Pairwise Learning With Gaussian Empirical Gain Function

Abstract

This article investigate the performance of Gaussian Empirical Gain Maximization (EGM) in a regression setting and conduct a detailed theoretical analysis, particularly in the presence of heavy-tailed noise, where this article establish improved convergence rates. To achieve this, this article introduce a new moment condition, from which this article derive several enhanced theoretical results for the Gaussian model. First, propose a new comparison theorem, proving that this theorem plays a crucial role in improving the estimation of approximation errors and variance. This theorem not only characterizes the regression properties of Gaussian EGM but also plays a key role in enhancing the convergence rate. Secondly, This article derive improved error bounds for the Gaussian model, providing theoretical support for the application of Gaussian EGM under different noise conditions. broadens our theoretical understanding of Gaussian EGM.

Keywords

• Empirical gain maximization (EGM)
• convergence rates
• gauss gain function
• heavy-tailed noise
• weak moment condition
• concentration inequality