Alpha-NML Universal Predictors

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We study continuous-domain linear inverse problems that involve a general data-fidelity term and a regularisation term. We consider a regularisation that is formed by the sparsity-promoting total-variation norm, pre-composed with a differential operator th ...

In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...

We propose a novel approach to evaluating the ionic Seebeck coefficient in electrolytes from relatively short equilibrium molecular dynamics simulations, based on the Green-Kubo theory of linear response and Bayesian regression analysis. By exploiting the ...

The p-Laplacian problem -del & sdot; ((mu + |del u|(p-2))del u) = f is considered, where mu is a given positive number. An anisotropic a posteriori residual-based error estimator is presented. The error estimator is shown to be equivalent, up to higher ord ...

We study the problem of learning unknown parameters in stochastic interacting particle systems with polynomial drift, interaction, and diffusion functions from the path of one single particle in the system. Our estimator is obtained by solving a linear sys ...

In inverse problems, the task is to reconstruct an unknown signal from its possibly noise-corrupted measurements. Penalized-likelihood-based estimation and Bayesian estimation are two powerful statistical paradigms for the resolution of such problems. They ...

Decision-making permeates every aspect of human and societal development, from individuals' daily choices to the complex decisions made by communities and institutions. Central to effective decision-making is the discipline of optimization, which seeks th ...

An a posteriori error estimator based on an equilibrated flux reconstruction is proposed for defeaturing problems in the context of finite element discretizations. Defeaturing consists in the simplification of a geometry by removing features that are consi ...

We present a framework for performing regression when both covariate and response are probability distributions on a compact and convex subset of

\R^d

. Our regression model is based on the theory of optimal transport and links the conditional Fr'echet m ...

Point clouds are effective data structures for the rep- resentation of three-dimensional media and hence adopted in a wide range of practical applications. In many cases, the portrayed data is expected to be visualized by humans. After acquisition, point c ...

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 ...

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 ...

Activity-based models offer the potential of a far deeper understanding of daily mobility behaviour than trip-based models. However, activity-based models used both in research and practice have often relied on applying sequential choice models between sub ...

We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...

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 ...

We introduce Neural Network (NN for short) approximation architectures for the numerical solution of Boundary Integral Equations (BIEs for short). We exemplify the proposed NN approach for the boundary reduction of the potential problem in two spatial dime ...

Many research questions concern treatment effects on outcomes that can recur several times in the same individual. For example, medical researchers are interested in treatment effects on hospitalizations in heart failure patients and sports injuries in ath ...

We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic signals as realizati ...

In certain cases of astronomical data analysis, the meaningful physical quantity to extract is the ratio R between two data sets. Examples include the lensing ratio, the interloper rate in spectroscopic redshift samples, and the decay rate of gravitational ...

In the Large Hadron Collider, the beam losses are continuously measured for machine protection. By design, most of the particle losses occur in the collimation system, where the particles with high oscilla-tion amplitudes or large momentum error are scrape ...

Alpha-NML Universal Predictors

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Convergence analysis of the discretization of continuous-domain inverse problems

Stability: a search for structure

Seebeck Coefficient of Ionic Conductors from Bayesian Regression Analysis

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem

A Method of Moments Estimator for Interacting Particle Systems and their Mean Field Limit

Statistical Inference for Inverse Problems: From Sparsity-Based Methods to Neural Networks

Reliable data-driven decision-making through optimal transport

An equilibrated flux a posteriori error estimator for defeaturing problems

Distributional Regression and Autoregression via Optimal Transport

Towards a multiscale point cloud structural similarity metric

Regularization for distributionally robust state estimation and prediction

Functional data analysis with rough sample paths?

OASIS: Optimisation-based Activity Scheduling with Integrated Simultaneous choice dimensions

Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective

Unbiased Likelihood Estimation of Wright–Fisher Diffusion Processes

ReLU Neural Network Galerkin BEM

Causal inference with recurrent and competing events

A Statistical Framework to Investigate the Optimality of Signal-Reconstruction Methods

An Unbiased Method of Measuring the Ratio of Two Data Sets

Data-driven modeling of beam loss in the LHC