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One of the most fundamental questions one can ask about a pair of random variables X and Y is the value of their mutual information. Unfortunately, this task is often stymied by the extremely large dimension of the variables. We might hope…

Statistical Mechanics · Physics 2017-06-21 Ryan G. James , John R. Mahoney , James P. Crutchfield

We study the performance of asymptotic and approximate consensus algorithms under harsh environmental conditions. The asymptotic consensus problem requires a set of agents to repeatedly set their outputs such that the outputs converge to a…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-06-28 Matthias Függer , Thomas Nowak , Manfred Schwarz

We analyze the geometry of a joint distribution over a set of discrete random variables. We briefly review Shannon's entropy, conditional entropy, mutual information and conditional mutual information. We review the entropic information…

As conventional communication systems based on classic information theory have closely approached the limits of Shannon channel capacity, semantic communication has been recognized as a key enabling technology for the further improvement of…

Information Theory · Computer Science 2023-06-06 Jiancheng Tang , Qianqian Yang , Zhaoyang Zhang

Reconstruction of population histories is a central problem in population genetics. Existing coalescent-based methods, like the seminal work of Li and Durbin (Nature, 2011), attempt to solve this problem using sequence data but have no…

Populations and Evolution · Quantitative Biology 2020-05-11 Younhun Kim , Frederic Koehler , Ankur Moitra , Elchanan Mossel , Govind Ramnarayan

Mutual information (MI) is a general measure of statistical dependence with widespread application across the sciences. However, estimating MI between multi-dimensional variables is challenging because the number of samples necessary to…

Quantitative Methods · Quantitative Biology 2025-03-06 Gokul Gowri , Xiao-Kang Lun , Allon M. Klein , Peng Yin

We address the practical problems of estimating the information relations that characterize large networks. Building on methods developed for analysis of the neural code, we show that reliable estimates of mutual information can be obtained…

Information Theory · Computer Science 2007-07-13 Noam Slonim , Gurinder S. Atwal , Gasper Tkacik , William Bialek

The sigmoidal tuning curve that maximizes the mutual information for a Poisson neuron, or population of Poisson neurons, is obtained. The optimal tuning curve is found to have a discrete structure that results in a quantization of the input…

Neurons and Cognition · Quantitative Biology 2009-09-24 Alexander P. Nikitin , Nigel G. Stocks , Robert P. Morse , Mark D. McDonnell

Shannon's seminal 1948 work gave rise to two distinct areas of research: information theory and mathematical coding theory. While information theory has had a strong influence on theoretical neuroscience, ideas from mathematical coding…

Neurons and Cognition · Quantitative Biology 2015-02-25 Carina Curto , Vladimir Itskov , Katherine Morrison , Zachary Roth , Judy L. Walker

Efficient information processing is crucial for both living organisms and engineered systems. The mutual information rate, a core concept of information theory, quantifies the amount of information shared between the trajectories of input…

Molecular Networks · Quantitative Biology 2025-09-01 Manuel Reinhardt , Age J. Tjalma , Anne-Lena Moor , Christoph Zechner , Pieter Rein ten Wolde

Analysis of a probabilistic system often requires to learn the joint probability distribution of its random variables. The computation of the exact distribution is usually an exhaustive precise analysis on all executions of the system. To…

Information Theory · Computer Science 2023-07-19 Fabrizio Biondi , Yusuke Kawamoto , Axel Legay , Louis-Marie Traonouez

Estimating the Shannon information associated with individual neurons is a non-trivial problem. Three key methods used to estimate the mutual information between neuron inputs and outputs are described, and a list of further readings is…

Neurons and Cognition · Quantitative Biology 2023-04-05 James V Stone

Deriving formulations for computing and estimating tight worst-case size increases for conjunctive queries with various constraints has been at the core of theoretical database research. If the problem has no constraints or only one…

Quantum Physics · Physics 2025-06-10 Valter Uotila , Jiaheng Lu

Probability theory is fundamental for modeling uncertainty, with traditional probabilities being real and non-negative. Complex probability extends this concept by allowing complex-valued probabilities, opening new avenues for analysis in…

Information Theory · Computer Science 2025-03-07 Chan Li , Hejun Xu , Zhu Cao

We derive a tight lower bound on equivocation (conditional entropy), or equivalently a tight upper bound on mutual information between a signal variable and channel outputs. The bound is in terms of the joint distribution of the signals and…

Information Theory · Computer Science 2019-01-14 Michal Hledík , Thomas R. Sokolowski , Gašper Tkačik

We conclude a sequence of work by giving near-optimal sketching and streaming algorithms for estimating Shannon entropy in the most general streaming model, with arbitrary insertions and deletions. This improves on prior results that obtain…

Data Structures and Algorithms · Computer Science 2008-12-18 Nicholas J. A. Harvey , Jelani Nelson , Krzysztof Onak

The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-04-01 Fabian Kuhn , Thomas Moscibroda , Roger Wattenhofer

Neuromorphic applications emulate the processing performed by the brain by using spikes as inputs instead of time-varying analog stimuli. Therefore, these time-varying stimuli have to be encoded into spikes, which can induce important…

Neural and Evolutionary Computing · Computer Science 2024-12-30 Ahmad El Ferdaoussi , Eric Plourde , Jean Rouat

Despite the growing popularity of deep learning technologies, high memory requirements and power consumption are essentially limiting their application in mobile and IoT areas. While binary convolutional networks can alleviate these…

Computer Vision and Pattern Recognition · Computer Science 2020-08-05 Dmitry Ignatov , Andrey Ignatov

We consider a set of probabilistic functions of some input variables as a representation of the inputs. We present bounds on how informative a representation is about input data. We extend these bounds to hierarchical representations so…

Machine Learning · Statistics 2015-02-03 Greg Ver Steeg , Aram Galstyan