Eigen-Stratified Models

• URL: http://arxiv.org/abs/2001.10389v1
• Date: Mon, 27 Jan 2020 16:26:08 GMT
• Title: Eigen-Stratified Models
• Authors: Jonathan Tuck, Stephen Boyd
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $m \leq n$ and $m \ll K$. 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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