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Structure Learning via Mutual Information

Jeremy Nixon

TL;DR

A framework for learning and representing functional relationships in data using MI-based features is proposed, offering a new perspective on how to leverage information theory for algorithm design and dataset analysis and proposing new mutual information theoretic foundations to learning algorithms.

Abstract

This paper presents a novel approach to machine learning algorithm design based on information theory, specifically mutual information (MI). We propose a framework for learning and representing functional relationships in data using MI-based features. Our method aims to capture the underlying structure of information in datasets, enabling more efficient and generalizable learning algorithms. We demonstrate the efficacy of our approach through experiments on synthetic and real-world datasets, showing improved performance in tasks such as function classification, regression, and cross-dataset transfer. This work contributes to the growing field of metalearning and automated machine learning, offering a new perspective on how to leverage information theory for algorithm design and dataset analysis and proposing new mutual information theoretic foundations to learning algorithms.

Structure Learning via Mutual Information

TL;DR

A framework for learning and representing functional relationships in data using MI-based features is proposed, offering a new perspective on how to leverage information theory for algorithm design and dataset analysis and proposing new mutual information theoretic foundations to learning algorithms.

Abstract

This paper presents a novel approach to machine learning algorithm design based on information theory, specifically mutual information (MI). We propose a framework for learning and representing functional relationships in data using MI-based features. Our method aims to capture the underlying structure of information in datasets, enabling more efficient and generalizable learning algorithms. We demonstrate the efficacy of our approach through experiments on synthetic and real-world datasets, showing improved performance in tasks such as function classification, regression, and cross-dataset transfer. This work contributes to the growing field of metalearning and automated machine learning, offering a new perspective on how to leverage information theory for algorithm design and dataset analysis and proposing new mutual information theoretic foundations to learning algorithms.
Paper Structure (22 sections, 5 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 22 sections, 5 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Mutual Information
  3. Mutual Information Gradients
  4. Mutual Information Gradient Approximation
  5. History of Mutual Information vs. Correlation
  6. History of MI in ML
  7. History of Mutual Information in Learning Algorithms
  8. Function and Shape Data Analysis
  9. Nature of "Pattern" and "Relationship"
  10. Methods
  11. Sliding window & mutual information gradients
  12. Window sizes & overlaps
  13. Scale and Translation Invariance
  14. Experiments
  15. Data Generation Process
  16. ...and 7 more sections

Figures (3)

  • Figure 1: In the mutual information embedding space, the patterns behind relationship classes are neatly picked out & can be represented in this low-dimensional projection. The linear functions cluster neatly in the upper right, well separated from both Gaussians and Quartics. The automatic detection of the relationships behind real-world data based on their mutual information embedding becomes possible.
  • Figure 2: Comparison of Various Mathematical Relationships. Top left: Linear relationships with varying slopes and intercepts. Top right: Quadratic relationships with varying coefficients. Bottom left: Gaussian distributions with different means and variances. Bottom right: Sinusoidal relationships with varying amplitudes, frequencies, and phase shifts. Each plot demonstrates the diversity of patterns that can emerge from these fundamental mathematical functions, highlighting their importance in modeling various phenomena across different scientific disciplines.
  • Figure 3: Figure: Windowed Correlation Gradients for Different Relationships. This figure displays how correlation between x and y values changes across different bins for four types of synthetic relationships: linear, quadratic, Gaussian, and sinusoidal. The Pearson correlation coefficient is calculated for each bin, and the correlation values are normalized between -1 and 1. The linear relationship shows consistent correlation across bins, while the quadratic and Gaussian relationships exhibit more variability due to their non-linear nature. The sinusoidal relationship has an oscillating pattern of positive and negative correlations corresponding to its periodic behavior.