Learning in the presence of malicious errors
SIAM Journal on Computing
The nature of statistical learning theory
The nature of statistical learning theory
Phase transitions and the search problem
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
Solving the multiple instance problem with axis-parallel rectangles
Artificial Intelligence
A framework for multiple-instance learning
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Propositionalization approaches to relational data mining
Relational Data Mining
Phase Transitions in Relational Learning
Machine Learning
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
Relational learning as search in a critical region
The Journal of Machine Learning Research
Image Categorization by Learning and Reasoning with Regions
The Journal of Machine Learning Research
ICML '05 Proceedings of the 22nd international conference on Machine learning
Marginalized multi-instance kernels
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Where the really hard problems are
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Phase transitions within grammatical inference
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
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This paper is concerned with Relational Support Vector Machines, at the intersection of Support Vector Machines (SVM) and Inductive Logic Programming or Relational Learning. The so-called phase transition framework, originally developed for constraint satisfaction problems, has been extended to relational learning and it has provided relevant insights into the limitations and difficulties thereof. The goal of this paper is to examine relational SVMs and specifically Multiple Instance (MI) Kernels along the phase transition framework. A relaxation of the MI-SVM problem formalized as a linear programming problem (LPP) is defined and we show that the LPP satisfiability rate induces a lower bound on the MI-SVM generalization error. An extensive experimental study shows the existence of a critical region, where both LPP unsatisfiability and MI-SVM error rates are high. An interpretation for these results is proposed.