Related papers: New Separations Results for External Information
We study belief revision when information is represented by a set of probability distributions, or general information. General information extends the standard event notion while including qualitative information (A is more likely than B),…
In this note we give a new separation between sensitivity and block sensitivity of Boolean functions: $bs(f)=(2/3)s(f)^2-(1/3)s(f)$.
We prove new upper and lower bounds on the sample complexity of $(\epsilon, \delta)$ differentially private algorithms for releasing approximate answers to threshold functions. A threshold function $c_x$ over a totally ordered domain $X$…
We show that the problem of analyzing the outage probability in cellular systems affected by co-channel interference and background noise is mathematically equivalent to the problem of analyzing the wireless information-theoretic security…
The detection of entanglement in a bipartite state is a crucial issue in quantum information science. Based on realignment of density matrices and the vectorization of the reduced density matrices, we introduce a new set of separability…
Information disclosure can compromise privacy when revealed information is correlated with private information. We consider the notion of inferential privacy, which measures privacy leakage by bounding the inferential power a Bayesian…
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is…
Building on previous results of Xing, we give new lower bounds on the rate of intersecting codes over large alphabets. The proof is constructive, and uses algebraic geometry, although nothing beyond the basic theory of linear systems on…
Quantum information decoupling is a fundamental quantum information processing task, which also serves as a crucial tool in a diversity of topics in quantum physics. In this paper, we characterize the reliability function of catalytic…
Bayesian integral functional measure of entropy-uncertainty (EF) on trajectories of Markov multi-dimensional diffusion process is cutting off by interactive impulses (controls). Each cutoff minimax of EF superimposes and entangles…
We reformulate the information causality in a more general framework by adopting the results of signal propagation and computation in a noisy circuit. In our framework, the information causality leads to a broad class of Tsirelson…
We prove a tight lower bound (up to constant factors) on the sample complexity of any non-interactive local differentially private protocol for optimizing a linear function over the simplex. This lower bound also implies a tight lower bound…
A machine that learns a task from observations must encounter and process uncertainty and novelty, especially when it is to maintain performance when observing new information and to select the hypothesis that best fits the current…
Recently, the partial information decomposition emerged as a promising framework for identifying the meaningful components of the information contained in a joint distribution. Its adoption and practical application, however, have been…
In data analysis, unexpected results often prompt researchers to revisit their procedures to identify potential issues. While some researchers may struggle to identify the root causes, experienced researchers can often quickly diagnose…
Given two jointly distributed random variables $(X,Y)$, a functional representation of $X$ is a random variable $Z$ independent of $Y$, and a deterministic function $g(\cdot, \cdot)$ such that $X=g(Y,Z)$. The problem of finding a minimum…
The design of a statistical signal processing privacy problem is studied where the private data is assumed to be observable. In this work, an agent observes useful data $Y$, which is correlated with private data $X$, and wants to disclose…
Motivated by the quest for a broader understanding of communication complexity of simple functions, we introduce the class of "permutation-invariant" functions. A partial function $f:\{0,1\}^n \times \{0,1\}^n\to \{0,1,?\}$ is…
Bayesian inference is often utilized for uncertainty quantification tasks. A recent analysis by Xu and Raginsky 2022 rigorously decomposed the predictive uncertainty in Bayesian inference into two uncertainties, called aleatoric and…
Information-theoretic methods have proven to be a very powerful tool in communication complexity, in particular giving an elegant proof of the linear lower bound for the two-party disjointness function, and tight lower bounds on…