Related papers: GS-PINN: Greedy Sampling for Parameter Estimation …
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
The sparse identification of nonlinear dynamical systems (SINDy) is a data-driven technique employed for uncovering and representing the fundamental dynamics of intricate systems based on observational data. However, a primary obstacle in…
Sampling is a fundamental topic in graph signal processing, having found applications in estimation, clustering, and video compression. In contrast to traditional signal processing, the irregularity of the signal domain makes selecting a…
This paper focuses on the development of novel greedy techniques for distributed learning under sparsity constraints. Greedy techniques have widely been used in centralized systems due to their low computational requirements and at the same…
Recently, neural networks have been widely applied for solving partial differential equations (PDEs). Although such methods have been proven remarkably successful on practical engineering problems, they have not been shown, theoretically or…
Obtaining high certainty in predictive models is crucial for making informed and trustworthy decisions in many scientific and engineering domains. However, extensive experimentation required for model accuracy can be both costly and…
In this paper, we address the problem of learning the structure of a pairwise graphical model from samples in a high-dimensional setting. Our first main result studies the sparsistency, or consistency in sparsity pattern recovery,…
We develop a framework for estimating unknown partial differential equations from noisy data, using a deep learning approach. Given noisy samples of a solution to an unknown PDE, our method interpolates the samples using a neural network,…
Inference tasks in signal processing are often characterized by the availability of reliable statistical modeling with some missing instance-specific parameters. One conventional approach uses data to estimate these missing parameters and…
Greedy Sampling Methods (GSMs) are widely used to construct approximate solutions of Configuration Optimization Problems (COPs), where a loss functional is minimized over finite configurations of points in a compact domain. While effective…
Motivated by modern applications such as computerized adaptive testing, sequential rank aggregation, and heterogeneous data source selection, we study the problem of active sequential estimation, which involves adaptively selecting…
Kernel-based schemes are state-of-the-art techniques for learning by data. In this work we extend some ideas about kernel-based greedy algorithms to exponential-polynomial splines, whose main drawback consists in possible overfitting and…
Approximating field variables and data vectors from sparse samples is a key challenge in computational science. Widely used methods such as gappy proper orthogonal decomposition and empirical interpolation rely on linear approximation…
We propose a greedy algorithm to select $N$ important features among $P$ input features for a non-linear prediction problem. The features are selected one by one sequentially, in an iterative loss minimization procedure. We use neural…
Models based on recursive adaptive partitioning such as decision trees and their ensembles are popular for high-dimensional regression as they can potentially avoid the curse of dimensionality. Because empirical risk minimization (ERM) is…
In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying…
Solving time-dependent partial differential equations (PDEs) that exhibit sharp gradients or local singularities is computationally demanding, as traditional physics-informed neural networks (PINNs) often suffer from inefficient point…
Sampling is often a necessary evil to reduce the processing and storage costs of distributed tracing. In this work, we describe a scalable and adaptive sampling approach that can preserve events of interest better than the widely used…
Kernel based regularized interpolation is a well known technique to approximate a continuous multivariate function using a set of scattered data points and the corresponding function evaluations, or data values. This method has some…
Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…