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A general information transmission model, under independent and identically distributed Gaussian codebook and nearest neighbor decoding rule with processed channel output, is investigated using the performance metric of generalized mutual…

Information Theory · Computer Science 2019-08-23 Wenyi Zhang , Yizhu Wang , Cong Shen , Ning Liang

Despite the widespread use and success of machine-learning techniques for detecting phase transitions from data, their working principle and fundamental limits remain elusive. Here, we explain the inner workings and identify potential…

Disordered Systems and Neural Networks · Physics 2023-11-20 Julian Arnold , Niels Lörch , Flemming Holtorf , Frank Schäfer

We correct claims about lower bounds on mutual information (MI) between real-valued random variables made in A. Kraskov {\it et al.}, Phys. Rev. E {\bf 69}, 066138 (2004). We show that non-trivial lower bounds on MI in terms of linear…

Data Analysis, Statistics and Probability · Physics 2013-05-29 David V. Foster , Peter Grassberger

We investigate the problem of representing information measures in terms of the moments of the underlying random variables. First, we derive polynomial approximations of the conditional expectation operator. We then apply these…

Information Theory · Computer Science 2021-09-03 Wael Alghamdi , Flavio P. Calmon

Recent advances in statistical learning theory have revealed profound connections between mutual information (MI) bounds, PAC-Bayesian theory, and Bayesian nonparametrics. This work introduces a novel mutual information bound for…

Machine Learning · Statistics 2025-08-18 El Mahdi Khribch , Pierre Alquier

In this paper, we study Sibson's $\alpha$-mutual information in the context of the additive Gaussian noise channel. While the classical case $\alpha = 1$ is well understood and admits deep connections to estimation-theoretic quantities,…

Information Theory · Computer Science 2026-04-14 Mohammad Milanian , Alex Dytso , Martina Cardone

We propose a Bayesian framework of Gaussian process in order to extend Fisher's discriminant to classify functional data such as spectra and images. The probability structure for our extended Fisher's discriminant is explicitly formulated,…

Machine Learning · Computer Science 2014-12-10 Yao-Hsiang Yang , Lu-Hung Chen , Chieh-Chih Wang , Chu-Song Chen

When training data are fragmented across batches or federated-learned across different geographic locations, trained models manifest performance degradation. That degradation partly owes to covariate shift induced by data having been…

Machine Learning · Computer Science 2025-10-07 Behraj Khan , Tahir Qasim Syed

It has been known for a long time that the mutual information between the input sequence and output of a binary symmetric channel (BSC) is upper bounded by the mutual information between the same input sequence and the output of a binary…

Information Theory · Computer Science 2024-01-29 Uri Erez , Or Ordentlich , Shlomo Shamai

We compute quantitative bounds for measuring the discrepancy between the distribution of two min-max statistics involving either pairs of Gaussian random matrices, or one Gaussian and one Gaussian-subordinated random matrix. In the fully…

Probability · Mathematics 2021-09-28 Giovanni Peccati , Nicola Turchi

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

A random Gaussian density field contains a fixed amount of Fisher information on the amplitude of its power spectrum. For a given smoothing scale, however, that information is not evenly distributed throughout the smoothed field. We…

Cosmology and Nongalactic Astrophysics · Physics 2025-12-23 Andrew Repp , Ravi K. Sheth , Istvan Szapudi , Yan-Chuan Cai

We have introduced a measure of Gaussian quantum correlations based on quantum Fisher information. For bipartite Gaussian states the minimum quantum Fisher information due to local unitary evolution on one of the parties reliably quantifies…

Quantum Physics · Physics 2014-06-20 Manabendra N. Bera

The Fisher information approximation (FIA) is an implementation of the minimum description length principle for model selection. Unlike information criteria such as AIC or BIC, it has the advantage of taking the functional form of a model…

Methodology · Statistics 2018-08-02 Daniel W. Heck , Morten Moshagen , Edgar Erdfelder

Feature selection is one of the most fundamental problems in machine learning. An extensive body of work on information-theoretic feature selection exists which is based on maximizing mutual information between subsets of features and class…

Machine Learning · Statistics 2016-06-10 Shuyang Gao , Greg Ver Steeg , Aram Galstyan

We consider the privacy problem of statistical estimation from distributed data, where users communicate to a central processor over a Gaussian multiple-access channel(MAC). To avoid the inevitable sacrifice of data utility for privacy in…

Information Theory · Computer Science 2020-11-03 Wenhao Zhan

In the era of big data, it is necessary to split extremely large data sets across multiple computing nodes and construct estimators using the distributed data. When designing distributed estimators, it is desirable to minimize the amount of…

Statistics Theory · Mathematics 2022-04-25 Azeem Zaman , Botond Szabó

The notion of low-noise channels was recently proposed and analyzed in detail in order to describe noise-processes driven by environment [M. Hotta, T. Karasawa and M. Ozawa, Phys. Rev. A72, 052334 (2005)]. An estimation theory of low-noise…

Quantum Physics · Physics 2009-11-13 M. Hotta , T. Karasawa , M. Ozawa

We investigate the connection between the time-evolution of averages of stochastic quantities and the Fisher information and its induced statistical length. As a consequence of the Cramer-Rao bound, we find that the rate of change of the…

Statistical Mechanics · Physics 2020-07-01 Sosuke Ito , Andreas Dechant

A family of skew information quantities is obtained, in which the well-known Wigner-Yanase skew information and quantum Fisher information stand as special cases. A transparent proof of convexity of the generalized skew information is…

Quantum Physics · Physics 2023-06-14 Ma-Cheng Yang , Cong-Feng Qiao