This paper introduces logistic regression with sparse and smooth regularizations (LR-SS), a novel framework that simultaneously enhances both classification and feature extraction capabilities of standard logistic regression. By incorporating a family of symmetric smoothness constraints into sparse logistic regression, LR-SS uniquely preserves underlying structures inherent in structured data, distinguishing it from existing approaches. Within the minorization–maximization (MM) framework, we develop an efficient optimization algorithm that combines coordinate descent with soft-thresholding techniques. Through extensive experiments on both simulated and real-world datasets, including time series and image data, we demonstrate that LR-SS significantly outperforms conventional sparse logistic regression in classification tasks while providing more interpretable feature extraction. The results highlight LR-SS’s ability to leverage sparse and symmetric smooth regularizations for capturing intrinsic data structures, making it particularly valuable for machine learning applications requiring both predictive accuracy and model interpretability.

This paper introduces logistic regression with sparse and smooth regularizations (LR-SS), a novel framework that enhances classification and feature extraction by incorporating both sparsity and smoothness constraints. We propose a family of smooth regularizations designed to capture temporal and spatial structural patterns inherent in data. The optimization problem is solved efficiently using the minorization-maximization (MM) framework combined with coordinate descent and soft-thresholding techniques. Through extensive experiments on both simulated and real-world datasets, including time series and image data, we demonstrate that LR-SS generally outperforms conventional sparse logistic regression methods in terms of classification accuracy and feature extraction quality. Therefore, LR-SS provides a powerful tool for machine learning applications requiring both accurate prediction and strong interpretability.

Background: The timely identification of mild cognitive impairment (MCI) in Parkinson’s disease (PD) is essential for early intervention and clinical management, yet it remains a challenge in practice. Methods: We conducted an analysis of 3,154 clinical visits from 896 participants in the Parkinson’s Progression Markers Initiative (PPMI) cohort. Participants were divided into two groups: cognitively normal (PD-NC, MoCA ≥ 26) and MCI (PD-MCI, 21 ≤ MoCA ≤ 25). To ensure no visit-level information leakage, subject-level stratified sampling was employed to split the data into training (70%) and hold-out test (30%) sets. From an initial set of twelve routinely assessed clinical features, seven were selected using LASSO logistic regression: Age, Sex, Education Years, Disease Duration, UPDRS-I, UPDRS-III, and Geriatric Depression Scale (GDS). Four machine learning models—logistic regression (LR), support vector machine (SVM), random forest (RF), and XGBoost—were trained using subject-level stratified 10-fold cross-validation with Bayesian optimization. Probabilistic outputs were dichotomized using three thresholding strategies: (i) default 0.5, (ii) F1-score maximization, and (iii) Youden index maximization. Results: On the independent test set, SVM achieved the highest overall performance with AUC-ROC of 0.7252 and AUC-PR of 0.5008. LR also performed competitively despite its simplicity. RF achieved the top performance in recall, reaching 0.8150. Feature importance analysis consistently highlighted Age, Education Years, and Disease Duration as the most informative predictors for distinguishing PD-MCI. Conclusion: This study developed and validated robust machine learning models for PD-MCI classification using only standard clinical assessments. The use of subject-level stratified design and Bayesian optimization enabled rigorous model evaluation and reduced overfitting risk. The results support the potential for data-driven, interpretable tools to enhance early cognitive impairment screening in PD care.