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This paper studies the recovery of a superposition of point sources from noisy bandlimited data. In the fewest possible words, we only have information about the spectrum of an object in a low-frequency band bounded by a certain cut-off…

The interdependence and high dimensionality of multivariate signals present significant challenges for denoising, as conventional univariate methods often struggle to capture the complex interactions between variables. A successful approach…

Feature selection has remained a daunting challenge in machine learning and artificial intelligence, where increasingly complex, high-dimensional datasets demand principled strategies for isolating the most informative predictors. Despite…

Split sample methods have recently been put forward as a way to reduce the coverage oscillations that haunt confidence intervals for parameters of lattice distributions, such as the binomial and Poisson distributions. We study split sample…

The analysis of high-frequency financial data is often impeded by the presence of noise. This article is motivated by intraday return data in which market microstructure noise appears to be rough, that is, best captured by a continuous-time…

In this note we consider spectral cut-off estimators to solve a statistical linear inverse problem under arbitrary white noise. The truncation level is determined with a recently introduced adaptive method based on the classical discrepancy…

Dimensional reduction techniques have long been used to visualize the structure and geometry of high dimensional data. However, most widely used techniques are difficult to interpret due to nonlinearities and opaque optimization processes.…

In this article, we consider two different statistical models. First, we focus on the estimation of the jump intensity of a compound Poisson process in the presence of unknown noise. This problem combines both the deconvolution problem and…

The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major…

We propose a deconvolution algorithm for images blurred and degraded by a Poisson noise. The algorithm uses a fast proximal backward-forward splitting iteration. This iteration minimizes an energy which combines a \textit{non-linear} data…

The Dirichlet forms methods, in order to represent errors and their propagation, are particularly powerful in infinite dimensional problems such as models involving stochastic analysis encountered in finance or physics, cf. [5]. Now, coming…

This paper presents a novel method for polynomial approximation (Hermite approximation) using the fusion of value and derivative information. Therefore, the least-squares error in both domains is simultaneously minimized. A covariance…

A frequently occurring challenge in experimental and numerical observation is how to resolve features, such as spectral peaks - with center, width, height - and derivatives from measured data with unavoidable noise. Therefore, we develop a…

As a defense strategy against adversarial attacks, adversarial detection aims to identify and filter out adversarial data from the data flow based on discrepancies in distribution and noise patterns between natural and adversarial data.…

Physical laws governing population dynamics are generally expressed as differential equations. Research in recent decades has incorporated fractional-order (non-integer) derivatives into differential models of natural phenomena, such as…

We compare a recently proposed multivariate spline based on mixed partial derivatives with two other standard splines for the scattered data smoothing problem. The splines are defined as the minimiser of a penalised least squares…

Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…

We study for the first time the Cauchy problem for semilinear fractional elliptic equation. This paper is concerned with the Gaussian white noise model for the initial Cauchy data. We establish the ill-posedness of the problem. Then, under…

This article considers a Cauchy problem of Helmholtz equations whose solution is well known to be exponentially unstable with respect to the inputs. In the framework of variational quasi-reversibility method, a Fourier truncation is applied…

Hyperspectral images play a crucial role in precision agriculture, environmental monitoring or ecological analysis. However, due to sensor equipment and the imaging environment, the observed hyperspectral images are often inevitably…