A robust scalar-on-function logistic regression for classification

TL;DR

This paper introduces a robust partial least squares approach for scalar-on-function logistic regression, effectively handling outliers and improving classification accuracy in functional data analysis.

Contribution

It proposes a novel weighted likelihood estimation method using functional partial least squares to enhance robustness against outliers in scalar-on-function logistic regression.

Findings

Outperforms existing methods in Monte Carlo simulations

Demonstrates improved classification accuracy on real data

Effectively downweighs outliers in functional predictors

Abstract

Scalar-on-function logistic regression, where the response is a binary outcome and the predictor consists of random curves, has become a general framework to explore a linear relationship between the binary outcome and functional predictor. Most of the methods used to estimate this model are based on the least-squares type estimators. However, the least-squares estimator is seriously hindered by outliers, leading to biased parameter estimates and an increased probability of misclassification. This paper proposes a robust partial least squares method to estimate the regression coefficient function in the scalar-on-function logistic regression. The regression coefficient function represented by functional partial least squares decomposition is estimated by a weighted likelihood method, which downweighs the effect of outliers in the response and predictor. The estimation and classification performance of the proposed method is evaluated via a series of Monte Carlo experiments and a strawberry puree data set. The results obtained from the proposed method are compared favorably with existing methods.