22 papers · ranked by Valyu relevance
Frank Nielsen
In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information sciences. The exposition is self-contained by concisely introducing the necessary…
Frank Nielsen
We describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some uses of these information manifolds in information sciences. The exposition is self-contained by concisely introducing the necessary concepts of differential…
Kumar Vijay Mishra, M. Ashok Kumar, Ting‐Kam Leonard Wong
—Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information, sufficient statistics, and efficient estimators. Today, information geometry…
Eun-jin Kim, Miguel Rubi
Information theory provides an interdisciplinary method to understand important phenomena in many research fields ranging from astrophysical and laboratory fluids/plasmas to biological systems. In particular, information geometric theory enables us to envision the evolution of non-equilibrium processes in terms of a…
Kumar Vijay Mishra, M. Ashok Kumar
We examine the role of information geometry in the context of classical Cramér-Rao (CR) type inequalities. In particular, we focus on Eguchi's theory of obtaining dualistic geometric structures from a divergence function and then applying Amari-Nagoaka's theory to obtain a CR type inequality. The classical…
Xuehao Ding, Dongsoo Lee, Josh B. Melander, George Sivulka + 2 more
The ability to discriminate visual stimuli is constrained by their retinal representations. Previous studies of visual discriminability were limited to either low-dimensional artificial stimuli or theoretical considerations without a realistic model. Here we propose a novel framework for understanding stimulus…
Ionas Erb, Nihat Ay
Information geometry uses the formal tools of differential geometry to describe the space of probability distributions as a Riemannian manifold with an additional dual structure. The formal equivalence of compositional data with discrete probability distributions makes it possible to apply the same description to the…
Viswa Virinchi Muppirala, Hong Qian
Thermodynamics, and Empirical Counting Frequencies Authors: ['Viswa Virinchi Muppirala' 'Hong Qian'] Combinatorics, probabilities, and measurements are fundamental to understanding information. This work explores how the application of large deviation theory (LDT) in counting phenomena leads to the emergence of various…
Sven Goedeke, Justus Kautz, Christian Leibold
Understanding how network connectivity shapes neural representations is central to systems neuroscience. While dimensionality reduction methods uncover low-dimensional manifold structure in population recordings, a rigorous framework connecting manifold geometry to network mechanisms and information encoding remains…
Simon Williams, Arthur George Suvorov, Zengfu Wang, Bill Moran + 1 more
In problems of parameter estimation from sensor data, the Fisher information provides a measure of the performance of the sensor; effectively, in an infinitesimal sense, how much information about the parameters can be obtained from the measurements. From the geometric viewpoint, it is a Riemannian metric on the…
Miao Huang, Junda Ying, Yuxuan Wang, Haijun Zhou + 2 more
Cell phenotype transition (CPT) plays a pivotal role in various biological processes like development. Recent advancements in single-cell sequencing techniques have uncovered that cell transition dynamics during development are confined on low-dimensional manifolds. However, existing methods are inadequate for directly…
Nicola Catenacci Volpi, Daniel Polani
Seeking goals carried out by agents with a level of competency requires an “understanding” of the structure of their world. While abstract formal descriptions of a world structure in terms of geometric axioms can be formulated in principle, it is not likely that this is the representation that is actually employed by…
Pierre Baudot
This short note revisit information metric, underlining that it is a pseudo metric on manifolds of observables (random variables), rather than as usual on probability laws. Geodesics are characterized in terms of their boundaries and conditional independence condition. Pythagorean theorem is given, providing in special…
Simon J. Williams, Arthur G. Suvorov, Wang Zeng Fu, Bill Moran
In problems of parameter estimation from sensor data, the Fisher Information provides a measure of the performance of the sensor; effectively, in an infinitesimal sense, how much information about the parameters can be obtained from the measurements. From the geometric viewpoint, it is a Riemannian metric on the…
Melvin M. Vopson, Miguel Rubi
In this paper we investigate the relationship between Shannon information entropy and symmetry in closed Euclidean polygons within the framework of the second law of information dynamics. Using Lagrange multiplier formalism, we derive the condition for minimum entropy in a system of fixed size, showing that it occurs…
Akhil Shajan, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…
Xiaolu Wang, Peter Dayan, Paul M Bays
The activity of neural populations typically encodes more information about sensory or motor variables than can be captured by point estimates of the variables. We present and compare two approaches to quantifying this additional or ancillary information and its relationship to uncertainty: the mutual information…
Akhil Shajan, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open- source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…
AKHIL SHAJAN, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open-source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…
Min Chen, Mateu Sbert, Éloi Bossé
Information theory can be used to analyze the cost-benefit of visualization processes. However, the current measure of benefit contains an unbounded term that is neither easy to estimate nor intuitive to interpret. In this work, we propose to revise the existing cost-benefit measure by replacing the unbounded term with…
Artemy Kolchinsky, Bernat Corominas-Murtra
In many real-world systems, information can be transmitted in two qualitatively different ways: by copying or by transformation. Copying occurs when messages are transmitted without modification, e.g., when an offspring receives an unaltered copy of a gene from its parent. Transformation occurs when messages are…
Authors not listed
The GENERIC framework provides a robust structure for nonequilibrium dynamics but lacks a principled method to select reversible ($L$) and irreversible ($M$) brackets. Similarly, finite-time optimizations minimizing path-averaged reciprocal temperature exist but remain isolated. Here, we introduce the \textbf{Entropy…