Efficient Cross-Validation for Semi-Supervised Learning

TL;DR

This paper introduces an efficient method to approximate cross-validation in manifold regularization techniques for semi-supervised learning, significantly reducing computational cost while maintaining accuracy.

Contribution

It develops a novel approximation strategy for CV using Bouligand influence functions, enabling model selection with only one training process.

Findings

Approximate CV matches traditional CV in statistical accuracy.

Method reduces computation time by orders of magnitude.

Applicable to various loss functions in manifold regularization.

Abstract

Manifold regularization, such as laplacian regularized least squares (LapRLS) and laplacian support vector machine (LapSVM), has been widely used in semi-supervised learning, and its performance greatly depends on the choice of some hyper-parameters. Cross-validation (CV) is the most popular approach for selecting the optimal hyper-parameters, but it has high complexity due to multiple times of learner training. In this paper, we provide a method to approximate the CV for manifold regularization based on a notion of robust statistics, called Bouligand influence function (BIF). We first provide a strategy for approximating the CV via the Taylor expansion of BIF. Then, we show how to calculate the BIF for general loss function,and further give the approximate CV criteria for model selection in manifold regularization. The proposed approximate CV for manifold regularization requires training only once, hence can significantly improve the efficiency of traditional CV. Experimental results show that our approximate CV has no statistical discrepancy with the original one, but much smaller time cost.