Related papers: Estimating Fisher Information Matrix in Latent Var…

Gravitational-wave astronomers often wish to characterize the expected parameter-estimation accuracy of future observations. The Fisher matrix provides a lower bound on the spread of the maximum-likelihood estimator across noise…

The Quantum Fisher Information Matrix (QFIM) plays a crucial role in quantum optimization algorithms such as Variational Quantum Imaginary Time Evolution and Quantum Natural Gradient Descent. However, computing the full QFIM incurs a…

Factorized information criterion (FIC) is a recently developed approximation technique for the marginal log-likelihood, which provides an automatic model selection framework for a few latent variable models (LVMs) with tractable inference…

The efficacy of mathematical models heavily depends on the quality of the training data, yet collecting sufficient data is often expensive and challenging. Many modeling applications require inferring parameters only as a means to predict…

We consider the problem of distributed estimation of a Gaussian vector with linear observation model. Each sensor makes a scalar noisy observation of the unknown vector, quantizes its observation, maps it to a digitally modulated symbol,…

Discrete events alter how parameter influence propagates in hybrid systems. Prevailing Fisher information formulations assume that sensitivities evolve smoothly according to continuous-time variational equations and therefore neglect the…

Stochastic gradient descent procedures have gained popularity for parameter estimation from large data sets. However, their statistical properties are not well understood, in theory. And in practice, avoiding numerical instability requires…

The instantaneous relative entropy (IRE) and the corresponding instanta- neous Fisher information matrix (IFIM) for transient stochastic processes are pre- sented in this paper. These novel tools for sensitivity analysis of stochastic…

Model merging has emerged as a practical approach to combine capabilities of specialized large language models (LLMs) without additional training. In the Long-to-Short (L2S) scenario, merging a base model with a long-chain-of-thought…

It is well known that a suggestive relation exists that links Schr\"odinger's equation (SE) to the information-optimizing principle based on Fisher's information measure (FIM). We explore here an approach that will allow one to infer the…

In recent years forecasting activities have become a very important tool for designing and optimising large scale structure surveys. To predict the performance of such surveys, the Fisher matrix formalism is frequently used as a fast and…

We study the problem of likelihood maximization when the likelihood function is intractable but model simulations are readily available. We propose a sequential, gradient-based optimization method that directly models the Fisher score based…

In the context of the usual calibration model, we consider the case in which the independent variable is unobservable, but a pre-fixed value on its surrogate is available. Thus, considering controlled variables and assuming that the…

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…

We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct completely new representations for the score function. We then use these representations to derive…

The problem of determining the intrinsic quality of a signal processing system with respect to the inference of an unknown deterministic parameter $\theta$ is considered. While the Fisher information measure $F(\theta)$ forms a classical…

Fisher information is a measure of the best precision with which a parameter can be estimated from statistical data. It can also be defined for a continuous random variable without reference to any parameters, in which case it has a…

Ionides, King et al. (see e.g. Inference for nonlinear dynamical systems, PNAS 103) have recently introduced an original approach to perform maximum likelihood parameter estimation in state-space models which only requires being able to…

In many statistical applications that concern mathematical psychologists, the concept of Fisher information plays an important role. In this tutorial we clarify the concept of Fisher information as it manifests itself across three different…

We review the introduction of likelihood functions and Fisher information in classical estimation theory, and we show how they can be defined in a very similar manner within quantum measurement theory. We show that the stochastic master…