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Financial Machine Learning / Learning Theory and Generalisation

Derivation: A Mathematical Decomposition of Bias and Variance

The previous lesson stated the bias-variance trade-off informally and confirmed it empirically via resampling. This note derives the exact algebraic identity behind it: for squared-error loss, expected test error splits additively into exactly three non-negative terms — variance, squared bias, and irreducible noise — with no cross-terms and no approximation.

In this lesson

  1. Learning objectives
  2. Setup
  3. The decomposition
  4. Worked numerical check

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