相关论文: A strengthened data processing inequality for the …
Compressed Counting (CC)} was recently proposed for approximating the $\alpha$th frequency moments of data streams, for $0<\alpha \leq 2$. Under the relaxed strict-Turnstile model, CC dramatically improves the standard algorithm based on…
Current approaches in approximate inference for Bayesian neural networks minimise the Kullback-Leibler divergence to approximate the true posterior over the weights. However, this approximation is without knowledge of the final application,…
We introduce a meta logarithmic-Sobolev (log-Sobolev) inequality for the Lindbladian of all single-mode phase-covariant Gaussian channels of bosonic quantum systems, and prove that this inequality is saturated by thermal states. We show…
We propose an extension of the quantum entropy power inequality for finite dimensional quantum systems, and prove a conditional quantum entropy power inequality by using the majorization relation as well as the concavity of entropic…
We discuss the relationship between entropic Einstein-Podolsky-Rosen (EPR)-steering inequalities and their underlying uncertainty relations, along with the hypothesis that improved uncertainty relations lead to tighter EPR-steering…
We show that for weakly dependent random variables the relative entropy functional satisfies an approximate version of the standard tensorization property which holds in the independent case. As a corollary we obtain a family of…
Our increasingly digital and connected world has led to the generation of unprecedented amounts of data. This data must be efficiently managed, transmitted, and stored to preserve resources and allow scalability. Data compression has…
Based on the problem of quantum data compression in a lossless way, we present here an operational interpretation for the family of quantum R\'enyi entropies. In order to do this, we appeal to a very general quantum encoding scheme that…
This study focuses on a Wasserstein-type gradient flow, which represents an optimization process of a continuous model of a Deep Neural Network (DNN). First, we establish the existence of a minimizer for an average loss of the model under…
The data processing inequality states that the quantum relative entropy between two states $\rho$ and $\sigma$ can never increase by applying the same quantum channel $\mathcal{N}$ to both states. This inequality can be strengthened with a…
We show that Frenkel's integral representation of the quantum relative entropy provides a natural framework to derive continuity bounds for quantum information measures. Our main general result is a dimension-independent semi-continuity…
We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$\epsilon$}-estimation…
We introduce a symmetrization technique that allows us to translate a problem of controlling the deviation of some functionals on a product space from their mean into a problem of controlling the deviation between two independent copies of…
Entropy in nonequilibrium statistical mechanics is investigated theoretically so as to extend the well-established equilibrium framework to open nonequilibrium systems. We first derive a microscopic expression of nonequilibrium entropy for…
This paper is dedicated to providing new tools and methods for studying the trend to equilibrium of gradient flows in metric spaces in the entropy and metric sense, to establish decay rates, finite time of extinction, and to characterize…
The inequality of Vapnik and Chervonenkis controls the expectation of the function by its sample average uniformly over a VC-major class of functions taking into account the size of the expectation. Using Talagrand's kernel method we prove…
The time evolution of complex systems usually can be described through stochastic processes. These processes are measured at finite resolution, what necessarily reduces them to finite sequences of real numbers. In order to relate these data…
We consider properties of quantum channels with use of unified entropies. Extremal unravelings of quantum channel with respect to these entropies are examined. The concept of map entropy is extended in terms of the unified entropies. The…
This paper proposes confidence regions for the identified set in conditional moment inequality models using Kolmogorov-Smirnov statistics with a truncated inverse variance weighting with increasing truncation points. The new weighting…
Bayesian optimal experimental design provides a principled framework for selecting experimental settings that maximize obtained information. In this work, we focus on estimating the expected information gain in the setting where the…