Related papers: The Fisher score on the closed simplex
Probabilistic sensitivity analysis identifies the influential uncertain input to guide decision-making. We propose a general sensitivity framework with respect to the input distribution parameters that unifies a wide range of sensitivity…
In this paper I discuss the relation between the concept of the Fisher metric and the concept of differentiability of a family of probability measures. I compare the concepts of smooth statistical manifolds, differentiable families of…
Fisher score is one of the most widely used supervised feature selection methods. However, it selects each feature independently according to their scores under the Fisher criterion, which leads to a suboptimal subset of features. In this…
This paper introduces a comprehensive framework to adjust a discrete test statistic for improving its hypothesis testing procedure. The adjustment minimizes the Wasserstein distance to a null-approximating continuous distribution, tackling…
We consider the processing of statistical samples $X\sim P_\theta$ by a channel $p(y|x)$, and characterize how the statistical information from the samples for estimating the parameter $\theta\in\mathbb{R}^d$ can scale with the mutual…
Relative Fisher information, also known as score matching, is a recently introduced learning method for parameter estimation. Fundamental relations between relative entropy and score matching have been established in the literature for…
In high-dimensional learning, models remain stable until they collapse abruptly once the sample size falls below a critical level. This instability is not algorithm-specific but a geometric mechanism: when the weakest Fisher eigendirection…
Uncertain input of a mathematical model induces uncertainties in the output and probabilistic sensitivity analysis identifies the influential inputs to guide decision-making. Of practical concern is the probability that the output would, or…
This paper provides a systematic approach to semiparametric identification that is based on statistical information as a measure of its "quality". Identification can be regular or irregular, depending on whether the Fisher information for…
We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…
We develop a unified nonparametric framework for sharp partial identification and inference on inequality indices when the data contain coarsened observations of the variable of interest. We characterize the extremal allocations for all…
A principled procedure to infer a hierarchy of statistical distributions possessing ill-conditioned eigenstructures, from incomplete constraints, is presented. The inference process of the \textit{pdf}'s employs the Fisher information as…
The mean of an unknown variance-$\sigma^2$ distribution $f$ can be estimated from $n$ samples with variance $\frac{\sigma^2}{n}$ and nearly corresponding subgaussian rate. When $f$ is known up to translation, this can be improved…
This note extends the results of classical parametric statistics like Fisher and Wilks theorem to modern setups with a high or infinite parameter dimension, limited sample size, and possible model misspecification. We consider a special…
We define a mixed topology on the fiber space $\cup_\mu \oplus^n L^n(\mu)$ over the space $\mathcal{M}(\Omega)$ of all finite non-negative measures $\mu$ on a separable metric space $\Omega$ provided with Borel $\sigma$-algebra. We define a…
This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…
Fisherian randomization inference is often dismissed as testing an uninteresting and implausible hypothesis: the sharp null of no effects whatsoever. We show that this view is overly narrow. Many randomization tests are also valid under a…
We introduce new classes of informational functionals, called \emph{upper moments}, respectively \emph{down-Fisher measures}, obtained by applying classical functionals such as $p$-moments and the Fisher information to the recently…
The Fisher metric on a manifold of probability distributions is usually treated as a metric on the tangent bundle. In this paper, we focus on the metric on the cotangent bundle induced from the Fisher metric with calling it the Fisher…
Fisher's Method of Maximum Likelihood is shown to be a procedure for the construction of likelihood intervals or regions, instead of a procedure of point estimation. Based on Fisher's articles and books it is justified that by estimation…