A bayesian approach to graph regression with relevant subgraph selection

Silvia Chiappa, Hiroto Saigo, Koji Tsuda

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

1 被引用数 (Scopus)

抄録

Many real-world applications with graph data require the 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 high dimensional binary vectors of indicators of subgraphs. However, since the dimensionality of such indicator vectors can be high even for small datasets, traditional regression algorithms become intractable and past approaches used to preselect a feasible subset of subgraphs. A different approach was recently proposed by a Lasso-type method where the objective function optimization with a large number of variables is reformulated as a dual mathematical programming problem with 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 Bayesian approach in which the regression parameters are considered as random variables and integrated out from the model likelihood, thus providing a posterior distribution on the target variable as opposed to a point estimate. We focus on a linear regression model with a Gaussian prior distribution on the parameters. We evaluate our approach on several molecular graph datasets and analyze whether the uncertainty in the target estimate given by the target posterior distribution variance can be used to improve model performance and therefore provides useful additional information.

本文言語英語
ホスト出版物のタイトルSociety for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics 133
ページ291-300
ページ数10
出版ステータス出版済み - 12 1 2009
外部発表はい
イベント9th SIAM International Conference on Data Mining 2009, SDM 2009 - Sparks, NV, 米国
継続期間: 4 30 20095 2 2009

出版物シリーズ

名前Society for Industrial and Applied Mathematics - 9th SIAM International Conference on Data Mining 2009, Proceedings in Applied Mathematics
1

その他

その他9th SIAM International Conference on Data Mining 2009, SDM 2009
国/地域米国
CitySparks, NV
Period4/30/095/2/09

All Science Journal Classification (ASJC) codes

  • 計算理論と計算数学
  • ソフトウェア
  • 応用数学

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