Alpha-NML Universal Predictors

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One of the most classical results in high-dimensional learning theory provides a closed-form expression for the generalisation error of binary classification with a single-layer teacher-student perceptron on i.i.d. Gaussian inputs. Both Bayes-optimal (BO) ...

Assessing the traversability of rugged terrain is a difficult challenge for legged robots, especially when they implement multiple, distinct gaits. We tackle this problem on the k-rock2 amphibious, sprawling gait robot by training a gait-dependent traversa ...

The aim of this paper is to define a nonlinear least squares estimator for the spectral parameters of a spherical autoregressive process of order 1 in a parametric setting. Furthermore, we investigate on its asymptotic properties, such as weak consistency ...

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 ...

This thesis focuses on non-parametric covariance estimation for random surfaces, i.e.~functional data on a two-dimensional domain. Non-parametric covariance estimation lies at the heart of functional data analysis, and considerations of statistical and com ...

The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the covariance, even ...

We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distribute ...

In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential models by the MLM ...

Local modifications of a computational domain are often performed in order to simplify the meshing process and to reduce computational costs and memory requirements. However, removing geometrical features of a domain often introduces a non-negligible error ...

We study the problem of learning unknown parameters of stochastic dynamical models from data. Often, these models are high dimensional and contain several scales and complex structures. One is then interested in obtaining a reduced, coarse-grained descript ...

Alpha-NML Universal Predictors

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Learning curves for the multi-class teacher-student perceptron

Gait-dependent Traversability Estimation on the k-rock2 Robot

Parametric Estimation For Functional Autoregressive Processes On The Sphere

Minimax rate for optimal transport regression between distributions

Covariance Estimation for Random Surfaces beyond Separability

Random Surface Covariance Estimation by Shifted Partial Tracing

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

Quantifying uncertain system outputs via the multi-level Monte Carlo method --- distribution and robustness measures

Analysis-aware defeaturing of complex geometries

Filtered data and eigenfunction estimators for statistical inference of multiscale and interacting diffusion processes