Interpretable Predictive Modeling for Climate Variables with Weighted Lasso
An important family of problems in climate science focus on finding predictive relationships between various climate variables. In this paper, we consider the problem of predicting monthly deseasonalized land temperature at different locations worldwide based on sea surface temperature (SST). Contrary to popular belief on the trade-off between (a) simple interpretable but inaccurate models and (b) complex accurate but uninterpretable models, we introduce a weighted Lasso model for the problem which yields interpretable results while being highly accurate. Covariate weights in the regularization of weighted Lasso are pre-determined, and proportional to the spatial distance of the covariate (sea surface location) from the target (land location). We establish finite sample estimation error bounds for weighted Lasso, and illustrate its superior empirical performance and interpretability over complex models such as deep neural networks (Deep nets) and gradient boosted trees (GBT). We also present a detailed empirical analysis of what went wrong with Deep nets here, which may serve as a helpful guideline for application of Deep nets to small sample scientific problems.