Related papers: Reweighted information inequalities
For a complete connected Riemannian manifold $M$ let $V\in C^2(M)$ be such that $\mu(d x)={\rm e}^{-V(x)} \mbox{vol}(d x)$ is a probability measure on $M$. Taking $\mu$ as reference measure, we derive inequalities for probability measures…
We prove that two well-known measures of information are interrelated in interesting and useful ways when applied to nonequilibrium circumstances. A nontrivial form of the lower bound for the Fisher information measure is derived in…
Relative to the Gaussian measure on $\mathbb{R}^d$, entropy and Fisher information are famously related via Gross' logarithmic Sobolev inequality (LSI). These same functionals also separately satisfy convolution inequalities, as proved by…
In this paper, we review Fisher information matrices properties in weighted version and discuss inequalities/bounds on it by using reduced weight functions. In particular, an extended form of the Fisher information inequality previously…
We prove upper bounds on the $L^\infty$-Wasserstein distance from optimal transport between strongly log-concave probability densities and log-Lipschitz perturbations. In the simplest setting, such a bound amounts to a transport-information…
We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…
We develop the optimal transportation approach to modified log-Sobolev inequalities and to isoperimetric inequalities. Various sufficient conditions for such inequalities are given. Some of them are new even in the classical log-Sobolev…
We study the mixing time guarantee for sampling in relative Fisher information via the Proximal Sampler algorithm, which is an approximate proximal discretization of the Langevin dynamics. We show that when the target probability…
We provide a Lyapunov convergence analysis for time-inhomogeneous variable coefficient stochastic differential equations (SDEs). Three typical examples include overdamped, irreversible drift, and underdamped Langevin dynamics. We first…
Quantum Markov semigroups characterize the time evolution of an important class of open quantum systems. Studying convergence properties of such a semigroup, and determining concentration properties of its invariant state, have been the…
Morozova and Chentsov (Morozova and Chentsov 90) studied Riemannian metrics on the set of probability measures. They showed that, up to a constant factor, the Fisher information is the only Riemannian metric which is monotone under…
One way to define the concentration of measure phenomenon is via Talagrand inequalities, also called transportation-information inequalities. That is, a comparison of the Wasserstein distance from the given measure to any other absolutely…
Uncertain input of a mathematical model induces uncertainties in the output and probabilistic sensitivity analysis identifies the influential inputs to guide decision-making. Of practical concern is the probability that the output would, or…
This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of…
An important theme in recent work in asymptotic geometric analysis is that many classical implications between different types of geometric or functional inequalities can be reversed in the presence of convexity assumptions. In this note,…
We study the query complexity of obtaining a relative Fisher information guarantee for sampling from a log-smooth non-log-concave distribution; this is a sampling analog of finding an approximate stationary point in optimization. Our…
We prove that the reciprocal of Fisher information of a log-concave probability density $X$ in ${\bf{R}}^n$ is concave in $t$ with respect to the addition of a Gaussian noise $Z_t = N(0, tI_n)$. As a byproduct of this result we show that…
We introduce the notion of an interpolating path on the set of probability measures on finite graphs. Using this notion, we first prove a displacement convexity property of entropy along such a path and derive Prekopa-Leindler type…
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…
We show that an information theoretic distance measured by the relative Fisher information between canonical equilibrium phase densities corresponding to forward and backward processes is intimately related to the gradient of the dissipated…