Classification with Minimax Fast Rates for Classes of Bayes Rules with Sparse Representation

2006/07/18 by Guillaume Lecué, Lecué, Guillaume
Computer Science · Mathematics · #62G05 #62H30 #68T10 #FOS: Mathematics #Machine Learning and Algorithms #Statistical Methods and Inference #Statistics Theory (math.ST) #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.math/0607439

openalex publication_date 2006/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a classifier which attains the rate of convergence log n/n under sparsity and margin assumptions. An approach close to the one met in approximation theory for the estimation of function is used to obtain this result. The idea is to develop the Bayes rule in a fundamental system of L²([0,1]^d) made of indicator of dyadic sets and to assume that coefficients, equal to -1,0 or 1, belong to a kind of L¹-ball. This assumption can be seen as a sparsity assumption, in the sense that the proportion of coefficients non equal to zero decreases as "frequency" grows. Finally, rates of convergence are obtained by using an usual trade-off between a bias term and a variance term.

Related

• Minimax estimation of linear and quadratic functionals on sparsity\n classes
• Approximate Sparsity Class and Minimax Estimation
• Fast learning rates for plug-in classifiers under the margin condition
• Minimax learning rates for estimating binary classifiers under margin conditions
• Fast classification rates without standard margin assumptions