[Paper Review] The minimum information principle for discriminative learning

Amir Globerson, Naftali Tishby|arXiv (Cornell University)|Jul 7, 2004

Statistical Mechanics and EntropyPhysics and Astronomy14 references19 citations

TL;DR

This paper proposes minimum mutual information (MMI) as a superior principle to maximum entropy for discriminative learning in classification. By optimizing mutual information between inputs and class labels, the framework generalizes maximum entropy, enables game-theoretic interpretation, and yields classifiers that outperform maximum entropy models on benchmark tasks.

ABSTRACT

Exponential models of distributions are widely used in machine learning for classification and modelling. It is well known that they can be interpreted as maximum entropy models under empirical expectation constraints. In this work, we argue that for classification tasks, mutual information is a more suitable information theoretic measure to be optimized. We show how the principle of minimum mutual information generalizes that of maximum entropy, and provides a comprehensive framework for building discriminative classifiers. A game theoretic interpretation of our approach is then given, and several generalization bounds provided. We present iterative algorithms for solving the minimum information problem and its convex dual, and demonstrate their performance on various classification tasks. The results show that minimum information classifiers outperform the corresponding maximum entropy models.

Motivation & Objective

• To address the limitations of maximum entropy models in discriminative classification by proposing a more suitable information-theoretic principle.
• To establish mutual information as the optimal criterion for discriminative learning, especially in classification tasks.
• To develop a unified framework that generalizes maximum entropy through the principle of minimum mutual information.
• To provide theoretical foundations via game theory and generalization bounds for the proposed approach.
• To design iterative algorithms for solving the minimum information problem and its convex dual, enabling practical implementation.

Proposed method

• Proposes a minimum mutual information (MMI) principle as the optimization objective for discriminative classifiers.
• Derives a game-theoretic interpretation of the MMI framework, framing classification as a minimax game.
• Develops iterative algorithms for solving the primal minimum information problem and its convex dual.
• Uses empirical expectation constraints to define the model space, similar to maximum entropy, but under mutual information minimization.
• Applies convex duality to derive a tractable optimization formulation suitable for iterative solvers.
• Demonstrates the framework on various classification tasks to validate performance.

Experimental results

Research questions

• RQ1 Can mutual information serve as a more appropriate information-theoretic criterion than entropy for discriminative classification?
• RQ2 How does the minimum mutual information principle generalize the maximum entropy principle in classification?
• RQ3 What are the theoretical properties, such as generalization bounds, of classifiers trained under the minimum mutual information principle?
• RQ4 How do the iterative algorithms for solving the minimum information problem perform in practice compared to maximum entropy models?
• RQ5 What is the game-theoretic interpretation of the minimum mutual information framework?

Key findings

• The minimum mutual information framework generalizes the maximum entropy principle, providing a more appropriate foundation for discriminative learning.
• The proposed classifiers based on minimum mutual information outperform their maximum entropy counterparts on various classification tasks.
• The game-theoretic interpretation offers a new perspective on discriminative learning, linking it to adversarial optimization.
• Generalization bounds are derived, providing theoretical justification for the framework's robustness.
• Iterative algorithms for the primal and dual problems converge and demonstrate practical effectiveness.
• The framework offers a comprehensive, information-theoretic alternative to maximum entropy with improved empirical performance.