Related papers: The Marcinkiewicz-type discretization theorems
Higher-dimensional binary shifts of number-theoretic origin with positive topological entropy are considered. We are particularly interested in analysing their symmetries and extended symmetries. They form groups, known as the topological…
The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…
This paper analyzes a full discretization of a three-dimensional stochastic Allen-Cahn equation with multiplicative noise. The discretization combines the Euler scheme for temporal approximation and the finite element method for spatial…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
In the last decades the estimation of the intrinsic dimensionality of a dataset has gained considerable importance. Despite the great deal of research work devoted to this task, most of the proposed solutions prove to be unreliable when the…
We develop a numerical method for solving a system of nonlinear integral equations involving two integral terms: at the current time t, one integral is taken from 0 to t, and a different integral is taken from t to infinity. We prove the…
We identify fundamental issues with discretization when estimating information-theoretic quantities in the analysis of data. These difficulties are theoretical in nature and arise with discrete datasets carrying significant implications for…
We have presented a new axiomatic derivation of Shannon Entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function.We have then modified shannon entropy to take account…
As a kind of independence of random variables under sublinear expectations, pseudo-independence is weaker than Peng's independence. We shall give Marcinkiewicz-type weak and strong laws of large numbers for pseudo-independent random…
Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…
The sub-linear expectation space is a nonlinear expectation space having advantages of modelling the uncertainty of probability and distribution. In the sub-linear expectation space, we use capacity and sub-linear expectation to replace…
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…
The paper search for the minimum of the entropy of a two- dimensional distribution in the Fr\'echet class, the class of distributions with given marginals. The main result for discrete distributions is an algorithm for building the…
This paper is dedicated to the investigation of a new numerical method to approximate the optimal stopping problem for a discrete-time continuous state space Markov chain under partial observations. It is based on a two-step discretization…
We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint…
We describe five types of results concerning information and concentration of discrete random variables, and relationships between them, motivated by their counterparts in the continuous case. The results we consider are information…
In this paper, we investigate the functional central limit theorem and the Marcinkiewicz strong law of large numbers for U-statistics having absolutely regular data and taking value in a separable Hilbert space. The novelty of our approach…
We develop a new functional-analytic technique for investigating the degree of noncompactness of an operator defined on a quasinormed space and taking values in a Marcinkiewicz space. The main result is a general principle from which it can…
The Bayesian approach to inverse problems provides a practical way to solve ill-posed problems by augmenting the observation model with prior information. Due to the measure-theoretic underpinnings, the approach has raised theoretical…
We study the entanglement entropy in lattice field theory using a simulation algorithm based on Jarzynski's theorem. We focus on the entropic c-function for the Ising model in two and in three dimensions: after validating our algorithm…