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Abstract:
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Machine learning methods provide a powerful approach for modeling a univariate response, however its application for the multivariate response is limited. We use machine learning approach for modeling longitudinal data in which repeated measurements are observed for a subject over time. We use gradient boosting approach to boost multivariate tree to fit a novel flexible semi-nonparametric marginal model for longitudinal data. In this model, features are modeled non-parametrically using multivariate tree, while feature-time interactions are modeled semi-nonparametrically utilizing P-splines with estimated smoothing parameter. In order to avoid overfitting, we describe a relatively simple in sample cross-validation method which can be used to estimate the optimal boosting iteration and which has the surprising added benefit of stabilizing certain parameter estimates. Our new multivariate tree boosting method is shown to be highly flexible, robust to covariance misspecification and unbalanced designs, and resistant to overfitting in high dimensions. Feature selection is performed using variable importance to identify important features and feature-time interactions.
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