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Related papers: Mutual Information Bounded by Fisher Information

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The Quantum Fisher Information (QFI) plays a crucial role in quantum information theory and in many practical applications such as quantum metrology. However, computing the QFI is generally a computationally demanding task. In this work we…

Quantum Physics · Physics 2021-06-25 M. Cerezo , Akira Sone , Jacob L. Beckey , Patrick J. Coles

Estimating mutual information (MI) is a fundamental yet challenging task in data science and machine learning. This work proposes a new estimator for mutual information. Our main discovery is that a preliminary estimate of the data…

Machine Learning · Computer Science 2024-08-20 Yanzhi Chen , Zijing Ou , Adrian Weller , Yingzhen Li

This paper provides a general technique for lower bounding the Bayes risk of statistical estimation, applicable to arbitrary loss functions and arbitrary prior distributions. A lower bound on the Bayes risk not only serves as a lower bound…

Statistics Theory · Mathematics 2016-12-26 Xi Chen , Adityanand Guntuboyina , Yuchen Zhang

In this paper, a uniform (over some parameter space) moment bound for the inverse of Fisher's information matrix is established. This result is then applied to develop moment bounds for the normalized least squares estimate in (nonlinear)…

Statistics Theory · Mathematics 2012-11-22 Ngai Hang Chan , Ching-Kang Ing

Mutual information has been successfully adopted in filter feature-selection methods to assess both the relevancy of a subset of features in predicting the target variable and the redundancy with respect to other variables. However,…

Machine Learning · Computer Science 2019-07-18 Mario Beraha , Alberto Maria Metelli , Matteo Papini , Andrea Tirinzoni , Marcello Restelli

We study the problem of community detection when there is covariate information about the node labels and one observes multiple correlated networks. We provide an asymptotic upper bound on the per-node mutual information as well as a…

Information Theory · Computer Science 2019-12-12 Vaishakhi Mayya , Galen Reeves

In this paper, we review Fisher information matrices properties in weighted version and discuss inequalities/bounds on it by using reduced weight functions. In particular, an extended form of the Fisher information inequality previously…

Information Theory · Computer Science 2016-02-01 Mark Kelbert , Yuri Suhov , Salimeh Yasaei Sekeh

Estimation of multiple parameters in an unknown Hamiltonian is investigated. We present upper and lower bounds on the time required to complete the estimation within a prescribed tolerance $\delta$. The lower bound is given on the basis of…

Quantum Physics · Physics 2018-01-10 Naoto Kura , Masahito Ueda

In this work, we introduce novel information-theoretic generalization bounds using the conditional $f$-information framework, an extension of the traditional conditional mutual information (MI) framework. We provide a generic approach to…

Machine Learning · Statistics 2024-10-31 Ziqiao Wang , Yongyi Mao

The minimum error of unbiased parameter estimation is quantified by the quantum Fisher information in accordance to the Cram\'{e}r-Rao bound. We indicate that only superposed NOON states by simultaneous measurements can achieve the maximum…

Quantum Physics · Physics 2015-05-28 Y. R. Zhang , G. R. Jin , J. P. Cao , W. M. Liu , H. Fan

We give a novel, unified derivation of conditional PAC-Bayesian and mutual information (MI) generalization bounds. We derive conditional MI bounds as an instance, with special choice of prior, of conditional MAC-Bayesian (Mean Approximately…

Machine Learning · Computer Science 2021-06-18 Peter Grünwald , Thomas Steinke , Lydia Zakynthinou

This work discusses how to derive upper bounds for the expected generalisation error of supervised learning algorithms by means of the chaining technique. By developing a general theoretical framework, we establish a duality between…

Machine Learning · Statistics 2022-07-01 Eugenio Clerico , Amitis Shidani , George Deligiannidis , Arnaud Doucet

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

The principle of minimum Fisher information states that in the set of acceptable probability distributions characterizing the given system, it is best done by the one that minimizes the corresponding Fisher information. This principle can…

General Finance · Quantitative Finance 2022-03-24 Marcin Makowski , Edward W. Piotrowski , Piotr Frąckiewicz , Marek Szopa

The quantum Fisher information, the quantum analogue of the classical Fisher information, is a central quantity in quantum metrology and quantum sensing due to its connection to parameter estimation and fidelity susceptibility. Using…

Noise affects the performance of quantum technologies, hence the importance of elaborating operative figures of merit that can capture its impact in exact terms. In quantum metrology, the introduction of the Fisher information measurement…

Quantum Physics · Physics 2024-09-30 Francesco Albarelli , Ilaria Gianani , Marco G. Genoni , Marco Barbieri

Estimating and optimizing Mutual Information (MI) is core to many problems in machine learning; however, bounding MI in high dimensions is challenging. To establish tractable and scalable objectives, recent work has turned to variational…

Machine Learning · Computer Science 2019-05-17 Ben Poole , Sherjil Ozair , Aaron van den Oord , Alexander A. Alemi , George Tucker

In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large…

Functional Analysis · Mathematics 2018-12-12 Bastian Hilder , Mark A. Peletier , Upanshu Sharma , Oliver Tse

We present a new family of information-theoretic generalization bounds within the framework of conditional mutual information (CMI). Most of our results are established based on the leave-$m$-out (L$m$O) cross-validation error, with $m$…

Information Theory · Computer Science 2026-05-21 Yang Lu , Matthias Frey , Margreta Kuijper , Jingge Zhu

This paper is concerned with factor of i.i.d. processes on the $d$-regular tree for $d \geq 3$. We study the mutual information of the values on two given vertices. If the vertices are neighbors (i.e., their distance is $1$), then a known…

Probability · Mathematics 2017-07-25 Balázs Gerencsér , Viktor Harangi
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