相关论文: Fisher Information in Group-Type Models
Skewed distributions are fundamental in modelling asymmetric data on the d-dimensional torus. In this context, asymmetry is introduced through the sine-skewing mechanism, which is the only skewing mechanism that has been proposed on the…
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…
We present a thermodynamic formulation for scale-invariant systems based on the minimization with constraints of Fisher's information measure. In such a way a clear analogy between these systems's thermal properties and those of gases and…
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 discuss species distribution models (SDM) for biodiversity studies in ecology. SDM plays an important role to estimate abundance of a species based on environmental variables that are closely related with the habitat of the species. The…
Following the recent ideas of Guillen and Silvestre in $[9]$, we prove that the Fisher information is non-increasing along the flow of the isotropic Landau equation. We then use this fact to deduce global existence for the equation…
We address the fundamental limits of learning unknown parameters of any stochastic process from time-series data, and discover exact closed-form expressions for how optimal inference scales with observation length. Given a parametrized…
Generative models that maximize model likelihood have gained traction in many practical settings. Among them, perturbation based approaches underpin many strong likelihood estimation models, yet they often face slow convergence and limited…
This paper demonstrates the robustness of Lipschitz-regularized $\alpha$-divergences as objective functionals in generative modeling, showing they enable stable learning across a wide range of target distributions with minimal assumptions.…
The Fisher information matrix (FIM) is a fundamental quantity to represent the characteristics of a stochastic model, including deep neural networks (DNNs). The present study reveals novel statistics of FIM that are universal among a wide…
It is shown that the diffusion equation and its adjoint (time reversed) equation can be derived with only a few assumptions, using an information-theoretic approach based on the principle of minimum Fisher information
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…
This paper is a strongly geometrical approach to the Fisher distance, which is a measure of dissimilarity between two probability distribution functions. The Fisher distance, as well as other divergence measures, are also used in many…
Logistic regression models with $n$ observations and $q$ linearly-independent covariates are shown to have Fisher information volumes which are bounded below by $\pi^q$ and above by ${n \choose q} \pi^q$. This is proved with a novel…
We show that using the most parsimonious version of Frieden and Soffer's extreme information principle (EPI) with a Fisher measure constructed with escort probabilities, the concomitant solutions obey a type of Naudts' duality for…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
We prove that two well-known measures of information are interrelated in interesting and useful ways when applied to nonequilibrium circumstances. A nontrivial form of the lower bound for the Fisher information measure is derived in…
Variational Inference is a powerful tool in the Bayesian modeling toolkit, however, its effectiveness is determined by the expressivity of the utilized variational distributions in terms of their ability to match the true posterior…
This article discusses the problem of estimation of parameters in finite mixtures when the mixture components are assumed to be symmetric and to come from the same location family. We refer to these mixtures as semi-parametric because no…
A common approach to analyzing categorical correlated time series data is to fit a generalized linear model (GLM) with past data as covariate inputs. There remain challenges to conducting inference for short time series length. By treating…