Related papers: The Maximal Probability that k-wise Independent Bi…
Suppose that we are given an infinite binary sequence which is random for a Bernoulli measure of parameter $p$. By the law of large numbers, the frequency of zeros in the sequence tends to~$p$, and thus we can get better and better…
A nonparametric variant of the Kiefer--Weiss problem is proposed and investigated. In analogy to the classical Kiefer--Weiss problem, the objective is to minimize the maximum expected sample size of a sequential test. However, instead of…
Many AI researchers argue that probability theory is only capable of dealing with uncertainty in situations where a full specification of a joint probability distribution is available, and conclude that it is not suitable for application in…
This paper studies distributed binary test of statistical independence under communication (information bits) constraints. While testing independence is very relevant in various applications, distributed independence test is particularly…
We explore the problem of distributed Hypothesis Testing (DHT) against independence, focusing specifically on Binary Symmetric Sources (BSS). Our investigation aims to characterize the optimal quantizer among binary linear codes, with the…
Independence testing is a fundamental problem in statistical inference: given samples from a joint distribution $p$ over multiple random variables, the goal is to determine whether $p$ is a product distribution or is $\epsilon$-far from all…
Quantum key distribution schemes which employ encoding on vacuum-one-photon qubits are capable of transferring more information bits per particle than the standard schemes employing polarization or phase coding. We calculate the maximum…
Maximum entropy distributions with discrete support in $m$ dimensions arise in machine learning, statistics, information theory, and theoretical computer science. While structural and computational properties of max-entropy distributions…
Given a graph $G$, a probability measure $\mu$ on the subsets of the edge set of $G$ is said to be $1$-independent if events determined by edge sets that are at graph distance at least $1$ apart in $G$ are independent. Call such a…
Inspired by the work of Karamata, we consider an extremization problem associated with the probability of intersecting two random chords inside a circle of radius $r, \, r \in (0,1]$, where the endpoints of the chords are drawn according to…
There is a growing body of work on sorting and selection in models other than the unit-cost comparison model. This work is the first treatment of a natural stochastic variant of the problem where the cost of comparing two elements is a…
Given a budget and arbitrary cost for selecting each node, the budgeted influence maximization (BIM) problem concerns selecting a set of seed nodes to disseminate some information that maximizes the total number of nodes influenced (termed…
We introduce the problem of finding a set $B$ of $k$ points in $[0,1]^n$ such that the expected cost of the cheapest point in $B$ that dominates a random point from $[0,1]^n$ is minimized. We study the case where the coordinates of the…
In this paper, we study the distribution of the minimal distance (in the Hamming metric) of a random linear code of dimension $k$ in $\mathbb{F}_q^n$. We provide quantitative estimates showing that the distribution function of the minimal…
For a graph $G$ and a parameter $k$, we call a vertex $k$-enabling if it belongs both to a clique of size $k$ and to an independent set of size $k$, and we call it $k$-excluding otherwise. Motivated by issues that arise in secret sharing…
Motivated by a greedy approach for generating {\it{information stable}} processes, we prove a universal maximum likelihood (ML) upper bound on the capacities of discrete information stable channels, including the binary erasure channel…
We show that rational data of bounded input length are uniformly distributed with respect to condition numbers of numerical analysis. We deal both with condition numbers of Linear Algebra and with condition numbers for systems of…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…
We show that any distribution on {-1,1}^n that is k-wise independent fools any halfspace h with error \eps for k = O(\log^2(1/\eps) /\eps^2). Up to logarithmic factors, our result matches a lower bound by Benjamini, Gurel-Gurevich, and…
We consider the problem of unambiguous (error-free) discrimination of N linearly independent pure quantum states with prior probabilities, where the goal is to find a measurement that maximizes the average probability of success. We derive…