Related papers: Fisher information lower bounds for sampling
The Fisher Information Matrix formalism is extended to cases where the data is divided into two parts (X,Y), where the expectation value of Y depends on X according to some theoretical model, and X and Y both have errors with arbitrary…
The quantum Fisher information (QFI) represents a fundamental concept in quantum physics. On the one hand, it quantifies the metrological potential of quantum states in quantum-parameter-estimation measurements. On the other hand, it is…
In this paper, we study the lower iteration complexity bounds for finding the saddle point of a strongly convex and strongly concave saddle point problem: $\min_x\max_yF(x,y)$. We restrict the classes of algorithms in our investigation to…
We address the "major open problem" of evaluating how much increased efficiency in estimation is possible using non-separable, as opposed to separable, measurements of N copies of m-level quantum systems. First, we study the six cases m =…
Fisher's criterion is a widely used tool in machine learning for feature selection. For large search spaces, Fisher's criterion can provide a scalable solution to select features. A challenging limitation of Fisher's criterion, however, is…
Estimating the quantum Fisher information (QFI) is a crucial yet challenging task with widespread applications across quantum science and technologies. The recently proposed Krylov shadow tomography (KST) opens a new avenue for this task by…
The subjects of the paper are the likelihood method (LM) and the expected Fisher information (FI) considered from the point od view of the construction of the physical models which originate in the statistical description of phenomena. The…
We revisit the problem of computing submatrices of the Cram\'er-Rao bound (CRB), which lower bounds the variance of any unbiased estimator of a vector parameter $\vth$. We explore iterative methods that avoid direct inversion of the Fisher…
Inference from limited data requires a notion of measure on parameter space, most explicit in the Bayesian framework as a prior. Here we demonstrate that Jeffreys prior, the best-known uninformative choice, introduces enormous bias when…
In the estimation for a parametric family of quantum state on a Hilbert space $\mathcal{H}$, the Gill and Massar bound is known as a lower bound of weighted traces of covariances of unbiased estimators. The Gill and Massar bound is derived…
Multiple players are each given one independent sample, about which they can only provide limited information to a central referee. Each player is allowed to describe its observed sample to the referee using a channel from a family of…
Maximum likelihood estimation is a popular method in statistical inference. As a way of assessing the accuracy of the maximum likelihood estimate (MLE), the calculation of the covariance matrix of the MLE is of great interest in practice.…
We propose and analyze several inexact regularized Newton-type methods for finding a global saddle point of convex-concave unconstrained min-max optimization problems. Compared to first-order methods, our understanding of second-order…
Computational capability often falls short when confronted with massive data, posing a common challenge in establishing a statistical model or statistical inference method dealing with big data. While subsampling techniques have been…
Fisher information and Shannon entropy are fundamental tools for understanding and analyzing dynamical systems from complementary perspectives. They can characterize unknown parameters by quantifying the information contained in variables,…
We study the problem of learning nonparametric distributions in a finite mixture, and establish tight bounds on the sample complexity for learning the component distributions in such models. Namely, we are given i.i.d. samples from a pdf…
This paper proposes a new framework for the optimization of excitation inputs for system identification. The optimization problem considered is to maximize a reduced Fisher information matrix in any of the classical D-, E-, or A-optimal…
Population risk is always of primary interest in machine learning; however, learning algorithms only have access to the empirical risk. Even for applications with nonconvex nonsmooth losses (such as modern deep networks), the population…
We consider the free non-commutative analogue Phi^*, introduced by D. Voiculescu, of the concept of Fisher information for random variables. We determine the minimal possible value of Phi^*(a,a^*), if a is a non-commutative random variable…
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…