English
Related papers

Related papers: Function reconstruction as a classical moment prob…

200 papers

We experimentally demonstrate that highly structured distributions of work emerge during even the simple task of erasing a single bit. These are signatures of a refined suite of time-reversal symmetries in distinct functional classes of…

Fixpoints are ubiquitous in computer science and when dealing with quantitative semantics and verification one often considers least fixpoints of (higher-dimensional) functions over the non-negative reals. We show how to approximate the…

Logic in Computer Science · Computer Science 2025-06-16 Paolo Baldan , Sebastian Gurke , Barbara König , Tommaso Padoan , Florian Wittbold

The Inexact Restoration approach has proved to be an adequate tool for handling the problem of minimizing an expensive function within an arbitrary feasible set by using different degrees of precision in the objective function. The Inexact…

Optimization and Control · Mathematics 2023-04-28 Ernesto G. Birgin , Natasa Krejić , José Mario Martínez

Under investigation is the problem of finding the best approximation of a function in a Hilbert space subject to convex constraints and prescribed nonlinear transformations. We show that in many instances these prescriptions can be…

Functional Analysis · Mathematics 2021-06-17 Patrick L. Combettes , Zev C. Woodstock

We study the approximation of a square-integrable function from a finite number of evaluations on a random set of nodes according to a well-chosen distribution. This is particularly relevant when the function is assumed to belong to a…

Machine Learning · Statistics 2024-11-13 Ayoub Belhadji , Rémi Bardenet , Pierre Chainais

Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. A clear example is the daily rainfall data. In this paper, we present a novel…

Methodology · Statistics 2021-06-17 Sai K. Popuri , Nagaraj K. Neerchal , Amita Mehta , Ahmad Mousavi

Material response of real, passive, linear, time-invariant media to external influences is described by complex analytic functions of frequency that can always be written in terms of Stieltjes functions -- a special class of analytic…

Optimization and Control · Mathematics 2022-03-25 Yury Grabovsky

In this work, we deal with an iteration method for approximating a fixed point of a contraction mapping using the Mann's algorithm under functional random errors. We first show its almost complete convergence to the fixed point by mean of…

Probability · Mathematics 2017-01-24 Bahia Barache , Idir Arab , Abdelnasser Dahmani

Composing previously mastered skills to solve novel tasks promises dramatic improvements in the data efficiency of reinforcement learning. Here, we analyze two recent works composing behaviors represented in the form of action-value…

Machine Learning · Computer Science 2019-07-08 Jonathan J Hunt , Andre Barreto , Timothy P Lillicrap , Nicolas Heess

We extend the problem of obtaining an estimator for the finite population mean parameter incorporating complete auxiliary information through calibration estimation in survey sampling but considering a functional data framework. The…

Statistics Theory · Mathematics 2013-02-06 Santiago Gallón , Jean-Michel Loubes , Fabrice Gamboa

Efficient approximation lies at the heart of large-scale machine learning problems. In this paper, we propose a novel, robust maximum entropy algorithm, which is capable of dealing with hundreds of moments and allows for computationally…

Machine Learning · Statistics 2019-06-05 Diego Granziol , Binxin Ru , Stefan Zohren , Xiaowen Doing , Michael Osborne , Stephen Roberts

We investigate a class of moment problems, namely recovering a measure supported on the graph of a function from partial knowledge of its moments, as for instance in some problems of optimal transport or density estimation. We show that the…

Optimization and Control · Mathematics 2021-06-24 Didier Henrion , Jean Lasserre

We study the problem of nonparametric estimation of density functions with a product form on the domain $\triangle=\{( x_1, \ldots, x_d)\in \mathbb{R}^d, 0\leq x_1\leq \dots \leq x_d \leq 1\}$. Such densities appear in the random truncation…

Statistics Theory · Mathematics 2016-04-22 Cristina Butucea , Jean-François Delmas , Anne Dutfoy , Richard Fischer

We consider the problem of coding for computing with maximal distortion, where the sender communicates with a receiver, which has its own private data and wants to compute a function of their combined data with some fidelity constraint…

Information Theory · Computer Science 2019-10-21 Sourya Basu , Daewon Seo , Lav R. Varshney

The focus of this paper is on the concurrent reconstruction of both the diffusion and potential coefficients present in an elliptic/parabolic equation, utilizing two internal measurements of the solutions. A decoupled algorithm is…

Numerical Analysis · Mathematics 2023-08-08 Siyu Cen , Zhi Zhou

In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…

Methodology · Statistics 2025-08-05 Aytijhya Saha , Aaditya Ramdas

This paper considers the problem of reconstructing missing parts of functions based on their observed segments. It provides, for Gaussian processes and arbitrary bijective transformations thereof, theoretical expressions for the…

Statistics Theory · Mathematics 2024-11-04 Pauliina Ilmonen , Nourhan Shafik , Tommi Sottinen , Germain Van Bever , Lauri Viitasaari

We describe a method for approximating a single-variable function $f$ using persistence diagrams of sublevel sets of $f$ from height functions in different directions. We provide algorithms for the piecewise linear case and for the smooth…

Algebraic Topology · Mathematics 2023-02-10 Aina Ferrà , Carles Casacuberta , Oriol Pujol

We apply a common measure of randomness, the entropy, in the context of iterated functions on a finite set with n elements. For a permutation, it turns out that this entropy is asymptotically (for a growing number of iterations) close to…

Number Theory · Mathematics 2017-12-20 Joachim von zur Gathen

A multi-scale approach to the inverse reconstruction of a pattern's microstructure is reported. Instead of a correlation function, a pair of entropic descriptors (EDs) is proposed for stochastic optimization method. The first of them…

Statistical Mechanics · Physics 2011-02-16 R. Piasecki