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We derive and showcase a novel approach to approximating Fourier transforms in higher dimensions, focusing specifically on the case of 2D radially concentrated ('ring-like') functions. We first reduce the problem to that of evaluating the…
The problem of efficient approximation of a linear operator induced by the Gaussian or softmax kernel is often addressed using random features (RFs) which yield an unbiased approximation of the operator's result. Such operators emerge in…
A method of approximating the inverse Radon transform on the plane by integrating against a smooth kernel is investigated. For piecewise smooth integrable functions, convergence theorems are proven and Gibbs phenomena are ruled out.…
The paper is an investigation of the analytic properties of a new class of special functions that appear in the kernels of a class of integral operators underlying the dynamics of matter relaxation processes in attractive fields. These…
We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is related to…
We investigate the strong convergence properties of a proximal-gradient inertial algorithm with two Tikhonov regularization terms in connection to the minimization problem of the sum of a convex lower semi-continuous function $f$ and a…
Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these…
We propose inferential tools for functional linear quantile regression where the conditional quantile of a scalar response is assumed to be a linear functional of a functional covariate. In contrast to conventional approaches, we employ…
The popular cubic smoothing spline estimate of a regression function arises as the minimizer of the penalized sum of squares $\sum_j(Y_j - {\mu}(t_j))^2 + {\lambda}\int_a^b [{\mu}"(t)]^2 dt$, where the data are $t_j,Y_j$, $j=1,..., n$. The…
Value approximation using deep neural networks is at the heart of off-policy deep reinforcement learning, and is often the primary module that provides learning signals to the rest of the algorithm. While multi-layer perceptron networks are…
We study the quantitative convergence of drift-diffusion PDEs that arise as Wasserstein gradient flows of linearly convex functions over the space of probability measures on ${\mathbb R}^d$. In this setting, the objective is in general not…
We study the asymptotic shape of the trajectory of the stochastic gradient descent algorithm applied to a convex objective function. Under mild regularity assumptions, we prove a functional central limit theorem for the properly rescaled…
We propose here a proof of existence of a minimizer of a segmentation functional based on a priori information on target shapes, and formulated with level sets. The existence of a minimizer is very important, because it guarantees the…
We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared quantum systems. The state is represented through the Wigner function, a generalized probability density on…
Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…
The Bayesian update can be viewed as a variational problem by characterizing the posterior as the minimizer of a functional. The variational viewpoint is far from new and is at the heart of popular methods for posterior approximation.…
Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…
For a class of stochastic models with Gaussian and rough mean-reverting volatility that embeds the genuine rough Stein-Stein model, we study the weak approximation rate when using a Euler type scheme with integrated kernels. Our first…
Random Fourier features (RFF) represent one of the most popular and wide-spread techniques in machine learning to scale up kernel algorithms. Despite the numerous successful applications of RFFs, unfortunately, quite little is understood…
This paper deals with local criteria for the convergence to a global minimiser for gradient flow trajectories and their discretisations. To obtain quantitative estimates on the speed of convergence, we consider variations on the classical…