Fast rate of convergence in high dimensional linear discriminant\n analysis

2009/09/11 by Robin Girard, Girard, Robin
Computer Science · Mathematics · #62C99 #Advanced Statistical Methods and Models #FOS: Mathematics #Face and Expression Recognition #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.0909.2191

openalex publication_date 2009/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper gives a theoretical analysis of high dimensional linear\ndiscrimination of Gaussian data. We study the excess risk of linear\ndiscriminant rules. We emphasis on the poor performances of standard procedures\nin the case when dimension p is larger than sample size n. The corresponding\ntheoretical results are non asymptotic lower bounds. On the other hand, we\npropose two discrimination procedures based on dimensionality reduction and\nprovide associated rates of convergence which can be O(log(p)/n) under sparsity\nassumptions. Finally all our results rely on a theorem that provides simple\nsharp relations between the excess risk and an estimation error associated to\nthe geometric parameters defining the used discrimination rule.\n

Citations

• Adapting to unknown sparsity by controlling the false discovery rate
• Ideal spatial adaptation by wavelet shrinkage

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