相关论文: Metric and probabilistic information associated wi…

This short note revisit information metric, underlining that it is a pseudo metric on manifolds of observables (random variables), rather than as usual on probability laws. Geodesics are characterized in terms of their boundaries and…

The amount of information available in spectro-polarimetric data is estimated. To this end, the intrinsic dimensionality of the data is inferred with the aid of a recently derived estimator based on nearest-neighbor considerations and…

Seismic networks provide data that are used as basis both for public safety decisions and for scientific research. Their configuration affects the data completeness, which in turn, critically affects several seismological scientific targets…

In this paper, we study the classification problem by estimating the conditional probability function of the given data. Different from the traditional expected risk estimation theory on empirical data, we calculate the probability via…

Estimating mutual information from observed samples is a basic primitive, useful in several machine learning tasks including correlation mining, information bottleneck clustering, learning a Chow-Liu tree, and conditional independence…

Mutual information is fundamentally important for measuring statistical dependence between variables and for quantifying information transfer by signaling and communication mechanisms. It can, however, be challenging to evaluate for…

Entropy and information can be considered dual: entropy is a measure of the subspace defined by the information constraining the given ambient space. Negative entropies, arising in na\"ive extensions of the definition of entropy from…

We address the practical problems of estimating the information relations that characterize large networks. Building on methods developed for analysis of the neural code, we show that reliable estimates of mutual information can be obtained…

These lectures present a survey of recent developments in the area of random matrices (finite and infinite) and random permutations. These probabilistic problems suggest matrix integrals (or Fredholm determinants), which arise very…

The information provided by a classical measurement is unambiguously determined by the mutual information between the output results and the measured quantity. However, quantum mechanically there are at least two notions of information…

We study compactness and the Fredholm property for linear operators on coorbit spaces over locally compact abelian phase spaces. In contrast to previous works, we do not impose any countability assumptions on the underlying groups. Our…

Information based thermodynamic logic is revisited. It consists of two parts: Part A applies the modern theory of probability in which an arbitrary convex function \phi is employed as an analytic "device" to express information as…

In this note known formulas for the product of Toeplitz operators are revisited in the context of their applications to the study of Fredholmness, boundedness of Toeplitz products, and the Berezin-Toeplitz quantization. A few open problems…

Additive measures for information and disturbance in quantum measurements of a system are defined from well-known multiplicative measures such as estimation and operation fidelities using a logarithm. This is motivated by the fact that…

Notwithstanding various attempts to construct a Partial Information Decomposition (PID) for multiple variables by defining synergistic, redundant, and unique information, there is no consensus on how one ought to precisely define either of…

Traditional channel capacity based on the discrete spatial dimensions mismatches the continuous electromagnetic fields. For the wireless communication system in a limited region, the spatial discretization may results in information loss…

The conditional mutual information I(X;Y|Z) measures the average information that X and Y contain about each other given Z. This is an important primitive in many learning problems including conditional independence testing, graphical model…

We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…

J. Hadamard's ideas of correct formulation of problems of mathematical physics as well as related Banach's theorem on the inverse operator are analyzed. Modern techniques of numerical simulations are shown to be in drastic contradiction to…

Fredholm integral operators that commute with the Hamiltonians of certain quantum mechanical problems with quartic potentials are introduced. The operators are expressed in terms of an Airy function, and their eigenvalues fall off…