Information Decomposition in Complex Systems Using Machine Learning

Core Concepts

Practical methodology using machine learning for information decomposition in complex systems.

Abstract

The content discusses the application of machine learning to decompose information in complex systems. It introduces a practical methodology that uses the distributed information bottleneck to identify relevant variation in data. The analysis focuses on two paradigms: Boolean circuits and amorphous materials undergoing plastic deformation. The study aims to bridge micro- and macroscale structures in complex systems.
Directory:

Introduction and Background

Mutual information as a measure of statistical dependence.
Importance of identifying relevant variation in complex systems.

Methodology: Distributed Information Bottleneck

Lossy compression of measurements using machine learning.
Optimization process for extracting important variation.

Results: Application to Boolean Circuits and Amorphous Materials

Analysis of Boolean circuits with logistic regression, Shapley values, and distributed IB.
Decomposing structural information in amorphous materials under deformation.

Discussion: Comparison with Logistic Regression and Shapley Values

Interpretability and insights provided by the distributed IB approach.

Conclusion: Practical implications for studying complex systems.

Stats

Mutual information provides a natural means of linking variation across scales of a system.
The distributed information bottleneck method is used to decompose the information contained in measurements.
For every point on the spectrum, there is an allocation of information over the inputs.

Quotes

Key Insights Distilled From

Information decomposition in complex systems via machine learning

by Kieran A. Mu... at arxiv.org 03-20-2024

https://arxiv.org/pdf/2307.04755.pdf

Deeper Inquiries

How does the distributed IB approach compare to traditional methods like logistic regression?

The distributed Information Bottleneck (IB) approach offers a unique perspective compared to traditional methods like logistic regression. Logistic regression fits a linear combination of inputs to predict an output, providing interpretability through model weights but restricting the relationships that can be captured due to linearity. On the other hand, the distributed IB decomposes information contained in inputs about an output by optimizing lossy compression schemes for each variable independently. This method provides global interpretability, offering insights into how different combinations of input variables contribute to predicting the output.
In contrast, logistic regression may struggle with non-linear relationships such as those involving XOR gates in Boolean circuits. While it can provide some insight into feature importance based on model coefficients, it may not capture complex interactions between variables effectively. The distributed IB excels at capturing higher-order interaction effects and provides a spectrum of importance values across all inputs rather than a single value per input.

How are limitations or challenges associated with estimating mutual information from data?

Estimating mutual information from data poses several limitations and challenges:

Computational Complexity: Calculating mutual information involves evaluating probabilities over joint distributions, which can be computationally intensive for high-dimensional data sets.

Sample Size: Mutual information estimation requires sufficient samples to accurately estimate probabilities and entropies, leading to challenges when dealing with limited data.

Bias and Variance Trade-off: Estimators of mutual information often face trade-offs between bias (underfitting) and variance (overfitting), impacting the accuracy of estimates.

Nonlinear Relationships: Mutual information assumes no functional relationship between variables; however, real-world systems often exhibit complex nonlinear dependencies that complicate estimation.

Data Preprocessing: Ensuring appropriate preprocessing steps such as discretization or normalization is crucial for accurate estimation but adds complexity and potential biases.

Model Selection: Choosing suitable models or algorithms for estimating mutual information that balance accuracy and computational efficiency is essential but challenging given diverse methodologies available.

How can the concept of lossy compression be applied to other fields beyond complex systems?

The concept of lossy compression has broad applications beyond complex systems:

Image & Video Processing: In image/video compression standards like JPEG/MPEG, lossy compression reduces file size while maintaining visual quality.

Audio Compression: Lossy audio codecs like MP3 use perceptual coding techniques for efficient storage without significant quality degradation.

Data Storage: Lossy compression techniques optimize storage space in databases by reducing redundancy without losing critical details.

4 .Machine Learning: Feature selection/extraction via dimensionality reduction techniques like PCA involve lossy transformations preserving key patterns while reducing dimensions.
5 .Genomics & Bioinformatics: Lossily compressing genetic sequences helps manage vast genomic datasets efficiently while retaining essential biological insights.
6 .Natural Language Processing: Word embedding models utilize lossy representations converting words into dense vectors capturing semantic relationships efficiently.
These applications demonstrate how lossy compression enhances data processing efficiency across various domains by balancing preservation of critical information with reduced storage requirements or improved performance metrics such as speed or accuracy.