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`local' vs. `global' parameters -- breaking the gaussian complexity barrier

2015/04/09 by Shahar Mendelson, Mendelson, Shahar
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Machine Learning and Algorithms #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.ML #stat.TH

paper · pdf · doi:10.48550/arxiv.1504.02191

arxiv created 2015/04/09 · openalex publication_date 2015/04/09 · arxiv updated 2015/04/10 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We show that if F is a convex class of functions that is L-subgaussian, the error rate of learning problems generated by independent noise is equivalent to a fixed point determined by `local' covering estimates of the class, rather than by the gaussian averages. To that end, we establish new sharp upper and lower estimates on the error rate for such problems.

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