Lazy Lasso for local regression

Locally weighted regression is a technique that predicts the response for new data items from their neighbors in the training data set, where closer data items are assigned higher weights in the prediction. However, the original method may suffer from overfitting and fail to select the relevant variables. In this paper we propose combining a regularization approach with locally weighted regression to achieve sparse models. Specifically, the lasso is a shrinkage and selection method for linear regression. We present an algorithm that embeds lasso in an iterative procedure that alternatively computes weights and performs lasso-wise regression. The algorithm is tested on three synthetic scenarios and two real data sets. Results show that the proposed method outperforms linear and local models for several kinds of scenarios