Boosting, Voting Classifiers and Randomized Sample Compression Schemes (2402.02976v2)

Abstract: In boosting, we aim to leverage multiple weak learners to produce a strong learner. At the center of this paradigm lies the concept of building the strong learner as a voting classifier, which outputs a weighted majority vote of the weak learners. While many successful boosting algorithms, such as the iconic AdaBoost, produce voting classifiers, their theoretical performance has long remained sub-optimal: The best known bounds on the number of training examples necessary for a voting classifier to obtain a given accuracy has so far always contained at least two logarithmic factors above what is known to be achievable by general weak-to-strong learners. In this work, we break this barrier by proposing a randomized boosting algorithm that outputs voting classifiers whose generalization error contains a single logarithmic dependency on the sample size. We obtain this result by building a general framework that extends sample compression methods to support randomized learning algorithms based on sub-sampling.

• The paper introduces a randomized boosting algorithm that reduces training sample complexity to a single logarithmic factor.
• It combines classifiers trained on multiple sub-samples to achieve stronger performance and break previous sample size bounds.
• The new framework for randomized compression schemes offers fresh analytical tools that could inspire future advances in ensemble learning.

Introduction to Boosting and Classifiers

Boosting is a foundational algorithm in machine learning, known for combining multiple "weak learners" to create a single "strong learner." Central to this approach is the use of voting classifiers, which work by aggregating the predictions of several base learners. A significant focus in the field has been on minimizing the number of training examples needed to achieve certain accuracy levels with voting classifiers. Although traditional boosting algorithms have been effective, they have not reached optimal bounds in terms of training example requirements.

Breaking the Logarithmic Barrier

The paper at hand marks a significant advancement in boosting algorithm theory. It presents a novel randomized boosting algorithm that outputs voting classifiers with a single logarithmic dependency on the sample size, improving upon previous algorithms which contained two such dependencies. This achievement hinges on the development of a general framework that extends sample compression to support randomized learning algorithms utilizing sub-sampling. This new work surpasses previous upper bounds known for voting classifiers.

The Innovative Algorithm

The cornerstone of this research is a new algorithm that produces voting classifiers with an improved error in relation to the number of samples. This approach, unlike traditional boosting techniques, creates multiple small sub-samples from the training data and generates classifiers trained on each subset, which are then combined. The central claim, backed by rigorous analysis, is that this algorithm generates classifiers that perform with only a single logarithmic factor based on the number of samples. This result was achieved by means of a new analysis technique, incorporating a novel framework for evaluating randomized learning algorithms.

Relevance and Future Directions

While existing algorithms such as AdaBoost and recent variants have proven effective and widely used, this research breaks ground by enhancing their sample complexity, thus paving the way for more efficient learning algorithms in practice. It also opens multiple new research avenues, such as whether one could achieve an algorithm with optimal sample complexity or improve other existing algorithms in a similar fashion. Additionally, the paper introduces a potential new toolbox for algorithm analysis through the proposed framework of randomized compression schemes.

In summary, this paper presents a pivotal step in boosting theory, offering a novel algorithm with significantly reduced sample complexity and a profound analytical framework potentially applicable to a wide range of learning algorithms. The implications are substantial, setting a new standard for future research in the field of ensemble learning and generalization.