# Foundations of Learning Theory

Machine Learning relates to many different domains: data analysis, data processing, information retrieval, statistics, knowledge discovery, reasoning under uncertainty, game theory, decision theory...

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

- Formalizing decision-making and interactions
- Decision Theory W
- Auction Theory W
- Rational Choice Theory, Public choice theory, Social choice theory, General equilibrium theory W...
- Portfolio Theory W, Sharpe ratio W
- Theory of Risk Aversion W, Utility W
- Game Theory W, W, What is Game Theory?, by D. K. Levine.
- Finance, Gambling Theory W, Arbitrage W, Prediction Markets W, Efficient market theory W, Value-at-Risk W, Hedge W
- Interpretation of Probability W

- Formalizing information and regularity
- Information Theory W
- Algorithmic Information Theory W
- Compression W, Universal compression
- Randomness W

- Formalizing Inference
- Logic Inference
- Inductive Inference W
- Statistical Inference
- Estimation Theory

- Tools
- Probability Theory
- Optimization Theory
- Algorithms, Computation Theory
- Functional Analysis
- Approximation Theory

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