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A Bayesian Approach to Graph Regression with Relevant Subgraph Selection

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons83858

Chiappa,  S
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84183

Saigo,  H
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84265

Tsuda,  K
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Zitation

Chiappa, S., Saigo, H., & Tsuda, K. (2009). A Bayesian Approach to Graph Regression with Relevant Subgraph Selection. Proceedings of the 2009 SIAM International Conference on Data Mining (SDM 2009), 295-304.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0013-C4E3-9
Zusammenfassung
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.