Related papers: A Sparse Bayesian Learning Algorithm for Estimatio…

We consider a system of $N$ interacting particles, governed by transport and diffusion, that converges in a mean-field limit to the solution of a McKean-Vlasov equation. From the observation of a trajectory of the system over a fixed time…

This work incorporates the multi-modality of the data distribution into a Gaussian Process regression model. We approach the problem from a discriminative perspective by learning, jointly over the training data, the target space variance in…

Nonlocal operators with integral kernels have become a popular tool for designing solution maps between function spaces, due to their efficiency in representing long-range dependence and the attractive feature of being resolution-invariant.…

This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear…

Normative and task-driven theories offer powerful top-down explanations for biological systems, yet the goals of quantitatively arbitrating between competing theories, and utilizing them as inductive biases to improve data-driven fits of…

We demonstrate an efficient algorithm for inverse problems in time-dependent quantum dynamics based on feedback loops between Hamiltonian parameters and the solutions of the Schr\"{o}dinger equation. Our approach formulates the inverse…

Bayesian nonparametric models, such as Gaussian processes, provide a compelling framework for automatic statistical modelling: these models have a high degree of flexibility, and automatically calibrated complexity. However, automating…

High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…

Network inference has been attracting increasing attention in several fields, notably systems biology, control engineering and biomedicine. To develop a therapy, it is essential to understand the connectivity of biochemical units and the…

This work focuses on the mean field stochastic partial differential equations with nonlinear kernels. We first prove the existence and uniqueness of strong and weak solutions for mean field stochastic partial differential equations in the…

Discovering the unknown governing equations of grid-connected inverters from external measurements holds significant attraction for analyzing modern inverter-intensive power systems. However, existing methods struggle to balance the…

Modern artificial intelligence has revolutionized our ability to extract rich and versatile data representations across scientific disciplines. Yet, the statistical properties of these representations remain poorly controlled, causing…

Nonparametric estimation of nonlocal interaction kernels is crucial in various applications involving interacting particle systems. The inference challenge, situated at the nexus of statistical learning and inverse problems, arises from the…

This paper introduces a new and effective algorithm for learning kernels in a Multi-Task Learning (MTL) setting. Although, we consider a MTL scenario here, our approach can be easily applied to standard single task learning, as well. As…

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…

Discovering interaction effects on a response of interest is a fundamental problem faced in biology, medicine, economics, and many other scientific disciplines. In theory, Bayesian methods for discovering pairwise interactions enjoy many…

In this paper, we propose a data-adaptive non-parametric kernel learning framework in margin based kernel methods. In model formulation, given an initial kernel matrix, a data-adaptive matrix with two constraints is imposed in an entry-wise…

This paper addresses a kernel-based learning problem for a network of agents locally observing a latent multidimensional, nonlinear phenomenon in a noisy environment. We propose a learning algorithm that requires only mild a priori…

Nonlinear system identification is important with a wide range of applications. The typical approaches for nonlinear system identification include Volterra series models, nonlinear autoregressive with exogenous inputs models,…

A different route to identification of time-invariant linear systems has been recently proposed which does not require committing to a specific parametric model structure. Impulse responses are described in a nonparametric Bayesian…