Machine Learning
The hardness of approximate optima in lattices, codes, and systems of linear equations
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
A decision-theoretic generalization of on-line learning and an application to boosting
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Machine Learning
The covering number in learning theory
Journal of Complexity
Duality and Geometry in SVM Classifiers
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
A robust minimax approach to classification
The Journal of Machine Learning Research
The Minimum Error Minimax Probability Machine
The Journal of Machine Learning Research
Neural Computation
Sparseness vs Estimating Conditional Probabilities: Some Asymptotic Results
The Journal of Machine Learning Research
ν-support vector machine as conditional value-at-risk minimization
Proceedings of the 25th international conference on Machine learning
Support Vector Machines
Sparse Semi-supervised Learning Using Conjugate Functions
The Journal of Machine Learning Research
Consistency of support vector machines and other regularized kernel classifiers
IEEE Transactions on Information Theory
On the optimal parameter choice for ν-support vector machines
IEEE Transactions on Pattern Analysis and Machine Intelligence
A geometric approach to Support Vector Machine (SVM) classification
IEEE Transactions on Neural Networks
A unified classification model based on robust optimization
Neural Computation
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There are two main approaches to binary classification problems: the loss function approach and the uncertainty set approach. The loss function approach is widely used in real-world data analysis. Statistical decision theory has been used to elucidate its properties such as statistical consistency. Conditional probabilities can also be estimated by using the minimum solution of the loss function. In the uncertainty set approach, an uncertainty set is defined for each binary label from training samples. The best separating hyperplane between the two uncertainty sets is used as the decision function. Although the uncertainty set approach provides an intuitive understanding of learning algorithms, its statistical properties have not been sufficiently studied. In this paper, we show that the uncertainty set is deeply connected with the convex conjugate of a loss function. On the basis of the conjugate relation, we propose a way of revising the uncertainty set approach so that it will have good statistical properties such as statistical consistency. We also introduce statistical models corresponding to uncertainty sets in order to estimate conditional probabilities. Finally, we present numerical experiments, verifying that the learning with revised uncertainty sets improves the prediction accuracy.