Probability and Statistical Foundations
Reason about uncertainty precisely, then meet the central problem of learning from data: separating the error you can remove from the error you cannot.
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Possible Worlds and the Axioms
25 min · 100 XPSample spaces, events, and the two axioms every other rule is derived from, including the complement and addition rules.
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Bayes and the Base Rate
25 min · 100 XPReversing a conditional probability, the law of total probability, and why a highly accurate test for a rare condition still yields mostly false positives.
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Reducible and Irreducible Error
20 min · 100 XPThe Y = f(X) + e framing, why some error can never be removed, and the difference between fitting for prediction and fitting for inference.
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Bias, Variance, and Cross-Validation
30 min · 120 XPThe exact three-term decomposition of expected test error, and how k-fold resampling estimates that error honestly from data you already have.
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Entropy and Information Gain
30 min · 120 XPMeasure uncertainty in bits, then measure how much a question removes - the quantity a decision tree greedily maximises at every split.
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