Eigen-Stratified Models

01/27/2020 ∙ by Jonathan Tuck, et al. ∙ 6

Stratified models depend in an arbitrary way on a selected categorical feature that takes K values, and depend linearly on the other n features. Laplacian regularization with respect to a graph on the feature values can greatly improve the performance of a stratified model, especially in the low-data regime. A significant issue with Laplacian-regularized stratified models is that the model is K times the size of the base model, which can be quite large. We address this issue by formulating eigen-stratifed models, which are stratified models with an additional constraint that the model parameters are linear combinations of some modest number m of bottom eigenvectors of the graph Laplacian, i.e., those associated with the m smallest eigenvalues. With eigen-stratified models, we only need to store the m bottom eigenvectors and the corresponding coefficients as the stratified model parameters. This leads to a reduction, sometimes large, of model size when m ≤ n and m ≪ K. In some cases, the additional regularization implicit in eigen-stratified models can improve out-of-sample performance over standard Laplacian regularized stratified models.

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