Mathematics / advanced
Statistical learning theory
Understand generalization through uniform convergence, capacity, stability, localized complexity, and online regret.
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Module 01 advanced
Statistical learning theory
Understand generalization through uniform convergence, capacity, stability, localized complexity, and online regret.
- 01
Risk, empirical risk, and excess risk
Separate population performance, sample fit, class approximation and optimization error.
29 min - 02
PAC learning and uniform convergence
Keep confidence, accuracy, realizability and sampling assumptions visible in finite-class guarantees.
29 min - 03
VC dimension and growth functions
Measure binary class capacity through realizable label patterns rather than parameter count.
29 min - 04
Rademacher complexity and contraction
Measure a class’s ability to align with random signs and transfer that control through Lipschitz losses.
29 min - 05
Covering numbers and chaining
Approximate a class at several resolutions and account for the geometry hidden by a single net.
29 min - 06
Algorithmic stability and generalization
Bound the change caused by replacing one observation and distinguish signed expected gaps from high probability control.
29 min - 07
Margins and surrogate calibration
Connect score confidence to generalization while checking that a surrogate targets classification.
29 min - 08
Localized complexities and fast rates
Use small excess-risk neighborhoods and variance control without promising universal inverse-sample rates.
29 min - 09
Online convex learning and regret
Compare a sequence of decisions with the best fixed hindsight decision without assuming iid losses.
29 min - 10
Distribution shift and impossibility results
Identify what changes between training and deployment and which assumptions make transfer identifiable.
29 min