Related papers: Balance-Guided Sparse Identification of Multiscale…

Discovering governing Partial Differential Equations (PDEs) from sparse and noisy data is a challenging issue in data-driven scientific computing. Conventional sparse regression methods often suffer from two major limitations: (i) the…

Data-driven discovery of partial differential equations (PDEs) offers a promising paradigm for uncovering governing physical laws from observational data. However, in practical scenarios, measurements are often contaminated by noise and…

Decision formation in perceptual decision-making involves sensory evidence accumulation instantiated by the temporal integration of an internal decision variable towards some decision criterion or threshold, as described by sequential…

Sparse inversion and classification problems are ubiquitous in modern data science and imaging. They are often formulated as non-smooth minimisation problems. In sparse inversion, we minimise, e.g., the sum of a data fidelity term and an…

Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional…

In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model…

The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…

In this paper, we investigate a Bayesian sparse reconstruction algorithm called compressive sensing via Bayesian support detection (CS-BSD). This algorithm is quite robust against measurement noise and achieves the performance of a minimum…

We study the performance of sparse regression methods and propose new techniques to distill the governing equations of dynamical systems from data. We first look at the generic methodology of learning interpretable equation forms from data,…

Modern agentic systems operate in environments with extremely large action spaces, such as tool-augmented language models with thousands of available APIs or retrieval operations. Despite this scale, empirical evidence suggests that only a…

Making predictions and quantifying their uncertainty when the input data is sequential is a fundamental learning challenge, recently attracting increasing attention. We develop SigGPDE, a new scalable sparse variational inference framework…

This short note studies a variation of the Compressed Sensing paradigm introduced recently by Vaswani et al., i.e. the recovery of sparse signals from a certain number of linear measurements when the signal support is partially known. The…

In this work, we study the problem of reconstructing a sparse signal from a limited number of linear 'incoherent' noisy measurements, when a part of its support is known. The known part of the support may be available from prior knowledge…

In this work we present a data-driven method for the discovery of parametric partial differential equations (PDEs), thus allowing one to disambiguate between the underlying evolution equations and their parametric dependencies. Group…

Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functions and noise…

New data-driven methods have advanced the discovery of governing equations from observations, enabling parsimonious models for complex systems. Here, we 'rediscover' a shallow-water equation closely related to Korteweg--de Vries (KdV) using…

Large-scale regression problems where both the number of variables, $p$, and the number of observations, $n$, may be large and in the order of millions or more, are becoming increasingly more common. Typically the data are sparse: only a…

Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition subjected to a global constraint on sparsity. The approach aims at producing a high quality sparse approximation of the whole signal, using highly…

Modeling realistic fluid and plasma flows is computationally intensive, motivating the use of reduced-order models for a variety of scientific and engineering tasks. However, it is challenging to characterize, much less guarantee, the…

This paper proposes a novel low-rank approximation to the multivariate State-Space Model. The Stochastic Partial Differential Equation (SPDE) approach is applied component-wise to the independent-in-time Mat\'ern Gaussian innovation term in…