Prediction games and arcing algorithms

Area of Science:

• Machine Learning
• Computational Theory

Background:

• The theoretical underpinnings of adaptive reweighting and combining algorithms (arcing), including Adaboost, remain incompletely understood.
• Existing research offers explanations for Adaboost's success, such as its margin maximization properties.

Purpose of the Study:

• To develop a theoretical framework for understanding arcing algorithms by formulating prediction as a game.
• To introduce an optimal arcing algorithm and provide a tighter bound on generalization error.
• To empirically evaluate the completeness of existing Adaboost explanations.

Main Methods:

• Formulating prediction as a two-player game involving instance selection and predictor combination.
• Utilizing the minimax theorem for convergence proofs.
• Developing and analyzing a novel optimal arcing algorithm.
• Empirically comparing Adaboost with the optimal arcing algorithm.

Main Results:

• Arcing algorithms are demonstrated to be strategies for finding optimal solutions in the formulated game.
• A new arcing algorithm is presented that converges to the optimal strategy.
• A sharper bound on generalization error for combined predictors is derived.
• Empirical results suggest that margin maximization alone does not fully explain Adaboost's effectiveness.

Conclusions:

• The game-theoretic perspective provides a robust theoretical foundation for arcing algorithms.
• The proposed optimal arcing algorithm offers improved performance and theoretical guarantees.
• Further research is needed to fully elucidate the mechanisms behind Adaboost's success.