Related papers: Mutual Information Bounded by Fisher Information
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…
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…
Alternative proofs for the superadditivity and the affinity (in the large system limit) of the usual and some fractional Fisher informations of a probability density of many variables are provided. They are consequences of the fact that…
The problem of determining the intrinsic quality of a signal processing system with respect to the inference of an unknown deterministic parameter $\theta$ is considered. While the Fisher information measure $F(\theta)$ forms a classical…
We establish lower bounds on the volume and the surface area of a geometric body using the size of its slices along different directions. In the first part of the paper, we derive volume bounds for convex bodies using generalized…
The Fisher information matrix is a quantity of fundamental importance for information geometry and asymptotic statistics. In practice, it is widely used to quickly estimate the expected information available in a data set and guide…
Quantum Fisher information, as an intrinsic quantity for quantum states, is a central concept in quantum detection and estimation. When quantum measurements are performed on quantum states, classical probability distributions arise, which…
We prove two lower bounds for the complexity of non-log-concave sampling within the framework of Balasubramanian et al. (2022), who introduced the use of Fisher information (FI) bounds as a notion of approximate first-order stationarity in…
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…
In this paper the relation between quantum covariances and quantum Fisher informations are studied. This study is applied to generalize a recently proved uncertainty relation based on quantum Fisher information. The proof given…
We investigate measurements of bipartite ensembles restricted to local operations and classical communication and find a universal Holevo-like upper bound on the locally accessible information. We analyze our bound and exhibit a class of…
We provide a mutual information lower bound that can be used to analyze the effect of training in models with unknown parameters. For large-scale systems, we show that this bound can be calculated using the difference between two…
Privacy is under threat from artificial intelligence revolution fueled by unprecedented abundance of data. Differential privacy, an established candidate for privacy protection, is susceptible to adversarial attacks, acts conservatively,…
An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is…
In this contribution, quantum Fisher information is utilized to estimate the parameters of a central qubit interacting with a single-spin qubit. The effect of the longitudinal, transverse and the rotating strengths of the magnetic field on…
Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of…
In this paper a numerical method is presented, which finds a lower bound for the mutual information between a binary and an arbitrary finite random variable with joint distributions that have a variational distance not greater than a known…
We examine important properties of the difference between the variance and the quantum Fisher information over four, i.e., $(\Delta A)^2-F_{\rm Q}[\varrho,A]/4.$ We find that it is equal to a generalized variance defined in Petz [J. Phys. A…
We employ a unified framework for computing the information capacity of biological signaling systems using Fisher Information. By deriving closed-form or easily computable information capacity formulas, we quantify how well different…
We present a numerical method to evaluate mutual information (MI) in nonlinear Gaussian noise channels by using denoising score matching (DSM) learning for estimating the score function of channel output. Via de Bruijn's identity, Fisher…