Related papers: Information metric from Riemannian superspaces
This note reviews a recent contribution about the Fisher information for the space-homogeneous Boltzmann equation by L. Silvestre, C. Villani and the author (arXiv, 2024). This classical functional from information theory is shown to be…
Understanding how well future cosmological experiments can reconstruct the mechanism that generated primordial inhomogeneities is key to assessing the extent to which cosmology can inform fundamental physics. In this work, we apply a…
Information geometry provides a tool to systematically investigate parameter sensitivity of the state of a system. If a physical system is described by a linear combination of eigenstates of a complex (that is, non-Hermitian) Hamiltonian,…
A principled procedure to infer a hierarchy of statistical distributions possessing ill-conditioned eigenstructures, from incomplete constraints, is presented. The inference process of the \textit{pdf}'s employs the Fisher information as…
We discuss different statistical distances in probability space, with emphasis on the Jensen-Shannon divergence, vis-a-vis {\it metrics} in Hilbert space and their relationship with Fisher's information measure. This study provides further…
It is developed a Riemannian reformulation of classical statistical mechanics for systems in thermodynamic equilibrium, which arises as a natural extension of Ruppeiner geometry of thermodynamics. The present proposal leads to interpret…
Many quantum statistical models are most conveniently formulated in terms of non-orthonormal bases. This is the case, for example, when mixtures and superpositions of coherent states are involved. In these instances, we show that the…
Quantum Fisher information plays a central role in the field of quantum metrology. In this paper we study the problem of quantum Fisher information of unitary processes. Associated to each parameter $\theta_i$ of unitary process…
We consider a hybrid bimetric model where, in addition to the ordinary metric tensor that determines geometry, an informational metric is introduced to describe the reference frame of an observer. We note that the local information metric…
In the search of appropriate riemannian metrics on quantum state space the concept of statistical monotonicity, or contraction under coarse graining, has been proposed by Chentsov. The metrics with this property have been classified by…
The problem of estimating a parametric or nonparametric regression function in a model with normal errors is considered. For this purpose, a novel objective prior for the regression function is proposed, defined as the distribution…
The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…
The information-theoretic representation of quantum systems, which complements the familiar energy description of the density-functional and wave-function-based theories, is here discussed. According to it, the internal disorder of the…
This paper studies large-scale optimization problems on Riemannian manifolds whose objective function is a finite sum of negative log-probability losses. Such problems arise in various machine learning and signal processing applications. By…
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…
We show that the metric (line element) is the first geometrical object to be associated to a discrete (quantum) structure of the spacetime without necessity of black hole-entropy-area arguments, in sharp contrast with other attempts in the…
With the help of the coherent states' basis we establish an interesting connection among i) the so-called Wehrl entropy, ii) Fisher's information measure $I$, and iii) the canonical ensemble entropy for the one-dimensional quantum harmonic…
We propose a Bayesian framework of Gaussian process in order to extend Fisher's discriminant to classify functional data such as spectra and images. The probability structure for our extended Fisher's discriminant is explicitly formulated,…
We prove that the (square root) Fisher information functional is a strong Wasserstein upper gradient of the entropy on non-convex Riemannian domains. This fills a gap in the literature by allowing one to completely dispense from…
We prove that for a large class of quantum Fisher information, a quantum channel is sufficient for a family of quantum states, i.e., the input states can be recovered from the output, if and only if the quantum Fisher information is…