Supervised Kernel PCA For Longitudinal Data
This work addresses the problem of robust prediction and inference for longitudinal data in statistical learning, representing an incremental improvement over existing methods.
The paper tackled the challenge of supervised dimension reduction for longitudinal data by deriving a decomposition of the Hilbert-Schmidt Independence Criterion to handle between- and within-cluster dependencies separately, proposing the sklPCA technique, which achieved superior model accuracy compared to the extended model.
In statistical learning, high covariate dimensionality poses challenges for robust prediction and inference. To address this challenge, supervised dimension reduction is often performed, where dependence on the outcome is maximized for a selected covariate subspace with smaller dimensionality. Prevalent dimension reduction techniques assume data are $i.i.d.$, which is not appropriate for longitudinal data comprising multiple subjects with repeated measurements over time. In this paper, we derive a decomposition of the Hilbert-Schmidt Independence Criterion as a supervised loss function for longitudinal data, enabling dimension reduction between and within clusters separately, and propose a dimensionality-reduction technique, $sklPCA$, that performs this decomposed dimension reduction. We also show that this technique yields superior model accuracy compared to the model it extends.