Related papers: Functional Epsilon Entropy
We put forth a new computational notion of entropy, measuring the (in)feasibility of sampling high-entropy strings that are consistent with a given generator. Specifically, the i'th output block of a generator G has accessible entropy at…
We propose a novel technique for constructing a graph representation of a code through which we establish a significant connection between the service rate problem and the well-known fractional matching problem. Using this connection, we…
We establish minimax convergence rates for classification of functional data and for nonparametric regression with functional design variables. The optimal rates are of logarithmic type under smoothness constraints on the functional density…
The paper proposes a new message passing algorithm for cycle-free factor graphs. The proposed "entropy message passing" (EMP) algorithm may be viewed as sum-product message passing over the entropy semiring, which has previously appeared in…
Quantum information processing is in real systems often limited by dissipation, stemming from remaining uncontrolled interaction with microscopic degrees of freedom. Given recent experimental progress, we consider weak dissipation,…
In a dynamic data structure problem we wish to maintain an encoding of some data in memory, in such a way that we may efficiently carry out a sequence of queries and updates to the data. A long-standing open problem in this area is to prove…
Transfer entropy is capable of capturing nonlinear source-destination relations between multi-variate time series. It is a measure of association between source data that are transformed into destination data via a set of linear…
In recent years, bootstrap methods have drawn attention for their ability to approximate the laws of "max statistics" in high-dimensional problems. A leading example of such a statistic is the coordinate-wise maximum of a sample average of…
I will show that there is a deep relation between error-correction codes and certain mathematical models of spin glasses. In particular minimum error probability decoding is equivalent to finding the ground state of the corresponding spin…
An encoder wishes to minimize the bit rate necessary to guarantee that a decoder is able to calculate a symbolwise function of a sequence available only at the encoder and a sequence that can be measured only at the decoder. This classical…
A statistical model for the fragmentation of a conserved quantity is analyzed, using the principle of maximum entropy and the theory of partitions. Upper and lower bounds for the restricted partitioning problem are derived and applied to…
We prove that the electron density function of a real physical system can be uniquely determined by its values on any finite subsystem. This establishes the existence of a rigorous density-functional theory for any open electronic system.…
The information rate-distortion-perception (RDP) function characterizes the three-way trade-off between description rate, average distortion, and perceptual quality measured by discrepancy between probability distributions and has been…
We address the problem of distributed computation of arbitrary functions of two correlated sources $X_1$ and $X_2$, residing in two distributed source nodes, respectively. We exploit the structure of a computation task by coding source…
This paper investigates achievable information rates and error exponents of mismatched decoding when the channel belongs to the class of channels that are close to the decoding metric in terms of relative entropy. For both discrete- and…
The paper introduces the recent results related to an entropy functional on trajectories of a controlled diffusion process, and the information path functional (IPF), analyzing their connections to the Kolmogorov's entropy, complexity and…
We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, for various models of random (multi)graphs. For our proofs we introduce the notion of \emph{patchworks} to describe the possible…
In the \textit{Distributed Storage Systems} (DSSs), an encoded fraction of information is stored in the distributed fashion on different chunk servers. Recently a new paradigm of \textit{Fractional Repetition} (FR) codes have been…
We review and extend recent attempts to find a precise relation between extremal black hole entropy and degeneracy of microstates using AdS_2/CFT_1 correspondence. Our analysis leads to a specific relation between degeneracy of black hole…
We study lossy compression of a finite statement source generated in a fixed deductive environment. The source symbols are statements in a knowledge base endowed with a shared proof system, and reconstruction fidelity is measured by…