Related papers: Analyticity and supershift with regular sampling
The Special Affine Fourier Transformation or the SAFT generalizes a number of well known unitary transformations as well as signal processing and optics related mathematical operations. Shift-invariant spaces also play an important role in…
Importance sampling is a popular technique in Bayesian inference: by reweighting samples drawn from a proposal distribution we are able to obtain samples and moment estimates from a Bayesian posterior over latent variables. Recent work,…
In this article, we investigate some of the fine properties of the value function associated to an optimal control problem in the Wasserstein space of probability measures. Building on new interpolation and linearisation formulas for…
This article is a natural continuation of the paper Tiwari, D., Giordano, P., Hyperseries in the non-Archimedean ring of Colombeau generalized numbers in this journal. We study one variable hyper-power series by analyzing the notion of…
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…
We study power series and analyticity in the quaternionic setting. We first consider a function f defined as the sum of a quaternionic power series centered at 0 in its domain of convergence (which is a ball B(0,R) centered at 0). At each…
Ensuring that analyses performed on a dataset are representative of the entire population is one of the central problems in statistics. Most classical techniques assume that the dataset is independent of the analyst's query and break down…
A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary…
A quantum mechanical generalization of superstatistics is presented here based on the positive operator valued measure transformation property of the system density matrix. This procedure reveals that the origin of the fluctuating factors…
Concentration inequalities quantify the deviation of a random variable from a fixed value. In spite of numerous applications, such as opinion surveys or ecological counting procedures, few concentration results are known for the setting of…
Classical, Quantum and Relativistic mechanics elect time and space as fundamentals, extracting the measure of motion -velocity- from this static space-time platform. Conversely, the timelessness of Statistical mechanics computes the…
The Special Affine Fourier Transformation(SAFT), which generalizes several well-known unitary transformations, has been demonstrated as a valuable tool in signal processing and optics. In this paper, we explore the multivariate dynamical…
Let $X$ be a separable real Hilbert space. We show that for every Lipschitz function $f:X\rightarrow\mathbb{R}$, and for every $\epsilon>0$, there exists a Lipschitz, real analytic function $g:X\rightarrow\mathbb{R}$ such that…
Sample average approximation (SAA) replaces an intractable expected objective by an empirical average and is a basic device of modern stochastic optimization. We develop a rate theory for optimal values and empirical…
We address the decision problem for a fragment of real analysis involving differentiable functions with continuous first derivatives. The proposed theory, besides the operators of Tarski's theory of reals, includes predicates for…
We expand the theoretical background of the recently introduced superadditive and subadditive transformations of aggregation functions $A$. Necessary and sufficient conditions ensuring that a transformation of a proper aggregation function…
This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…
We generalize the classical Bernstein theorem concerning the constructive description of classes of functions uniformly continuous on the real line. The approximation of continuous bounded functions by entire functions of exponential type…
The present article is an extended version of [6] containing new results and an updated list of references. We review the notion of polar analyticity introduced in a previous paper and succesfully applied in Mellin analysis and quadrature…
This article provides an original understanding of the behavior of a class of graph-oriented semi-supervised learning algorithms in the limit of large and numerous data. It is demonstrated that the intuition at the root of these methods…