Related papers: Probabilistic size-and-shape functional mixed mode…

We consider the inverse problem of estimating an unknown function $u$ from noisy measurements $y$ of a known, possibly nonlinear, map $\mathcal{G}$ applied to $u$. We adopt a Bayesian approach to the problem and work in a setting where the…

We propose a novel definition of Shapley values with uncertain value functions based on first principles using probability theory. Such uncertain value functions can arise in the context of explainable machine learning as a result of…

Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…

Motivated by problems on Brownian motion, we introduce a recursive scheme for a basis construction in the Hilbert space L^2(0,1) which is analogous to that of Haar and Walsh. More generally, we find a new decomposition theory for the…

The binary Mumford-Shah model is a widespread tool for image segmentation and can be considered as a basic model in shape optimization with a broad range of applications in computer vision, ranging from basic segmentation and labeling to…

Persistence diagrams are efficient descriptors of the topology of a point cloud. As they do not naturally belong to a Hilbert space, standard statistical methods cannot be directly applied to them. Instead, feature maps (or representations)…

This paper concerns with iterative schemes for the perfect reconstruction of functions belonging to multiresolution spaces on bounded manifolds from nonuniform sampling. The schemes have optimal complexity in the sense that the…

The renormalization properties of two local BRST invariant composite operators, $(O,V_\mu)$, corresponding respectively to the gauge invariant description of the Higgs particle and of the massive gauge vector boson, are scrutinized in the…

Shape-constrained functional data encompass a wide array of application fields, such as activity profiling, growth curves, healthcare and mortality. Most existing methods for general functional data analysis often ignore that such data are…

Let $\nu$ be a rotation invariant Borel probability measure on the complex plane having moments of all orders. Given a positive integer $q$, it is proved that the space of $\nu$-square integrable $q$-analytic functions is the closure of…

In many applications, smooth processes generate data that is recorded under a variety of observation regimes, such as dense, sparse or fragmented observations that are often contaminated with error. The statistical goal of registering and…

In imaging inverse problems, one seeks to recover an image from missing/corrupted measurements. Because such problems are ill-posed, there is great motivation to quantify the uncertainty induced by the measurement-and-recovery process.…

We introduce a multivariate multidimensional mixed-effects regression model in a finite mixture framework. We relax the usual unidimensionality assumption on the random effects multivariate distribution. Thus, we introduce a…

We consider the problem of reconstructing an unknown bounded function $u$ defined on a domain $X\subset \mathbb{R}^d$ from noiseless or noisy samples of $u$ at $n$ points $(x^i)_{i=1,\dots,n}$. We measure the reconstruction error in a norm…

Linear mixed-effects models are a central analytical tool for modeling hierarchical and longitudinal data, as they allow simultaneous representation of fixed and random sources of variation. In practice, inference for such models is most…

We consider robust estimation of wrapped models to multivariate circular data that are points on the surface of a $p$-torus based on the weighted likelihood methodology.Robust model fitting is achieved by a set of weighted likelihood…

In this paper we extend results taken from compressed sensing to recover Hilbert-space valued vectors. This is an important problem in parametric function approximation in particular when the number of parameters is high. By expanding our…

This paper considers reparameterization invariant Bayesian point estimates and credible regions of model parameters for scientific inference and communication. The effect of intrinsic loss function choice in Bayesian intrinsic estimates and…

We consider the problem of multi-task learning in the high dimensional setting. In particular, we introduce an estimator and investigate its statistical and computational properties for the problem of multiple connected linear regressions…

We propose simple inferential approaches for the fixed effects in complex functional mixed effects models. We estimate the fixed effects under the independence of functional residuals assumption and then bootstrap independent units (e.g.…