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Some situations are discussed where subquantum oscillations in momentum arise in connectiion with Fisher information and the quantum potential.

Mathematical Physics · Physics 2008-07-28 Robert Carroll

This paper introduces a novel information-theoretic perspective on the relationship between prominent group fairness notions in machine learning, namely statistical parity, equalized odds, and predictive parity. It is well known that…

Information Theory · Computer Science 2024-10-25 Faisal Hamman , Sanghamitra Dutta

Certain new inequalities for the sums of factorials are presented.

General Mathematics · Mathematics 2008-06-03 Mihaly Bencze , Florentin Smarandache

The Fisher information matrix can be used to characterize the local geometry of the parameter space of neural networks. It elucidates insightful theories and useful tools to understand and optimize neural networks. Given its high…

Machine Learning · Computer Science 2024-10-31 Alexander Soen , Ke Sun

In this note, we give a simple, counting based proof of Fisher's Inequality that does not use any tools from linear algebra.

Combinatorics · Mathematics 2020-06-05 Rogers Mathew , Tapas Kumar Mishra

Forecasting techniques for assessing the power of future experiments to discriminate between theories or discover new laws of nature are of great interest in many areas of science. In this paper, we introduce a Bayesian forecasting method…

Data Analysis, Statistics and Probability · Physics 2024-09-24 Mohammad Hossein Namjoo

In future gravitational-wave (GW) detections, a large number of overlapping GW signals will appear in the data stream of detectors. When extracting information from one signal, the presence of other signals can cause large parameter…

Instrumentation and Methods for Astrophysics · Physics 2024-02-07 Ziming Wang , Dicong Liang , Junjie Zhao , Chang Liu , Lijing Shao

In many applications, it is important to be able to explain the decisions of machine learning systems. An increasingly popular approach has been to seek to provide \emph{counterfactual instance explanations}. These specify close possible…

Artificial Intelligence · Computer Science 2021-09-22 Adam White , Artur d'Avila Garcez

Many statistical models require an estimation of unknown (co)-variance parameter(s) in a model. The estimation usually obtained by maximizing a log-likelihood which involves log determinant terms. In principle, one requires the…

Computation · Statistics 2016-09-05 Shengxin Zhu , Tongxiang Gu , Xiaowen Xu , Zeyao Mo

The estimation of continuous parameters from measured data plays a central role in many fields of physics. A key tool in understanding and improving such estimation processes is the concept of Fisher information, which quantifies how…

We provide a new perspective on Stein's so-called density approach by introducing a new operator and characterizing class which are valid for a much wider family of probability distributions on the real line. We prove an elementary…

Probability · Mathematics 2013-04-05 Christophe Ley , Yvik Swan

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…

The Bayesian decision-theoretic approach to design of experiments involves specifying a design (values of all controllable variables) to maximise the expected utility function (expectation with respect to the distribution of responses and…

Statistics Theory · Mathematics 2021-09-24 Antony M. Overstall

The optimal quantum measurements for estimating individual parameters might be incompatible with each other so that they cannot be jointly performed. The tradeoff between the estimation precision for different parameters can be…

Quantum Physics · Physics 2022-06-13 Jingjing Shao , Xiao-Ming Lu

Most information dynamics and statistical causal analysis frameworks rely on the common intuition that causal interactions are intrinsically pairwise -- every 'cause' variable has an associated 'effect' variable, so that a 'causal arrow'…

Neurons and Cognition · Quantitative Biology 2019-09-06 Pedro A. M. Mediano , Fernando Rosas , Robin L. Carhart-Harris , Anil K. Seth , Adam B. Barrett

We study the existence of the maximal quantum Fisher information matrix in multi-parameter quantum estimation, which bounds the ultimate precision limit. We show that when the maximal quantum Fisher information matrix exists, it can be…

Quantum Physics · Physics 2017-08-02 Yu Chen , Haidong Yuan

We study the evolution of the nonlinear version of the Fisher information along the quasilinear heat equation. We also provide a nonlinear version of a recent functional inequality (Cie\'slak--Fuest--Hajduk--Sier\.z\k{e}ga, 2024),…

Analysis of PDEs · Mathematics 2025-09-03 Tomasz Cieślak , Kentaro Fujie , Tatsuya Hosono

Quantum data processing inequality bounds the set of bipartite states that can be generated by two far apart parties under local operations; Having access to a bipartite state as a resource, two parties cannot locally transform it to…

Quantum Physics · Physics 2023-03-14 Salman Beigi

The quantum Fisher information (FI), when applied to the estimation of the separation of two point sources, has been shown to be non-zero in cases where the coherence between the sources are known. Although it has been claimed that…

Optics · Physics 2020-12-16 Kevin Liang , S. A. Wadood , A. N. Vamivakas

Many imaging systems are used to estimate a vector of parameters associated with the object being imaged. In many cases there are other parameters in the model for the imaging data that are not of interest for the task at hand. We refer to…

Information Theory · Computer Science 2019-02-14 Eric Clarkson