Characterizing Directed and Undirected Metrics of High-Order Interdependence

Kernekoncepter

The paper investigates the relationship between two practical metrics of high-order interdependencies: the redundancy-synergy index (RSI), which captures directed interdependencies, and the O-information, which captures undirected interdependencies. The results reveal tight links between these two quantities and provide interpretations in terms of likelihood ratios and information geometry.

Resumé

The paper focuses on characterizing and relating two metrics of high-order statistical interdependencies: the redundancy-synergy index (RSI) and the O-information.
Key highlights:

The RSI captures directed high-order effects, measuring the extent to which correlations within a set of variables X are created or destroyed by conditioning on a target variable Y.
The O-information captures undirected high-order effects, measuring the differences between the total and dual total correlations within X.
The paper presents analytical expressions relating the RSI and O-information, showing that the RSI can be expressed as the difference between the O-information of the joint system (X,Y) and the conditional O-information of X given Y.
It is shown that the RSI and O-information can be interpreted in terms of log-likelihood ratios between models with predominantly redundant or synergistic high-order interdependencies.
The O-information is further characterized as the sum of RSI-like quantities, each considering a different partition of the system.
These results provide insights into the similarities and differences between directed and undirected approaches to quantifying high-order statistical relationships.

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Characterising directed and undirected metrics of high-order interdependence

by Fernando E. ... kl. arxiv.org 04-11-2024

https://arxiv.org/pdf/2404.07140.pdf

Dybere Forespørgsler

How can the insights from this work be leveraged to better understand the role of redundancy and synergy in neural information processing

The insights from this work can significantly enhance our understanding of the role of redundancy and synergy in neural information processing. By utilizing metrics like the Redundancy-Synergy Index (RSI) and O-information, researchers can quantify and analyze the high-order interdependencies within neural systems. Understanding how information is shared and processed among different variables can shed light on how neural networks encode and represent information.
Specifically, the RSI can help identify the balance between redundant and synergistic interdependencies in neural systems. This can provide valuable insights into how neural circuits optimize information flow, adapt to changing environments, and balance the trade-off between reliability and flexibility. By applying these metrics to neural data, researchers can uncover the underlying mechanisms that govern neural information processing, leading to a deeper understanding of neural computation and network dynamics.

What are the implications of the information-geometric interpretation of the RSI and O-information for studying the structure of high-dimensional data manifolds

The information-geometric interpretation of the RSI and O-information offers a powerful framework for studying the structure of high-dimensional data manifolds. By viewing these metrics as lengths of projections onto different classes of models (e.g., tail-to-tail and head-to-head), researchers can gain insights into the underlying information processing mechanisms in complex systems.
This interpretation allows for a geometric understanding of how information is distributed and shared within a system. By analyzing the lengths of these projections, researchers can quantify the degree of redundancy and synergy present in the data. This approach can be particularly valuable for studying complex datasets, such as those found in neural recordings or high-dimensional biological systems, where traditional analytical methods may fall short.
By leveraging the information-geometric interpretation of these metrics, researchers can uncover hidden structures, patterns, and relationships within high-dimensional data manifolds. This can lead to new discoveries, insights, and applications in various fields, including neuroscience, machine learning, and complex systems analysis.

Can the relationships between directed and undirected metrics be extended to other information-theoretic frameworks beyond partial information decomposition

The relationships between directed and undirected metrics, as explored in the context of partial information decomposition, can indeed be extended to other information-theoretic frameworks beyond PID. These relationships provide a deeper understanding of how information is processed, shared, and structured in complex systems, offering valuable insights into the underlying dynamics of interdependencies.
By applying similar principles to other information-theoretic frameworks, researchers can develop a more comprehensive understanding of information processing in diverse systems. For example, in the context of causal inference or network analysis, exploring the connections between directed and undirected metrics can reveal causal relationships, information flow patterns, and emergent properties in complex networks.
Furthermore, extending these relationships to other frameworks can facilitate the development of novel metrics, models, and algorithms for analyzing and interpreting complex data. By building upon the insights gained from the study of directed and undirected metrics in high-order interdependence, researchers can advance the field of information theory and its applications across various disciplines.