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For a known weak signal in additive white noise, the asymptotic performance of a locally optimum processor (LOP) is shown to be given by the Fisher information (FI) of a standardized even probability density function (PDF) of noise in three…

Data Analysis, Statistics and Probability · Physics 2011-11-28 Fabing Duan , Francois Chapeau-Blondeau , Derek Abbott

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…

Probability · Mathematics 2024-09-23 Nguyen Tien Dung

We prove two lower bounds for the complexity of non-log-concave sampling within the framework of Balasubramanian et al. (2022), who introduced the use of Fisher information (FI) bounds as a notion of approximate first-order stationarity in…

Machine Learning · Statistics 2022-10-07 Sinho Chewi , Patrik Gerber , Holden Lee , Chen Lu

We propose the generalised Fisher information or the one-parameter extended class of the Fisher information for the case of one random variable. This new form of the Fisher information is obtained from the intriguing connection between the…

Statistics Theory · Mathematics 2022-08-25 Worachet Bukaew , Sikarin Yoo-Kong

We give conditions for an O(1/n) rate of convergence of Fisher information and relative entropy in the Central Limit Theorem. We use the theory of projections in L2 spaces and Poincare inequalities, to provide a better understanding of the…

Statistics Theory · Mathematics 2007-06-13 Oliver Johnson , Andrew Barron

Training-free conditional diffusion models have received great attention in conditional image generation tasks. However, they require a computationally expensive conditional score estimator to let the intermediate results of each step in…

Computer Vision and Pattern Recognition · Computer Science 2024-11-13 Kaiyu Song , Hanjiang Lai

We develop data processing inequalities that describe how Fisher information from statistical samples can scale with the privacy parameter $\varepsilon$ under local differential privacy constraints. These bounds are valid under general…

Information Theory · Computer Science 2020-05-22 Leighton Pate Barnes , Wei-Ning Chen , Ayfer Ozgur

The concept of Fisher information can be useful even in cases where the probability distributions of interest are not absolutely continuous with respect to the natural reference measure on the underlying space. Practical examples where this…

Statistics Theory · Mathematics 2018-03-28 Jeremie Houssineau , Ajay Jasra , Sumeetpal S. Singh

This paper studies the asymptotic behavior of the Fisher information for a Levy process discretely sampled at an increasing frequency. We show that it is possible to distinguish not only the continuous part of the process from its jumps…

Probability · Mathematics 2007-05-23 Yacine Ait-Sahalia , Jean Jacod

The basic properties of the Fisher information allow to reveal the statistical meaning of classical inequalities between mean functions. The properties applied to scale mixtures of Gaussian distributions lead to a new mean function of…

Statistics Theory · Mathematics 2019-04-09 Abram M. Kagan , Paul J. Smith

Expected Fisher information can be found a priori and as a result its inverse is the primary variance approximation used in the design of experiments. This is in contrast to the common claim that the inverse of observed Fisher information…

Methodology · Statistics 2022-08-04 Adam Lane

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…

Data Analysis, Statistics and Probability · Physics 2013-10-08 E. W. Piotrowski , J. Sladkowski , J. Syska , S. Zajac

Recently proposed methods in data subset selection, that is active learning and active sampling, use Fisher information, Hessians, similarity matrices based on gradients, and gradient lengths to estimate how informative data is for a…

Machine Learning · Computer Science 2022-11-08 Andreas Kirsch , Yarin Gal

This paper deals with Cram\'er-Rao inequalities in the context of nonextensive statistics and in estimation theory. It gives characterizations of generalized q-Gaussian distributions, and introduces generalized versions of Fisher…

Mathematical Physics · Physics 2012-06-05 J. -F. Bercher

We study fairness in collaborative-filtering recommender systems, which are sensitive to discrimination that exists in historical data. Biased data can lead collaborative-filtering methods to make unfair predictions for users from minority…

Information Retrieval · Computer Science 2017-12-04 Sirui Yao , Bert Huang

In 2003 Luo proved an inequality relating the Wigner-Yanase information and the $SLD$-information. In this paper we prove that Luo's inequality is a particular case of a general inequality which holds for any regular quantum Fisher…

Mathematical Physics · Physics 2011-11-10 Paolo Gibilisco , Daniele Imparato , Tommaso Isola

Quantum mechanics gives a new breakthrough to the field of parameter estimation. In the realm of quantum metrology, the precision of parameter estimation is limited by the quantum Fisher information. We introduce the measures of partial…

Quantum Physics · Physics 2024-11-14 Dong-Ping Xuan , Zhong-Xi Shen , Wen Zhou , Hua Nan , Shao-Ming Fei , Zhi-Xi Wang

Fair and trustworthy AI is becoming ever more important in both machine learning and legal domains. One important consequence is that decision makers must seek to guarantee a 'fair', i.e., non-discriminatory, algorithmic decision procedure.…

Computers and Society · Computer Science 2024-12-23 Meike Zehlike , Alex Loosley , Håkan Jonsson , Emil Wiedemann , Philipp Hacker

We introduce Fisher consistency in the sense of unbiasedness as a desirable property for estimators of class prior probabilities. Lack of Fisher consistency could be used as a criterion to dismiss estimators that are unlikely to deliver…

Machine Learning · Statistics 2019-07-23 Dirk Tasche

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…

Data Analysis, Statistics and Probability · Physics 2009-03-22 S. Prasad , N. C. Menicucci