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Computational Complexity of Learning

Before setting out to build a learning system, practitioners, students, and consumers of machine learning should be able to rigorously show that learning methods can be applied successfully to a given learning problem. Using statistics and probability, we can show how a supervised classifying learning system can achieve a level of success called “probably approximately correct.” Given the desired probability that a learner will correctly classify a problem, we can determine how expensive it will be to approximate the target function in terms of computation (generally time and space) and how many training examples would be required to achieve that level of correctness.

The Hoeffding Inequality showed that learning is a theoretical possibility.

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