On the ERM Principle with Networked Data

TL;DR

This paper develops a new weighted ERM framework for networked data, providing universal risk bounds and an efficient approximation scheme to optimize example weights, addressing limitations of classical ERM in non-i.i.d. settings.

Contribution

It introduces a general weighted ERM approach with universal risk bounds and a polynomial-time approximation scheme for networked data.

Findings

New universal risk bounds for weighted ERM on networked data

Optimization framework for determining example weights

Efficient FPTAS algorithm for non-convex weight optimization

Abstract

Networked data, in which every training example involves two objects and may share some common objects with others, is used in many machine learning tasks such as learning to rank and link prediction. A challenge of learning from networked examples is that target values are not known for some pairs of objects. In this case, neither the classical i.i.d.\ assumption nor techniques based on complete U-statistics can be used. Most existing theoretical results of this problem only deal with the classical empirical risk minimization (ERM) principle that always weights every example equally, but this strategy leads to unsatisfactory bounds. We consider general weighted ERM and show new universal risk bounds for this problem. These new bounds naturally define an optimization problem which leads to appropriate weights for networked examples. Though this optimization problem is not convex in general, we devise a new fully polynomial-time approximation scheme (FPTAS) to solve it.