Publications related to MATHICSE Technical Report : Density estimation in RKHS with application to Korobov spaces in high dimensions

Testing Theories of the Glass Transition with the Same Liquid but Many Kinetic Rules

Matthieu Wyart, Carolina Brito Carvalho dos Santos

We study the glass transition by exploring a broad class of kinetic rules that can significantly modify the normal dynamics of supercooled liquids while maintaining thermal equilibrium. Beyond the usual dynamics of liquids, this class includes dynamics in ...

Amer Physical Soc2024

Density Estimation In Rkhs With Application To Korobov Spaces In High Dimensions

Fabio Nobile, Yoshihito Kazashi

A kernel method for estimating a probability density function from an independent and identically distributed sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined b ...

SIAM PUBLICATIONS2023

Dynamically Orthogonal Approximation for Stochastic Differential Equations

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In this paper, we set the mathematical foundations of the Dynamical Low Rank Approximation (DLRA) method for high-dimensional stochastic differential equations. DLRA aims at approximating the solution as a linear combination of a small number of basis vect ...

2023

Multikernel Regression with Sparsity Constraint

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In this paper, we provide a Banach-space formulation of supervised learning with generalized total-variation (gTV) regularization. We identify the class of kernel functions that are admissible in this framework. Then, we propose a variation of supervised l ...

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Deterministic error bounds for kernel-based learning techniques under bounded noise

Colin Neil Jones, Paul Scharnhorst, Emilio Maddalena

We consider the problem of reconstructing a function from a finite set of noise-corrupted samples. Two kernel algorithms are analyzed, namely kernel ridge regression and epsilon-support vector regression. By assuming the ground-truth function belongs to th ...

PERGAMON-ELSEVIER SCIENCE LTD2021

MATHICSE Technical Report: Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval

Fabio Nobile, Yoshihito Kazashi

An existence result is presented for the dynamical low rank (DLR) approximation for random semi-linear evolutionary equations. The DLR solution approximates the true solution at each time instant by a linear combination of products of deterministic and sto ...

MATHICSE2020

Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval

Fabio Nobile, Yoshihito Kazashi

An existence result is presented for the dynamical low rank (DLR) approximation for random semi-linear evolutionary equations. The DLR solution approximates the true solution at each time instant by a linear combination of products of deterministic and sto ...

2020

Kernel Density Estimation through Density Constrained Near Neighbor Search

Mikhail Kapralov, Navid Nouri

In this paper we revisit the kernel density estimation problem: given a kernel K(x, y) and a dataset of n points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query q, a (1 + epsilon)-approximation to mu := ...

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Sublinear Bounds on the Distinguishing Advantage for Multiple Samples

Serge Vaudenay

The maximal achievable advantage of a (computationally unbounded) distinguisher to determine whether a source

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Machine-Learning of Atomic-Scale Properties Based on Physical Principles

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We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train from linear fun ...

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MATHICSE Technical Report : Density estimation in RKHS with application to Korobov spaces in high dimensions

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Testing Theories of the Glass Transition with the Same Liquid but Many Kinetic Rules

Density Estimation In Rkhs With Application To Korobov Spaces In High Dimensions

Dynamically Orthogonal Approximation for Stochastic Differential Equations

Multikernel Regression with Sparsity Constraint

Deterministic error bounds for kernel-based learning techniques under bounded noise

MATHICSE Technical Report: Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval

Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval

Kernel Density Estimation through Density Constrained Near Neighbor Search

Sublinear Bounds on the Distinguishing Advantage for Multiple Samples

Machine-Learning of Atomic-Scale Properties Based on Physical Principles

Testing Theories of the Glass Transition with the Same Liquid but Many Kinetic Rules

Density Estimation In Rkhs With Application To Korobov Spaces In High Dimensions

Dynamically Orthogonal Approximation for Stochastic Differential Equations

MATHICSE Technical Report: Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval

Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval

Sublinear Bounds on the Distinguishing Advantage for Multiple Samples

Multikernel Regression with Sparsity Constraint

Deterministic error bounds for kernel-based learning techniques under bounded noise

Kernel Density Estimation through Density Constrained Near Neighbor Search

Machine-Learning of Atomic-Scale Properties Based on Physical Principles