In-sample calibration of logistic regression
ProofIntermediate⏱ 30 minClassical MLcalibrationscore equationslimits
Problem
Show that at any stationary point , and deduce that with an intercept the predicted and observed positive counts agree exactly. Then explain precisely why this is a weak form of calibration.
Write a complete argument. Every inequality you use should be one you could state precisely.
Solution
Opening this before you have a real attempt on paper is the fastest way to feel like you understand something you cannot reproduce.
Related problems
All problems| Solved | Problem | Field | Type | Difficulty | Time |
|---|---|---|---|---|---|
| Convexity of the logistic loss | Classical ML | Proof | 15 min | ||
| IRLS is a weighted least-squares solve | Classical ML | Proof | 30 min | ||
| Logistic regression diverges on separable data | Classical ML | Proof | 30 min | ||
| The floor that correlated failure puts under redundancy | AI Systems | Proof | 30 min |