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Composite likelihood estimation has an important role in the analysis of multivariate data for which the full likelihood function is intractable. An important issue in composite likelihood inference is the choice of the weights associated…

Methodology · Statistics 2015-12-15 Davide Ferrari , Chao Zheng

When the von Neumann entropy (VNE) of a system increases due to measurements, certain information is lost, some of which may be recoverable. We define information retrievability (IR) and information loss (IL) as functions of the density…

Quantum Physics · Physics 2025-03-27 Xing M. Wang

In this paper we study an application of an information distance between two measurements to the problem of non-contextuality and local realism. We postulate the triangle principle which states that any information distance is well defined…

Quantum Physics · Physics 2013-09-27 Pawel Kurzynski , Dagomir Kaszlikowski

The profile of a sample is the multiset of its symbol frequencies. We show that for samples of discrete distributions, profile entropy is a fundamental measure unifying the concepts of estimation, inference, and compression. Specifically,…

Machine Learning · Statistics 2020-02-27 Yi Hao , Alon Orlitsky

We provide a simple physical interpretation, in the context of the second law of thermodynamics, to the information inequality (a.k.a. the Gibbs' inequality, which is also equivalent to the log-sum inequality), asserting that the relative…

Information Theory · Computer Science 2009-03-29 Neri Merhav

Two new information-theoretic methods are introduced for establishing Poisson approximation inequalities. First, using only elementary information-theoretic techniques it is shown that, when $S_n=\sum_{i=1}^nX_i$ is the sum of the (possibly…

Probability · Mathematics 2010-10-21 Ioannis Kontoyiannis , Peter Harremoes , Oliver Johnson

Accurately treating strong electron correlation in quantum chemistry typically requires multireference wave-function methods with steep computational scaling. The recently proposed i-DMFT method promises near configuration-interaction…

Chemical Physics · Physics 2026-04-23 Paul G. Graf , Florian Matz , Lexin Ding , Julia Liebert , Markus Penz , Christian Schilling

The Mutual Information (MI) is an often used measure of dependency between two random variables utilized in information theory, statistics and machine learning. Recently several MI estimators have been proposed that can achieve parametric…

Information Theory · Computer Science 2018-11-26 Morteza Noshad , Yu Zeng , Alfred O. Hero

Recently, a Distribution Separation Method (DSM) is proposed for relevant feedback in information retrieval, which aims to approximate the true relevance distribution by separating a seed irrelevance distribution from the mixture one. While…

Information Retrieval · Computer Science 2015-10-19 Peng Zhang , Qian Yu , Yuexian Hou , Dawei Song , Jingfei Li , Bin Hu

Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{\'e}r-Rao lower bound (efficiency bound), which is the minimum possible variance for…

Machine Learning · Statistics 2019-11-05 Song Liu , Takafumi Kanamori , Wittawat Jitkrittum , Yu Chen

Information entropy and its extension, which are important generalization of entropy, have been applied in many research domains today. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional…

Information Theory · Computer Science 2017-04-24 Shuai Liu , Mengye Lu , Gaocheng Liu , Zheng Pan

A new finite form of de Finetti's representation theorem is established using elementary information-theoretic tools. The distribution of the first $k$ random variables in an exchangeable vector of $n\geq k$ random variables is close to a…

Information Theory · Computer Science 2024-04-29 Mario Berta , Lampros Gavalakis , Ioannis Kontoyiannis

Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…

Machine Learning · Computer Science 2020-07-08 Silviu Pitis , Harris Chan , Kiarash Jamali , Jimmy Ba

This paper presents a unified framework, integrating information theory and statistical mechanics, to connect metric failure in high-dimensional data with emergence in complex systems. We propose the "Information Dilution Theorem,"…

Information Theory · Computer Science 2025-04-15 HongZheng Liu , YiNuo Tian , Zhiyue Wu

Divergences often play important roles for study in information science so that it is indispensable to investigate their fundamental properties. There is also a mathematical significance of such results. In this paper, we introduce some…

Statistical Mechanics · Physics 2011-10-19 S. Furuichi , F. -C. Mitroi

We derive a simple lower bound on the geometric measure of entanglement for mixed quantum states in the case of a general multipartite system. The main ingredient of the presented derivation is the triangle inequality applied to the root…

Quantum Physics · Physics 2016-05-11 Łukasz Rudnicki , Zbigniew Puchała , Paweł Horodecki , Karol Zyczkowski

Information theory is a mathematical theory of learning with deep connections with topics as diverse as artificial intelligence, statistical physics, and biological evolution. Many primers on information theory paint a broad picture with…

Information Theory · Computer Science 2019-03-26 Philip Chodrow

We introduce a multipartite extension of an information-theoretic distance first introduced in [Nature 341, 119 (1989)]. We use this new distance to derive entropic tests of multipartite nonlocality for three and for an arbitrary even…

Quantum Physics · Physics 2015-05-27 Sadegh Raeisi , Pawel Kurzynski , Dagomir Kaszlikowski

Dithering is a technique that can improve human perception of low-resolution data by reducing quantization artifacts. In this work we formalize and analytically justify two metrics for quantization artifact prominence, using them to design…

Signal Processing · Electrical Eng. & Systems 2024-02-27 Morriel Kasher , Michael Tinston , Predrag Spasojevic

The quadratic decaying property of the information rate function states that given a fixed conditional distribution $p_{\mathsf{Y}|\mathsf{X}}$, the mutual information between the (finite) discrete random variables $\mathsf{X}$ and…

Information Theory · Computer Science 2023-05-15 Michael X. Cao , Marco Tomamichel