Related papers: Pearson information-based lower bound on Fisher in…

Optimal input design is an important step of the identification process in order to reduce the model variance. In this work a D-optimal input design method for finite-impulse-response-type nonlinear systems is presented. The optimization of…

We establish an expansion by Gamma-convergence of the Fisher information relative to the reference measure exp(-beta V), where V is a generic multiwell potential and beta goes to infinity. The expansion reveals a hierarchy of multiple…

We introduce the Fisher information in the basis of decay modes of Markovian dynamics, arguing that it encodes important information about the behavior of nonequilibrium systems. In particular we generalize an orthonormality relation…

For statistical inference on regression models with a diverging number of covariates, the existing literature typically makes sparsity assumptions on the inverse of the Fisher information matrix. Such assumptions, however, are often…

Super-resolution estimation is the problem of recovering a stream of spikes (point sources) from the noisy observation of a few numbers of its first trigonometric moments. The performance of super-resolution is recognized to be intimately…

Quantum Fisher information and signal-to-noise ratio bounds are derived for the estimation of moments of general partially coherent objects. Under an asymptotic analysis in the sub-Rayleigh regime, these bounds are shown to be less…

In some estimation problems, not all the parameters can be identified, which results in singularity of the Fisher Information Matrix (FIM). The Cram\'er-Rao Bound (CRB), which is the inverse of the FIM, is then not defined. To regularize…

We propose a modified $\chi^{\beta}$-divergence, give some of its properties, and show that this leads to the definition of a generalized Fisher information. We give generalized Cram\'er-Rao inequalities, involving this Fisher information,…

We consider torsion in parameter manifolds that arises via conformal transformations of the Fisher information metric, and define it for information geometry of a wide class of physical systems. The torsion can be used to differentiate…

Training large-scale neural networks requires solving nonconvex optimization where the choice of optimizer fundamentally determines both convergence behavior and computational efficiency. While adaptive methods like Adam have long dominated…

Invariant Causal Prediction (Peters et al., 2016) is a technique for out-of-distribution generalization which assumes that some aspects of the data distribution vary across the training set but that the underlying causal mechanisms remain…

We show that the mathematical form of the information measure of Fisher's I for a Gibbs' canonical probability distribution (the most important one in statistical mechanics) incorporates important features of the intrinsic structure of…

Many statistical models require an estimation of unknown (co)-variance parameter(s) in a model. The estimation usually obtained by maximizing a log-likelihood which involves log determinant terms. In principle, one requires the…

Braunstein and Caves (1994) proposed to use Helstrom's {\em quantum information} number to define, meaningfully, a metric on the set of all possible states of a given quantum system. They showed that the quantum information is nothing else…

Many statistical estimands of interest (e.g., in regression or causality) are functions of the joint distribution of multiple random variables. But in some applications, data is not available that measures all random variables on each…

For a given metric $g_{\mu\nu}$, which is identified as Fisher information metric, we generate new constraints for the probability distributions for physical systems. We postulate the existence of intrinsic probability distributions for…

We present a dispersive quantum thermometry protocol for simultaneous estimation of inverse temperature $\beta$ and interaction strength $x$ using a nonlinear Mach-Zehnder interferometer coupled to a thermal ancilla. We derive closed-form…

We derive an information criterion to select a parametric model of complete-data distribution when only incomplete or partially observed data is available. Compared with AIC, our new criterion has an additional penalty term for missing…

A simple method is shown to provide optimal variational bounds on $f$-divergences with possible constraints on relative information extremums. Known results are refined or proved to be optimal as particular cases.

We deal with the maximization of classical Fisher information in a quantum system depending on an unknown parameter. This problem has been raised by physicists, who defined [Helstrom (1967) Phys. Lett. A 25 101-102] a quantum counterpart of…