相关论文: Extracting analytic proofs from numerically solved…
Tight Bell inequalities are facets of Pitowsky's correlation polytope and are usually obtained from its extreme points by solving the hull problem. Here we present an alternative method based on a combination of algebraic results on…
We introduce the problem of \emph{entropy equivalence testing} for probability distributions, a relaxation of the well-studied closeness testing problem, where the distribution testing algorithm is now only required to distinguish, given…
In this paper, we propose a new method for removing all the redundant inequalities generated by Fourier-Motzkin elimination. This method is based on an improved version of Balas' work and can also be used to remove all the redundant…
Algorithms are now routinely used to make consequential decisions that affect human lives. Examples include college admissions, medical interventions or law enforcement. While algorithms empower us to harness all information hidden in vast…
Deriving formulations for computing and estimating tight worst-case size increases for conjunctive queries with various constraints has been at the core of theoretical database research. If the problem has no constraints or only one…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using It\^o's formula and on a new…
We propose a general methodology for testing whether a given polynomial with integer coefficients is identically zero. The methodology evaluates the polynomial at efficiently computable approximations of suitable irrational points. In…
This thesis addresses the interplay between asymptotic hypothesis testing and entropy inequalities in quantum information theory. In the first part of the thesis we focus on hypothesis testing. We consider two main settings; one can either…
Spline functions are smooth piecewise polynomials widely used for interpolation and smoothing, and nonnegative spline smoothing is also studied for nonnegative data. Previous research used sufficient conditions for the nonnegativity of…
A polynomial matrix inequality is a formula asserting that a polynomial matrix is positive semidefinite. Polynomial matrix optimization concerns minimizing the smallest eigenvalue of a symmetric polynomial matrix subject to a tuple of…
The problems of estimating the similarity index of inhomogeneous scientific publications containing equations and formulas are discussed for the first time. It is shown that the presence of equations and formulas (as well as figures,…
We propose a new way to measure inequalities such as the glass ceiling effect in attributed networks. Existing measures typically rely solely on node degree distribution or degree assortativity, but our approach goes beyond these measures…
We show that there is equality in Shannon's Entropy Power Inequality (EPI) if and only if the random variables involved are Gaussian, assuming nothing beyond the existence of differential entropies. This is done by justifying de Bruijn's…
This work presents a systematic study of objective evaluations of abstaining classifications using Information-Theoretic Measures (ITMs). First, we define objective measures for which they do not depend on any free parameter. This…
In this paper, we study optimization problems of numerical differentiation and summation methods on classes of univariate functions. Sharp estimates (in order) of the optimal recovery error and information complexity are calculated for…
Statistical matching is a technique for integrating two or more data sets when information available for matching records for individual participants across data sets is incomplete. Statistical matching can be viewed as a missing data…
Feature selection is a key step when dealing with high dimensional data. In particular, these techniques simplify the process of knowledge discovery from the data by selecting the most relevant features out of the noisy, redundant and…
Logical Probability (LP) is strictly distinguished from Statistical Probability (SP). To measure semantic information or confirm hypotheses, we need to use sampling distribution (conditional SP function) to test or confirm fuzzy truth…
Through the lens of information-theoretic reductions, we examine a reductions approach to fair optimization and learning where a black-box optimizer is used to learn a fair model for classification or regression. Quantifying the complexity,…
Error estimation is given for a regularized Shannon's sampling formulae, which was found to be accurate and robust for numerically solving partial differential equations.