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A Bayesian Approach to Graph Regression with Relevant Subgraph Selection

2009

Conference Paper

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Many real-world applications with graph data require the efficient solution of a given regression task as well as the identification of the subgraphs which are relevant for the task. In these cases graphs are commonly represented as binary vectors of indicators of subgraphs, giving rise to an intractable input dimensionality. An efficient solution to this problem was recently proposed by a Lasso-type method where the objective function optimization over an intractable number of variables is reformulated as a dual mathematical programming problem over a small number of variables but a large number of constraints. The dual problem is then solved by column generation where the subgraphs corresponding to the most violated constraints are found by weighted subgraph mining. This paper proposes an extension of this method to a fully Bayesian approach which defines a prior distribution on the parameters and integrate them out from the model, thus providing a posterior distribution on the target variable as opposed to a single estimate. The advantage of this approach is that the extra information given by the target posterior distribution can be used for improving the model in several ways. In this paper, we use the target posterior variance as a measure of uncertainty in the prediction and show that, by rejecting unconfident predictions, we can improve state-of-the-art performance on several molecular graph datasets.

Author(s): Chiappa, S. and Saigo, H. and Tsuda, K.
Book Title: SIAM International Conference on Data Mining
Journal: Proceedings of the 2009 SIAM International Conference on Data Mining (SDM 2009)
Pages: 295-304
Year: 2009
Month: May
Day: 0
Editors: Park, H. , S. Parthasarathy, H. Liu
Publisher: Society for Industrial and Applied Mathematics

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: SDM 2009
Event Place: Sparks, NV, USA

Address: Philadelphia, PA, USA
Institution: Society for Industrial and Applied Mathematics
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{5653,
  title = {A Bayesian Approach to Graph Regression with Relevant Subgraph Selection},
  author = {Chiappa, S. and Saigo, H. and Tsuda, K.},
  journal = {Proceedings of the 2009 SIAM International Conference on Data Mining (SDM 2009)},
  booktitle = {SIAM International Conference on Data Mining},
  pages = {295-304},
  editors = {Park, H. , S. Parthasarathy, H. Liu},
  publisher = {Society for Industrial and Applied Mathematics},
  organization = {Max-Planck-Gesellschaft},
  institution = {Society for Industrial and Applied Mathematics},
  school = {Biologische Kybernetik},
  address = {Philadelphia, PA, USA},
  month = may,
  year = {2009},
  month_numeric = {5}
}