Related papers: On Non-Interactive Simulation of Binary Random Var…
Ahlswede and Katona (1977) posed the following isodiametric problem in Hamming spaces: For every $n$ and $1\le M\le2^{n}$, determine the minimum average Hamming distance of binary codes with length $n$ and size $M$. Fu, Wei, and Yeung…
We develop our previous works concerning the identification of the collection of significant factors determining some, in general, non-binary random response variable. Such identification is important, e.g., in biological and medical…
Given a binary nonlinear code, we provide a deterministic algorithm to compute its weight and distance distribution, and in particular its minimum weight and its minimum distance, which takes advantage of fast Fourier techniques. This…
New lower bounds on the minimum average Hamming distance of binary codes are derived. The bounds are obtained using linear programming approach.
We develop novel empirical Bernstein inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further assumptions like independence or identical distribution of…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
This paper resolves two open problems from a recent paper, arXiv:2403.16981, concerning the sample complexity of distributed simple binary hypothesis testing under information constraints. The first open problem asks whether interaction…
Discrete Markov random fields form a natural class of models to represent images and spatial data sets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes parameter estimation and…
A key assumption in the theory of nonlinear adaptive control is that the uncertainty of the system can be expressed in the linear span of a set of known basis functions. While this assumption leads to efficient algorithms, it limits…
A causal query will commonly not be identifiable from observed data, in which case no estimator of the query can be contrived without further assumptions or measured variables, regardless of the amount or precision of the measurements of…
Studies on simulation input uncertainty often built on the availability of input data. In this paper, we investigate an inverse problem where, given only the availability of output data, we nonparametrically calibrate the input models and…
We consider the following non-interactive simulation problem: Alice and Bob observe sequences $X^n$ and $Y^n$ respectively where $\{(X_i, Y_i)\}_{i=1}^n$ are drawn i.i.d. from $P(x,y),$ and they output $U$ and $V$ respectively which is…
This paper starts by considering the minimization of the Renyi divergence subject to a constraint on the total variation distance. Based on the solution of this optimization problem, the exact locus of the points $\bigl( D(Q\|P_1),…
This paper investigates and bounds the expected solution quality of combinatorial optimization problems when feasible solutions are chosen at random. Loose general bounds are discovered, as well as families of combinatorial optimization…
Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds…
We establish the first known upper bound on the exact and Wyner's common information of $n$ continuous random variables in terms of the dual total correlation between them (which is a generalization of mutual information). In particular, we…
Inspired by classical sensitivity results for nonlinear optimization, we derive and discuss new quantitative bounds to characterize the solution map and dual variables of a parametrized nonlinear program. In particular, we derive explicit…
In this paper, we establish an iterative data-driven approach to derive guaranteed bounds on nonlinearity measures of unknown nonlinear systems. In this context, nonlinearity measures quantify the strength of the nonlinearity of a dynamical…
The performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid…
A classic result of Cook et al. (1986) bounds the distances between optimal solutions of mixed-integer linear programs and optimal solutions of the corresponding linear relaxations. Their bound is given in terms of the number of variables…