Hints

The systematic use of hints in the learning-from-examples paradigm is the subject of this review. Hints are the properties of the target function that are known to use independently of the training examples. The use of hints is tantamount to combining rules and data in learning, and is compatible with different learning models, optimization techniques, and regularization techniques. The hints are represented to the learning process by virtual examples, and the training examples of the target function are treated on equal footing with the rest of the hints. A balance is achieved between the information provided by the different hints through the choice of objective functions and learning schedules. The Adaptive Minimization algorithm achieves this balance by relating the performance on each hint to the overall performance. The application of hints in forecasting the very noisy foreign-exchange markets is illustrated. On the theoretical side, the information value of hints is contrasted to the complexity value and related to the VC dimension.