Localized Linear Regression in Networked Data
This work addresses the problem of efficient learning in massive networked datasets for researchers in machine learning and data science, offering incremental theoretical analysis of an existing method.
The paper analyzes the statistical properties of network Lasso (nLasso) for localized linear regression on networked data, providing a sufficient condition on network structure and labeled data for accurate learning from few labels.
The network Lasso (nLasso) has been proposed recently as an efficient learning algorithm for massive networked data sets (big data over networks). It extends the well-known least absolute shrinkage and selection operator (Lasso) from learning sparse (generalized) linear models to network models. Efficient implementations of the nLasso have been obtained using convex optimization methods lending to scalable message passing protocols. In this paper, we analyze the statistical properties of nLasso when applied to localized linear regression problems involving networked data. Our main result is a sufficient condition on the network structure and available label information such that nLasso accurately learns a localized linear regression model from a few labeled data points. We also provide an implementation of nLasso for localized linear regression by specializing a primaldual method for solving the convex (non-smooth) nLasso problem.