  Regression is an important task in machine learning and data mining. It has
several applications in various domains, including finance, biomedical, and
computer vision. Recently, network Lasso, which estimates local models by
making clusters using the network information, was proposed and its superior
performance was demonstrated. In this study, we propose a simple yet effective
local model training algorithm called the fast anchor regularized local linear
method (FALL). More specifically, we train a local model for each sample by
regularizing it with precomputed anchor models. The key advantage of the
proposed algorithm is that we can obtain a closed-form solution with only
matrix multiplication; additionally, the proposed algorithm is easily
interpretable, fast to compute and parallelizable. Through experiments on
synthetic and real-world datasets, we demonstrate that FALL compares favorably
in terms of accuracy with the state-of-the-art network Lasso algorithm with
significantly smaller training time (two orders of magnitude).
