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  A Bayesian Approach to Graph Regression with Relevant Subgraph Selection

Chiappa, S., Saigo, H., & Tsuda, K. (2009). A Bayesian Approach to Graph Regression with Relevant Subgraph Selection. In H. Park, S. Parthasarathy, & H. Liu (Eds.), 2009 SIAM International Conference on Data Mining (pp. 295-304). Philadelphia, PA, USA: Society for Industrial and Applied Mathematics.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-C4E3-9 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-F924-D
Genre: Conference Paper

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 Creators:
Chiappa, S1, 2, Author              
Saigo, H, Author              
Tsuda, K1, 2, Author              
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: 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.

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Language(s):
 Dates: 2009-05
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: 5653
DOI: 10.1137/1.9781611972795.26
 Degree: -

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Title: SIAM International Conference on Data Mining (SDM 2009)
Place of Event: Sparks, NV, USA
Start-/End Date: 2009-04-30 - 2009-05-02

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Title: 2009 SIAM International Conference on Data Mining
Source Genre: Proceedings
 Creator(s):
Park, H, Editor
Parthasarathy, S, Editor
Liu, H, Editor
Affiliations:
-
Publ. Info: Philadelphia, PA, USA : Society for Industrial and Applied Mathematics
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 295 - 304 Identifier: ISBN: 978-0-89871-682-5