator, into a…