Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is imposed to allow for ...
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 ...
We present a framework for performing regression when both covariate and response are probability distributions on a compact and convex subset of Rd. Our regression model is based on the theory of optimal transport and links the conditional Fr'echet m ...
The increasing availability of sensing techniques provides a great opportunity for engineers to design state estimation methods, which are optimal for the system under observation and the observed noise patterns. However, these patterns often do not fulfil ...
Atomic simulations using machine learning interatomic potential (MLIP) have gained a lot of popularity owing to their accuracy in comparison to conventional empirical potentials. However, the transferability of MLIP to systems outside the training set pose ...
Autoregressive Neural Networks (ARNNs) have shown exceptional results in generation tasks across image, language, and scientific domains. Despite their success, ARNN architectures often operate as black boxes without a clear connection to underlying physic ...
In this paper we propose a Monte Carlo maximum likelihood estimation strategy for discretely observed Wright–Fisher diffusions. Our approach provides an unbiased estimator of the likelihood function and is based on exact simulation techniques that are of s ...
This thesis focuses on two selected learning problems: 1) statistical inference on graphs models, and, 2) gradient descent on neural networks, with the common objective of defining and analysing the measures that characterize the fundamental limits.In th ...
Many methods exist to model snow densification in order to calculate the depth of a single snow layer or the depth of the total snow cover from its mass. Most of these densification models need to be tightly integrated with an accumulation and melt model a ...
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 ...
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 ...
