The Interplay Between Interpolation and Aggregation in Regression: Optimal Sample Complexity
arXiv:2605.29819v1 Announce Type: new Abstract: This work investigates theoretically the interplay between interpolation and aggregation in regression. We establish that the $\gamma$-graph dimension characterizes learnability for a broad class of natural aggregation procedures. Furthermore, we prove that an extremely simple aggregation procedure, combining three interpolating hypotheses via the median, is optimal among all these aggregation procedures, and is strictly more powerful than proper learning. Finally, we show that some hypothesis classes are learnable only by aggregating infinitely
This research is published as AI advancements continue at a rapid pace, with a strong focus on improving model performance and generalization capabilities.
Improved understanding of optimal learning procedures, particularly aggregation, could lead to more robust and efficient AI models, foundational for future AI development.
This theoretical work suggests that very simple aggregation methods can be optimally powerful, potentially simplifying certain aspects of model design and improving learnability.
- · AI researchers
- · Machine learning developers
Refined theoretical understanding of machine learning model learnability and aggregation techniques.
Potential for designing more data-efficient and robust AI systems across various applications.
Accelerated progress in areas requiring high precision and generalization from AI, such as autonomous systems or scientific discovery tools.
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