Related papers: Generalised Fisher Matrices
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
Assuming a Euclid-like weak lensing data set, we compare different methods of dealing with its inherent parameter degeneracies. Including priors into a data analysis can mask the information content of a given data set alone. However, since…
Fine-tuning and naturalness, the sensitivity of low-energy observables to small changes in the fundamental parameters of a theory, are cornerstones of physics beyond the Standard Model. We propose a new measure of fine-tuning based on…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
Bayesian inference has many advantages for complex models, but standard Monte Carlo methods for summarizing the posterior can be computationally demanding, and it is attractive to consider optimization-based variational methods. Our work…
In this work, we show that the sample complexity required in quantum learning theory within a general parametric framework, is fundamentally governed by the inverse Fisher information matrix. More specifically, we derive upper and lower…
Given a set of measurements, observability characterizes the distinguishability of a system's initial state, whereas constructability focuses on the final state in a trajectory. In the presence of process and/or measurement noise, the…
The Quantum Fisher Information (QFI) is a geometric measure of state deformation calculated along the trajectory parameterizing an ensemble of quantum states. It serves as a key concept in quantum metrology, where it is linked to the…
Learning robust models that generalize well under changes in the data distribution is critical for real-world applications. To this end, there has been a growing surge of interest to learn simultaneously from multiple training domains -…
In many practical situations we would like to estimate the covariance matrix of a set of variables from an insufficient amount of data. More specifically, if we have a set of $N$ independent, identically distributed measurements of an $M$…
Starting from the Fisher matrix for counts in cells, I derive the full Fisher matrix for surveys of multiple tracers of large-scale structure. The key assumption is that the inverse of the covariance of the galaxy counts is given by the…
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…
When training data are fragmented across batches or federated-learned across different geographic locations, trained models manifest performance degradation. That degradation partly owes to covariate shift induced by data having been…
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…
The formalism of quantum estimation theory with a specific focus on classical data postprocessing is applied to a two-level system driven by an external gyrating magnetic field. We employed both Bayesian and frequentist approaches to…
Skew-symmetric densities recently received much attention in the literature, giving rise to increasingly general families of univariate and multivariate skewed densities. Most of those families, however, suffer from the inferential drawback…
Learning machines which have hierarchical structures or hidden variables are singular statistical models because they are nonidentifiable and their Fisher information matrices are singular. In singular statistical models, neither the Bayes…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
Combining dependent tests of significance has broad applications but the $p$-value calculation is challenging. Current moment-matching methods (e.g., Brown's approximation) for Fisher's combination test tend to significantly inflate the…
A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution. Markov Chain Monte Carlo is a fundamental tool to consistently compute these expectations via averaging samples drawn…