Semi-parametric Functional Classification via Path Signatures Logistic Regression
This work addresses limitations in functional data analysis for researchers and practitioners dealing with irregularly sampled data, offering a novel semi-parametric approach.
The paper tackled the problem of classifying vector-valued functional data with scalar covariates by proposing Path Signatures Logistic Regression (PSLR), which outperformed traditional functional classifiers in accuracy, robustness, and interpretability, especially under non-uniform sampling schemes.
We propose Path Signatures Logistic Regression (PSLR), a semi-parametric framework for classifying vector-valued functional data with scalar covariates. Classical functional logistic regression models rely on linear assumptions and fixed basis expansions, which limit flexibility and degrade performance under irregular sampling. PSLR overcomes these issues by leveraging truncated path signatures to construct a finite-dimensional, basis-free representation that captures nonlinear and cross-channel dependencies. By embedding trajectories as time-augmented paths, PSLR extracts stable, geometry-aware features that are robust to sampling irregularity without requiring a common time grid, while still preserving subject-specific timing patterns. We establish theoretical guarantees for the existence and consistent estimation of the optimal truncation order, along with non-asymptotic risk bounds. Experiments on synthetic and real-world datasets show that PSLR outperforms traditional functional classifiers in accuracy, robustness, and interpretability, particularly under non-uniform sampling schemes. Our results highlight the practical and theoretical benefits of integrating rough path theory into modern functional data analysis.