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Publication Detail
Empirical Risk Minimization and Stochastic Gradient Descent for Relational Data
  • Publication Type:
  • Authors:
    Veitch V, Austern M, Zhou W, Blei DM, Orbanz P
  • Publication date:
  • Published proceedings:
    Proceedings of Machine Learning Research, vol 89
  • Name of conference:
    22nd International Conference on Artificial Intelligence and Statistics - AISTATS 2019
  • Conference place:
    Okinawa, Japan
  • Conference start date:
  • Conference finish date:
  • Keywords:
    stat.ML, stat.ML, cs.LG, cs.SI
  • Notes:
    Accepted as AISTATS 2019 Oral
Empirical risk minimization is the main tool for prediction problems, but its extension to relational data remains unsolved. We solve this problem using recent ideas from graph sampling theory to (i) define an empirical risk for relational data and (ii) obtain stochastic gradients for this empirical risk that are automatically unbiased. This is achieved by considering the method by which data is sampled from a graph as an explicit component of model design. By integrating fast implementations of graph sampling schemes with standard automatic differentiation tools, we provide an efficient turnkey solver for the risk minimization problem. We establish basic theoretical properties of the procedure. Finally, we demonstrate relational ERM with application to two non-standard problems: one-stage training for semi-supervised node classification, and learning embedding vectors for vertex attributes. Experiments confirm that the turnkey inference procedure is effective in practice, and that the sampling scheme used for model specification has a strong effect on model performance. Code is available at https://github.com/wooden-spoon/relational-ERM.
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