Supervised Kernel PCA For Longitudinal Data
| Autor: | Staples, Patrick, Ouyang, Min, Dougherty, Robert F., Ryslik, Gregory A., Dagum, Paul |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 17 pages, 4 figures, 1 table |
| Databáze: | arXiv |
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