Conditional Expectation as an L² Projection

Medium·12 min read·Interactive lab
ProbabilityHilbert SpacesConditional Expectation
Interactive VizHard30 min lab·Probability & Statistics·Core hiring signal5 challenges

Conditional Expectation as an L² Projection

Probability · Projection · Regression

Explore how E[X|Y] is the orthogonal projection onto L²(σ(Y)): the minimal MSE predictor that exhausts all information in Y. Verify the projection theorem numerically via an information ladder and orthogonality diagnostics.

Loading interactive lab…

Role relevance

Quant ResearcherPricing QuantRisk Quant

Continue with

Go deeper in the course
Article

Explored the parameters? Review the full derivation in code.

View Notebook