相关论文: Support and Quantile Tubes

A simpler approach to the characterization of vanishing conditional mutual information is presented. Some remarks are given as well. More specifically, relating the conditional mutual information to a commutator is a very promising approach…

We calculate the propagator of a particle caught in a Paul trap and subject to the continuous quantum measurement of its position. The probabilities of the measurement outputs, the possible trajectories of the particle, are also found. This…

It is presented a generalization of the von Neumann mutual information in the context of Tsallis' nonextensive statistics. As an example, entanglement between two (two-level) quantum subsystems is discussed. Important changes occur in the…

In statistical inference problems, we wish to obtain lower bounds on the minimax risk, that is to bound the performance of any possible estimator. A standard technique to obtain risk lower bounds involves the use of Fano's inequality. In an…

We highlight the underlying category-theoretic structure of measures of information flow. We present an axiomatic framework in which communication systems are represented as morphisms, and information flow is characterized by its behavior…

We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections, a problem relevant in compressed sensing, sparse superposition codes or code division multiple access just to cite few. There has…

Generalized contextuality is a possible indicator of non-classical behaviour in quantum information theory. In finite-dimensional systems, this is justified by the fact that noncontextual theories can be embedded into some simplex, i.e.…

We review some universal features of the colour flux tube of gauge theories in the confining phase predicted by the infrared conformal limit of the underlying string theory. In particular we discuss shape effects in Wilson loops and…

Conditional copulas are flexible statistical tools that couple joint conditional and marginal conditional distributions. In a linear regression setting with more than one covariate and two dependent outcomes, we propose the use of additive…

We consider a diffusion process under a local weak H\"{o}rmander condition on the coefficients. We find Gaussian estimates for the density in short time and exponential lower and upper bounds for the probability that the diffusion remains…

We study nonparametric estimators of conditional Kendall's tau, a measure of concordance between two random variables given some covariates. We prove non-asymptotic bounds with explicit constants, that hold with high probabilities. We…

Fields like public health, public policy, and social science often want to quantify the degree of dependence between variables whose relationships take on unknown functional forms. Typically, in fact, researchers in these fields are…

We study the problem of communication over a compound quantum channel in the presence of entanglement. Classically such channels are modeled as a collection of conditional probability distributions wherein neither the sender nor the…

The mutual information is bounded from above by a decreasing affine function of the square of the distance between the input distribution and the set of all capacity-achieving input distributions $\Pi_{\mathcal{A}}$, on small enough…

We propose a unified framework for likelihood-based regression modeling when the response variable has finite support. Our work is motivated by the fact that, in practice, observed data are discrete and bounded. The proposed methods assume…

A conjecture of Batyrev and Manin relates arithmetic properties of varieties with ample anticanonical class to geometric invariants; in particular, counting functions defined by metrized ample line bundles and the corresponding asymptotics…

The use of quantiles to obtain insights about multivariate data is addressed. It is argued that incisive insights can be obtained by considering directional quantiles, the quantiles of projections. Directional quantile envelopes are…

Fano's inequality is one of the most elementary, ubiquitous, and important tools in information theory. Using majorization theory, Fano's inequality is generalized to a broad class of information measures, which contains those of Shannon…

We examine the relationship between the mutual information between the output model and the empirical sample and the generalization of the algorithm in the context of stochastic convex optimization. Despite increasing interest in…

The Fano Resonance, involving the mixing between a quasi-bound `discrete' state of an inelastic channel lying in the continuum of scattering states belonging to the elastic channel, has several subtle features. The underlying ideas have…