Related papers: Thinning and Information Projections
We are interested in a fragmentation process. We observe fragments frozen when their sizes are less than {\epsilon} ({\epsilon} > 0). It is known ([BM05]) that the empirical measure of these fragments converges in law, under some…
Minimizing divergence measures under a constraint is an important problem. We derive a sufficient condition that binary divergence measures provide lower bounds for symmetric divergence measures under a given triangular discrimination or…
This paper presents a stochastic geometry model for the investigation of fundamental information theoretic limitations in wireless networks. We derive a new unified multi-parameter cut-set bound on the capacity of networks of arbitrary…
We study diffusion and consensus dynamics in a Network of Networks model. In this model, there is a collection of sub-networks, connected to one another using a small number of links. We consider a setting where the links between networks…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
Multiple players are each given one independent sample, about which they can only provide limited information to a central referee. Each player is allowed to describe its observed sample to the referee using a channel from a family of…
Subspace clustering becomes inherently difficult near intersections, where points from different subspaces are barely separated. Most existing theoretical results address this issue by imposing separation or sampling assumptions that limit…
We study a local thinning $T_r$ that retains a point with probability $p(n_r)$, where $n_r$ counts neighbors within radius $r$. For Poisson input with spatially varying intensity, we obtain an exact intensity via a Poisson--mixture formula…
We present some new and explicit error bounds for the approximation of distributions. The approximation error is quantified by the maximal density ratio of the distribution $Q$ to be approximated and its proxy $P$. This non-symmetric…
Statistical divergences are important tools in data analysis, information theory, and statistical physics, and there exist well known inequalities on their bounds. However, in many circumstances involving temporal evolution, one needs…
An important notion of common information between two random variables is due to Wyner. In this paper, we derive a lower bound on Wyner's common information for continuous random variables. The new bound improves on the only other general…
The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an…
Benford's law states that many data sets have a bias towards lower leading digits (about $30\%$ are 1s). There are numerous applications, from designing efficient computers to detecting tax, voter and image fraud. It's important to know…
We study the information-theoretic lower bound of the sample complexity of the correct recovery of diffusion network structures. We introduce a discrete-time diffusion model based on the Independent Cascade model for which we obtain a lower…
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…
Given a network of fixed size $n$ and an initial distribution of data, we derive sufficient connectivity conditions on a sequence of time-varying digraphs for (a) data collection and (b) data dissemination, within at most $(n-1)$…
Information and uncertainty are closely related and extensively studied concepts in a number of scientific disciplines such as communication theory, probability theory, and statistics. Increasing the information arguably reduces the…
The most effective differentially private machine learning algorithms in practice rely on an additional source of purportedly public data. This paradigm is most interesting when the two sources combine to be more than the sum of their…
In this article we use rate-distortion theory, a branch of information theory devoted to the problem of lossy compression, to shed light on an important problem in latent variable modeling of data: is there room to improve the model? One…
We study the information leakage to a guessing adversary in index coding with a general message distribution. Under both vanishing-error and zero-error decoding assumptions, we develop lower and upper bounds on the optimal leakage rate,…