Detecting whether a stochastic process is finitely expressed in a basis

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Outliers in discrete choice response data may result from misclassification and misreporting of the response variable and from choice behaviour that is inconsistent with modelling assumptions (e.g. random utility maximisation). In the presence of outliers, ...

Magnetic resonance spectroscopy is a powerful, non-invasive, quantitative imaging technique that allows for the measurement of brain metabolites that has demonstrated utility in diagnosing and characterizing a broad range of neurological diseases. Its impa ...

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 ...

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 ...

Population equations for infinitely large networks of spiking neurons have a long tradition in theoret-ical neuroscience. In this work, we analyze a recent generalization of these equations to populations of finite size, which takes the form of a nonlinear ...

How can we discern whether the covariance operator of a stochastic pro-cess is of reduced rank, and if so, what its precise rank is? And how can we do so at a given level of confidence? This question is central to a great deal of methods for functional dat ...

This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...

Data-driven and model-driven methodologies can be regarded as competitive fields since they tackle similar problems such as prediction. However, these two fields can learn from each other to improve themselves. Indeed, data-driven methodologies have been d ...

In the field of choice modeling, the availability of ever-larger datasets has the potential to significantly expand our understanding of human behavior, but this prospect is limited by the poor scalability of discrete choice models (DCMs): as sample sizes ...

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 ...

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 ...

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 ...

Today, automatic control is integrated into a wide spectrum of real-world systems such as electrical grids and transportation networks. Many of these systems comprise numerous interconnected agents, perform safety-critical operations, or generate large amo ...

Detecting whether a stochastic process is finitely expressed in a basis

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Robust discrete choice models with t-distributed kernel errors

Harmonization of multi-scanner in vivo magnetic resonance spectroscopy: ENIGMA consortium task group considerations

Regularization for distributionally robust state estimation and prediction

ReLU Neural Network Galerkin BEM

On a Finite-Size Neuronal Population Equation

Testing For The Rank Of A Covariance Operator

Positive Definite Completions and Continuous Graphical Models

Bridging the gap between model-driven and data-driven methods in the era of Big Data

Stochastic adaptive resampling for the estimation of discrete choice models

Covariance Estimation for Random Surfaces beyond Separability

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

Density estimation in RKHS with application to Korobov spaces in high dimensions

Data-driven and Safe Networked Control with Applications to Microgrids