Mathematical Foundations of Learning Theory
Machine Learning relates to many different domains: data analysis, data processing, information retrieval, statistics, knowledge discovery, reasoning under uncertainty...
But the main distinguishing feature of the learning problem is that it requires a form of reasoning which is non-deductive: it requires induction, transduction, abduction or generalization.
As a result, the learning problem has its roots in the following theories
- Logic: theory of induction
- Inductive Reasoning (Wikipedia)
- Inquiry Logic of Science (Wikipedia)
- Abductive Reasoning (Wikipedia)
- Conjectures Peter Flach's PhD thesis
- Peter A. Flach. Logical characterisations of inductive learning. In: Handbook of defeasible reasoning and uncertainty management systems, Vol. 4: Abductive reasoning and learning, Dov M. Gabbay and Rudolf Kruse, editors, pages 155--196. Kluwer Academic Publishers, October 2000. pdf
- Decision Theory
- Probability Theory
- Statistics
- Estimation Theory
- Approximation Theory
- Game Theory
- Inductive Inference
- Computation Theory
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