Robust Functional Logistic Regression

2025-10-13

AI Summary

Functional logistic regression is highly sensitive to outliers, leading to biased parameter estimates and degraded classification performance. To address this, we propose a robust estimation framework: first, robust functional principal component analysis (RFPCA) is employed for dimensionality reduction to mitigate the influence of outliers in predictor functions; second, an M-estimator is integrated to simultaneously handle contamination in both responses and predictors. The method ensures both computational efficiency and statistical robustness. Monte Carlo simulations and real-world hand radiograph data experiments demonstrate that, under outlier-contaminated settings, our approach significantly outperforms existing robust and non-robust methods—yielding more stable parameter estimates and higher classification accuracy. Under clean data conditions, it achieves comparable performance while exhibiting superior computational efficiency.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Intelligent Robots: State Estimation
• Natural Language Processing: Safety and Robustness

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Functional logistic regression is a popular model to capture a linear relationship between binary response and functional predictor variables. However, many methods used for parameter estimation in functional logistic regression are sensitive to outliers, which may lead to inaccurate parameter estimates and inferior classification accuracy. We propose a robust estimation procedure for functional logistic regression, in which the observations of the functional predictor are projected onto a set of finite-dimensional subspaces via robust functional principal component analysis. This dimension-reduction step reduces the outlying effects in the functional predictor. The logistic regression coefficient is estimated using an M-type estimator based on binary response and robust principal component scores. In doing so, we provide robust estimates by minimizing the effects of outliers in the binary response and functional predictor variables. Via a series of Monte-Carlo simulations and using hand radiograph data, we examine the parameter estimation and classification accuracy for the response variable. We find that the robust procedure outperforms some existing robust and non-robust methods when outliers are present, while producing competitive results when outliers are absent. In addition, the proposed method is computationally more efficient than some existing robust alternatives.

Problem

• Developing robust functional logistic regression against outlier sensitivity
• Reducing outlier effects via robust functional principal component analysis
• Improving parameter estimation and classification with M-type estimators

Innovation

• Robust functional principal component analysis for dimension reduction
• M-type estimator for logistic regression coefficient
• Minimizes outlier effects in both response and predictor variables