The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
Least Squares Support Vector Machine Classifiers
Neural Processing Letters
Node-and edge-deletion NP-complete problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Large Margin Methods for Structured and Interdependent Output Variables
The Journal of Machine Learning Research
A general regression technique for learning transductions
ICML '05 Proceedings of the 22nd international conference on Machine learning
Learning as search optimization: approximate large margin methods for structured prediction
ICML '05 Proceedings of the 22nd international conference on Machine learning
Learning hierarchical multi-category text classification models
ICML '05 Proceedings of the 22nd international conference on Machine learning
Learning structured prediction models: a large margin approach
ICML '05 Proceedings of the 22nd international conference on Machine learning
EMNLP '02 Proceedings of the ACL-02 conference on Empirical methods in natural language processing - Volume 10
Simulated Annealing for Convex Optimization
Mathematics of Operations Research
Training structural SVMs when exact inference is intractable
Proceedings of the 25th international conference on Machine learning
Protein-ligand interaction prediction
Bioinformatics
Beating the Random Ordering is Hard: Inapproximability of Maximum Acyclic Subgraph
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Combinatorial Optimization: Theory and Algorithms
Combinatorial Optimization: Theory and Algorithms
Probabilistic structured predictors
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Input space versus feature space in kernel-based methods
IEEE Transactions on Neural Networks
Guest editors' introduction: special issue of selected papers from ECML PKDD 2009
Data Mining and Knowledge Discovery
Guest editors' introduction: Special Issue from ECML PKDD 2009
Machine Learning
On Structured Output Training: Hard Cases and an Efficient Alternative
ECML PKDD '09 Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part I
Hierarchical annotation of medical images
Pattern Recognition
Tree ensembles for predicting structured outputs
Pattern Recognition
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We consider a class of structured prediction problems for which the assumptions made by state-of-the-art algorithms fail. To deal with exponentially sized output sets, these algorithms assume, for instance, that the best output for a given input can be found efficiently. While this holds for many important real world problems, there are also many relevant and seemingly simple problems where these assumptions do not hold. In this paper, we consider route prediction, which is the problem of finding a cyclic permutation of some points of interest, as an example and show that state-of-the-art approaches cannot guarantee polynomial runtime for this output set. We then present a novel formulation of the learning problem that can be trained efficiently whenever a particular `super-structure counting' problem can be solved efficiently for the output set. We also list several output sets for which this assumption holds and report experimental results.