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By selecting different filter functions, spectral algorithms can generate various regularization methods to solve statistical inverse problems within the learning-from-samples framework. This paper combines distributed spectral algorithms…
Registration of multivariate functional data involves handling of both cross-component and cross-observation phase variations. Allowing for the two phase variations to be modelled as general diffeomorphic time warpings, in this work we…
Predicting missing segments in partially observed functions is challenging due to infinite-dimensionality, complex dependence within and across observations, and irregular noise. These challenges are further exacerbated by the existence of…
Universal approximation theorems show that neural networks can approximate any continuous function; however, the number of parameters may grow exponentially with the ambient dimension, so these results do not fully explain the practical…
Random smoothing data augmentation is a unique form of regularization that can prevent overfitting by introducing noise to the input data, encouraging the model to learn more generalized features. Despite its success in various…
We introduce a novel geometric framework for separating the phase and the amplitude variability in functional data of the type frequently studied in growth curve analysis. This framework uses the Fisher-Rao Riemannian metric to derive a…
In machine learning it is common to interpret each data point as a vector in Euclidean space. However the data may actually be functional i.e.\ each data point is a function of some variable such as time and the function is discretely…
Functional registration algorithms represent point clouds as functions (e.g. spacial occupancy field) avoiding unreliable correspondence estimation in conventional least-squares registration algorithms. However, existing functional…
Alignment or registration of functions is a fundamental problem in statistical analysis of functions and shapes. While there are several approaches available, a more recent approach based on Fisher-Rao metric and square-root velocity…
We present an approach for variational regularization of inverse and imaging problems for recovering functions with values in a set of vectors. We introduce regularization functionals, which are derivative-free double integrals of such…
A new set of symmetric correction functions is presented for high-order flux reconstruction, that expands upon, while incorporating, all previous correction function sets and opens the possibility for improved performance. By considering FR…
In this paper, we propose to use the general $L^2$-based Sobolev norms, i.e., $H^s$ norms where $s\in \mathbb{R}$, to measure the data discrepancy due to noise in image processing tasks that are formulated as optimization problems. As…
We study numerical integration of functions depending on an infinite number of variables. We provide lower error bounds for general deterministic linear algorithms and provide matching upper error bounds with the help of suitable multilevel…
In this paper, we describe in detail a model of geometric-functional variability between fshapes. These objects were introduced for the first time by the authors in [Charlier et al. 2015] and are basically the combination of classical…
Modern high-dimensional methods often adopt the "bet on sparsity" principle, while in supervised multivariate learning statisticians may face "dense" problems with a large number of nonzero coefficients. This paper proposes a novel…
This paper constructs unique compactly supported functions in Sobolev spaces that have minimal norm, maximal support, and maximal central value, under certain renormalizations. They may serve as optimized basis functions in interpolation or…
Learning rates for least-squares regression are typically expressed in terms of $L_2$-norms. In this paper we extend these rates to norms stronger than the $L_2$-norm without requiring the regression function to be contained in the…
Unsupervised registration strategies bypass requirements in ground truth transforms or segmentations by optimising similarity metrics between fixed and moved volumes. Among these methods, a recent subclass of approaches based on…
A new representation is proposed for functions in a Sobolev space with dominating mixed smoothness on an $N$-dimensional hyperrectangle. In particular, it is shown that these functions can be expressed in terms of their highest-order mixed…
Deep Learning in Image Registration (DLIR) methods have been tremendously successful in image registration due to their speed and ability to incorporate weak label supervision at training time. However, existing DLIR methods forego many of…