Related papers: Functional Covering of Point Processes
Deblurring is a fundamental inverse problem in bioimaging. It requires modelling the point spread function (PSF), which captures the optical distortions entailed by the image formation process. The PSF limits the spatial resolution…
We derive the posterior contraction rate for non-parametric Bayesian estimation of the intensity function of a Poisson point process.
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…
Given a homogeneous Poisson process on ${\mathbb{R}}^d$ with intensity $\lambda$, we prove that it is possible to partition the points into two sets, as a deterministic function of the process, and in an isometry-equivariant way, so that…
Density functional perturbation theory is a well-established method to study responses of molecules and solids, especially responses to atomic displacements or to different perturbing fields (electric, magnetic). Like for density functional…
We study the statistical complexity of estimating partition functions given sample access to a proposal distribution and an unnormalized density ratio for a target distribution. While partition function estimation is a classical problem,…
Rate distortion theory treats the problem of encoding a source with minimum codebook size while at the same time allowing for a certain amount of errors in the reconstruction measured by a fidelity criterion and distortion level. Similar to…
A secrecy system with side information at the decoders is studied in the context of lossy source compression over a noiseless broadcast channel. The decoders have access to different side information sequences that are correlated with the…
In this work, based on a realization of an inhomogeneous Poisson process whose intensity function depends on a real unknown parameter, we consider a simple hypothesis against a sequence of close (contiguous) alternatives. Under certain…
In optical imaging, light propagation is affected by the inhomogeneities of the medium. Sample-induced aberrations and multiple scattering can strongly degrade the image resolution and contrast. Based on a dynamic correction of the incident…
This paper introduces the sparse functional boxplot and the intensity sparse functional boxplot as practical exploratory tools. Besides being available for complete functional data, they can be used in sparse univariate and multivariate…
This work studies nonparametric Bayesian estimation of the intensity function of an inhomogeneous Poisson point process in the important case where the intensity depends on covariates, based on the observation of a single realisation of the…
We propose a comprehensive theoretical description of hysteresis in capillary condensation of gases in mesoporous disordered materials. Applying mean-field density functional theory to a coarse-grained lattice-gas model, we show that the…
This paper deals with Poisson processes on an arbitrary measurable space. Using a direct approach, we derive formulae for moments and cumulants of a vector of multiple Wiener-It\^o integrals with respect to the compensated Poisson process.…
In this paper, we consider the rate-distortion-perception (RDP) trade-off for the lossy compression of a Bernoulli vector source, which is a finite collection of independent binary random variables. The RDP function quantifies in a way the…
Lossy image coding is the art of computing that is principally bounded by the image's rate-distortion function. This bound, though never accurately characterized, has been approached practically via deep learning technologies in recent…
We recount recent history behind building compact models of nonlinear, complex processes and identifying their relevant macroscopic patterns or "macrostates". We give a synopsis of computational mechanics, predictive rate-distortion theory,…
The rate-distortion function (RDF) has long been an information-theoretic benchmark for data compression. As its natural extension, the indirect rate-distortion function (iRDF) corresponds to the scenario where the encoder can only access…
Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…
We consider the nonparametric estimation of the intensity function of a Poisson point process in a circular model from indirect observations $N_1,\ldots,N_n$. These observations emerge from hidden point process realizations with the target…