On the ERM Principle with Networked Data
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 Ustatistics 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 polynomialtime approximation scheme (FPTAS) to solve it.
 Publication:

arXiv eprints
 Pub Date:
 November 2017
 arXiv:
 arXiv:1711.04297
 Bibcode:
 2017arXiv171104297W
 Keywords:

 Computer Science  Machine Learning;
 Computer Science  Data Structures and Algorithms;
 Computer Science  Social and Information Networks;
 Statistics  Machine Learning
 EPrint:
 accepted by AAAI. arXiv admin note: substantial text overlap with arXiv:math/0702683 by other authors