Gaussian Process Regression for Maximum Entropy Distribution

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This thesis is situated at the crossroads between machine learning and control engineering. Our contributions are both theoretical, through proposing a new uncertainty quantification methodology in a kernelized context; and experimental, through investigat ...

Given two jointly distributed random variables (X,Y), a functional representation of X is a random variable Z independent of Y, and a deterministic function g(⋅,⋅) such that X=g(Y,Z). The problem of finding a minimum entropy functional representation is kn ...

Image noise can often be accurately fitted to a Poisson-Gaussian distribution. However, estimating the distribution parameters from a noisy image only is a challenging task. Here, we study the case when paired noisy and noise-free samples are accessible. N ...

We discuss the use of likelihood asymptotics for inference on risk measures in univariate extreme value problems, focusing on estimation of high quantiles and similar summaries of risk for uncertainty quantification. We study whether higher-order approxima ...

Advances in computing have enabled widespread access to pose estimation, creating new sources of data streams. Unlike mock set-ups for data collection, tapping into these data streams through on-device active learning allows us to directly sample from the ...

Distribution-on-distribution regression considers the problem of formulating and es-timating a regression relationship where both covariate and response are probability distributions. The optimal transport distributional regression model postulates that th ...

We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain Omega of a rectangular domain I x I to a covariance kernel on the entire domain I x I. For a broad class of domains Omega call ...

Randomized trace estimation is a popular and well-studied technique that approximates the trace of a large-scale matrix B by computing the average of x(T) Bx for many samples of a random vector X. Often, B is symmetric positive definite (SPD) but a number ...

The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very a ...

Recently, several theories including the replica method made predictions for the generalization error of Kernel Ridge Regression. In some regimes, they predict that the method has a 'spectral bias': decomposing the true function f* on the eigenbasis of the ...

Many robotics problems are formulated as optimization problems. However, most optimization solvers in robotics are locally optimal and the performance depends a lot on the initial guess. For challenging problems, the solver will often get stuck at poor loc ...

This article presents the Lightning Performance (LP) assessment of a realistic portion of the Italian distribution network with the use of probability distributions for lightning parameters inferred from local data recorded by a Lightning Location System ( ...

Gaussian Process Regression for Maximum Entropy Distribution

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Machine Learning Methods for Robust Uncertainty Quantification and Controller Approximation

Information Spectrum Converse for Minimum Entropy Couplings and Functional Representations

PoGaIN: Poisson-Gaussian Image Noise Modeling From Paired Samples

Improved Inference On Risk Measures For Univariate Extremes

VL4Pose: Active Learning Through Out-Of-Distribution Detection For Pose Estimation

Minimax rate for optimal transport regression between distributions

The Completion Of Covariance Kernels

On Randomized Trace Estimates for Indefinite Matrices with an Application to Determinants

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

Failure and success of the spectral bias prediction for Laplace Kernel Ridge Regression: the case of low-dimensional data

Memory of Motion for Initializing Optimization in Robotics

Assessment of the Lightning Performance of overhead distribution lines based on Lightning Location Systems data