Related papers: Oversampling and Donoho-Logan type theorems in mod…

For the purpose of minimizing the number of sample model evaluations, we propose and study algorithms that utilize (sequential) versions of likelihood-to-evidence ratio neural estimation.We apply our algorithms to a supersymmetric…

We demonstrate a measure for the effective number of parameters constrained by a posterior distribution in the context of cosmology. In the same way that the mean of the Shannon information (i.e. the Kullback-Leibler divergence) provides a…

In this paper we establish a version of the Paley-Wiener theorem of Fourier analysis in the frame of the Mellin transform. We provide two different proofs, one involving complex analysis arguments, namely the Riemann surface of the…

The aim of this article is to give an overview of several types of Paley-Wiener theorems occuring in harmonic analysis related to symmetric spaces. This will serve as a motivation for the introduction of the $\Theta$-spherical functions,…

Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…

We extend Lerner's recent approach to sparse domination of Calder\'on--Zygmund operators to upper doubling (but not necessarily doubling), geometrically doubling metric measure spaces. Our domination theorem is different from the one…

We present a theoretical framework for analyzing spatial sampling of fields in three-dimensional space. The framework bridges Shannon's sampling and information theory to Bayesian probabilistic inference and experimental design. Based on…

We show that a considerable part of the theory of (ultra)distributions and hyperfunctions can be extended to more singular generalized functions, starting from an angular localizability notion introduced previously. Such an extension is…

Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two…

We show that there are sampling projections on arbitrary $n$-dimensional subspaces of $B(D)$ with at most $2n$ samples and norm of order $\sqrt{n}$, where $B(D)$ is the space of complex-valued bounded functions on a set $D$. This gives a…

Given a set $S$ of small measure, we discuss existence of sampling sequences for the Paley-Wiener space $PW_S$, which have both densities and sampling bounds close to the optimal ones.

Here we give a new approach to the Paley--Wiener theorem in a Mellin analysis setting which avoids the use of the Riemann surface of the logarithm and analytical branches and is based on new concepts of "polar-analytic function" in the…

For Paley-Wiener functions on weighted combinatorial finite or infinite graphs we develop a weighted sampling theory in which samples are defined as inner products with weight functions (measuring devices). Three reconstruction methods are…

The N=1 supersymmetric version of generalized 2d dilaton gravity can be cast into the form of a Poisson Sigma Model, where the target space and its Poisson bracket are graded. The target space consists of a 1+1 superspace and the dilaton,…

In probability theory and statistics, the IID model represents a single population, and a large, potentially infinite sample from this population. Main theorems, in particular the central limit theorem and laws of large number (LLN) assure…

In part \textit{I} we proposed a structure for a general Hypotheses Space $\mathcal{H}$, the Learning Space $\mathbb{L}(\mathcal{H})$, which can be employed to avoid \textit{overfitting} when estimating in a complex space with relative…

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion…

Sampling theory is a discipline in communications engineering involved with the exact reconstruction of continuous signals from discrete sets of sample points. From a physics perspective, this is interesting in relation to the question of…

Paley-Wiener type theorems describe the image of a given space of functions, often compactly supported functions, under an integral transform, usually a Fourier transform on a group or homogeneous space. Several authors have studied…

We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent…