Related papers: Uniform Deconvolution for Poisson Point Processes
We consider the high energy physics unfolding problem where the goal is to estimate the spectrum of elementary particles given observations distorted by the limited resolution of a particle detector. This important statistical inverse…
Deconvolution is the important problem of estimating the distribution of a quantity of interest from a sample with additive measurement error. Nearly all methods in the literature are based on Fourier transformation because it is…
We present new Poisson process approximation results for stabilizing functionals of Poisson and binomial point processes. These functionals are allowed to have an unbounded range of interaction and encompass many examples in stochastic…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…
We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover…
In the context of high-dimensional linear regression models, we propose an algorithm of exact support recovery in the setting of noisy compressed sensing where all entries of the design matrix are independent and identically distributed…
Gaussian processes offers a convenient way to perform nonparametric reconstructions of observational data assuming only a kernel which describes the covariance between neighbouring points in a data set. We approach the ambiguity in the…
A method for correcting smearing effects using machine learning technique is presented. Compared to the standard deconvolution approaches in high energy particle physics, the method can use more than one reconstructed variable to predict…
In the Gaussian white noise model, we study the estimation of an unknown multidimensional function $f$ in the uniform norm by using kernel methods. The performances of procedures are measured by using the maxiset point of view: we determine…
We propose a novel tree-based ensemble method, named XGBoostPP, to nonparametrically estimate the intensity of a point process as a function of covariates. It extends the use of gradient-boosted regression trees (Chen & Guestrin, 2016) to…
We consider the problem of localization of Poisson source by the observations of inhomogeneous Poisson processes. We suppose that there are $k$ detectors on the plane and each detector provides the observations of Poisson processes whose…
We propose an estimation procedure for linear functionals based on Gaussian model selection techniques. We show that the procedure is adaptive, and we give a non asymptotic oracle inequality for the risk of the selected estimator with…
This article develops an analytical framework for studying information divergences and likelihood ratios associated with Poisson processes and point patterns on general measurable spaces. The main results include explicit analytical…
This study proposes a data condensation method for multivariate kernel density estimation by genetic algorithm. First, our proposed algorithm generates multiple subsamples of a given size with replacement from the original sample. The…
We study point processes that consist of certain centers of point tuples of an underlying Poisson process. Such processes arise in stochastic geometry in the study of exceedances of various functionals describing geometric properties of the…
The paper develops new methods of non-parametric estimation a compound Poisson distribution. Such a problem arise, in particular, in the inference of a Levy process recorded at equidistant time intervals. Our key estimator is based on…
We are motivated by problems that arise in a number of applications such as Online Marketing and Explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…
The recovery of images from the observations that are degraded by a linear operator and further corrupted by Poisson noise is an important task in modern imaging applications such as astronomical and biomedical ones. Gradient-based…
We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…
We consider the convex hull of the perturbed point process comprised of $n$ i.i.d. points, each distributed as the sum of a uniform point on the unit sphere $\S^{d-1}$ and a uniform point in the $d$-dimensional ball centered at the origin…