Semiparametric Gaussian copula classification

TL;DR

This paper introduces a semiparametric approach for binary classification under Gaussian copula models in high dimensions, achieving faster convergence rates by leveraging sparsity and low noise conditions.

Contribution

It develops an accurate semiparametric estimator of the log density ratio and an empirical decision rule with near-optimal convergence rates, advancing Gaussian copula classification methods.

Findings

Achieves near $n^{-1/2}$ convergence rate in simple Gaussian cases.

Utilizes sparsity and low noise to improve estimation efficiency.

Provides theoretical bounds on excess risk.

Abstract

This paper studies the binary classification of two distributions with the same Gaussian copula in high dimensions. Under this semiparametric Gaussian copula setting, we derive an accurate semiparametric estimator of the log density ratio, which leads to our empirical decision rule and a bound on its associated excess risk. Our estimation procedure takes advantage of the potential sparsity as well as the low noise condition in the problem, which allows us to achieve faster convergence rate of the excess risk than is possible in the existing literature on semiparametric Gaussian copula classification. We demonstrate the efficiency of our empirical decision rule by showing that the bound on the excess risk nearly achieves a convergence rate of $n^{-1/2}$ in the simple setting of Gaussian distribution classification.