Ellipsoidal Multiple Instance Learning

Gabriel Krummenacher, Cheng Soon Ong, Joachim Buhmann
Proceedings of the 30th International Conference on Machine Learning, PMLR 28(2):73-81, 2013.

Abstract

We propose a large margin method for asymmetric learning with ellipsoids, called eMIL, suited to multiple instance learning (MIL). We derive the distance between ellipsoids and the hyperplane, generalising the standard support vector machine. Negative bags in MIL contain only negative instances, and we treat them akin to uncertain observations in the robust optimisation framework. However, our method allows positive bags to cross the margin, since it is not known which instances within are positive. We show that representing bags as ellipsoids under the introduced distance is the most robust solution when treating a bag as a random variable with finite mean and covariance. Two algorithms are derived to solve the resulting non-convex optimization problem: a concave-convex procedure and a quasi-Newton method. Our method achieves competitive results on benchmark datasets. We introduce a MIL dataset from a real world application of detecting wheel defects from multiple partial observations, and show that eMIL outperforms competing approaches.

Cite this Paper

BibTeX
@InProceedings{pmlr-v28-krummenacher13, title = {Ellipsoidal Multiple Instance Learning}, author = {Krummenacher, Gabriel and Soon Ong, Cheng and Buhmann, Joachim}, booktitle = {Proceedings of the 30th International Conference on Machine Learning}, pages = {73--81}, year = {2013}, editor = {Dasgupta, Sanjoy and McAllester, David}, volume = {28}, number = {2}, series = {Proceedings of Machine Learning Research}, address = {Atlanta, Georgia, USA}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v28/krummenacher13.pdf}, url = {https://proceedings.mlr.press/v28/krummenacher13.html}, abstract = {We propose a large margin method for asymmetric learning with ellipsoids, called eMIL, suited to multiple instance learning (MIL). We derive the distance between ellipsoids and the hyperplane, generalising the standard support vector machine. Negative bags in MIL contain only negative instances, and we treat them akin to uncertain observations in the robust optimisation framework. However, our method allows positive bags to cross the margin, since it is not known which instances within are positive. We show that representing bags as ellipsoids under the introduced distance is the most robust solution when treating a bag as a random variable with finite mean and covariance. Two algorithms are derived to solve the resulting non-convex optimization problem: a concave-convex procedure and a quasi-Newton method. Our method achieves competitive results on benchmark datasets. We introduce a MIL dataset from a real world application of detecting wheel defects from multiple partial observations, and show that eMIL outperforms competing approaches.} }
Endnote
%0 Conference Paper %T Ellipsoidal Multiple Instance Learning %A Gabriel Krummenacher %A Cheng Soon Ong %A Joachim Buhmann %B Proceedings of the 30th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2013 %E Sanjoy Dasgupta %E David McAllester %F pmlr-v28-krummenacher13 %I PMLR %P 73--81 %U https://proceedings.mlr.press/v28/krummenacher13.html %V 28 %N 2 %X We propose a large margin method for asymmetric learning with ellipsoids, called eMIL, suited to multiple instance learning (MIL). We derive the distance between ellipsoids and the hyperplane, generalising the standard support vector machine. Negative bags in MIL contain only negative instances, and we treat them akin to uncertain observations in the robust optimisation framework. However, our method allows positive bags to cross the margin, since it is not known which instances within are positive. We show that representing bags as ellipsoids under the introduced distance is the most robust solution when treating a bag as a random variable with finite mean and covariance. Two algorithms are derived to solve the resulting non-convex optimization problem: a concave-convex procedure and a quasi-Newton method. Our method achieves competitive results on benchmark datasets. We introduce a MIL dataset from a real world application of detecting wheel defects from multiple partial observations, and show that eMIL outperforms competing approaches.
RIS
TY - CPAPER TI - Ellipsoidal Multiple Instance Learning AU - Gabriel Krummenacher AU - Cheng Soon Ong AU - Joachim Buhmann BT - Proceedings of the 30th International Conference on Machine Learning DA - 2013/05/13 ED - Sanjoy Dasgupta ED - David McAllester ID - pmlr-v28-krummenacher13 PB - PMLR DP - Proceedings of Machine Learning Research VL - 28 IS - 2 SP - 73 EP - 81 L1 - http://proceedings.mlr.press/v28/krummenacher13.pdf UR - https://proceedings.mlr.press/v28/krummenacher13.html AB - We propose a large margin method for asymmetric learning with ellipsoids, called eMIL, suited to multiple instance learning (MIL). We derive the distance between ellipsoids and the hyperplane, generalising the standard support vector machine. Negative bags in MIL contain only negative instances, and we treat them akin to uncertain observations in the robust optimisation framework. However, our method allows positive bags to cross the margin, since it is not known which instances within are positive. We show that representing bags as ellipsoids under the introduced distance is the most robust solution when treating a bag as a random variable with finite mean and covariance. Two algorithms are derived to solve the resulting non-convex optimization problem: a concave-convex procedure and a quasi-Newton method. Our method achieves competitive results on benchmark datasets. We introduce a MIL dataset from a real world application of detecting wheel defects from multiple partial observations, and show that eMIL outperforms competing approaches. ER -
APA
Krummenacher, G., Soon Ong, C. & Buhmann, J.. (2013). Ellipsoidal Multiple Instance Learning. Proceedings of the 30th International Conference on Machine Learning, in Proceedings of Machine Learning Research 28(2):73-81 Available from https://proceedings.mlr.press/v28/krummenacher13.html.

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