- Block 16 — The regression metrics
- Objective
- define
MAE = (1/n) Σ |y − ŷ|, establish that its unit is the unit
of the target — "off by $58,691 on an apartment worth $591,687" — and prove that
the constant minimizing it is the median, flat on [553.71, 560.82] here;
derive the consequence that an MAE-trained model estimates the conditional
median, recovering 139.84 against a true 140.00 where least squares returns
158.74; measure robustness at Δ = 6,400, MAE ×1.73 against RMSE ×6.79;
exhibit the kink at zero, its subdifferential [−1, 1] and its cost, 76
iterations against 7; document sample_weight, multioutput and the
neg_mean_absolute_error sign; supply the missing baseline, 226.48 against
58.69, an improvement of 74.09 percent; price a weighted fit at $176,536
against $184,505; state the linear-cost assumption and exhibit a case where MAE
prefers the model with twelve catastrophic errors; find 17 apartments
under-predicted 17 times out of 17 behind an aggregate of 58.69; and attach a
bootstrap interval of $50,768 to $67,055. - Estimated duration
- 120 minutes
- Prerequisites
- chapters 010, 021, 026, 029, 030, 044, 045, 047 and 066
- Associated quizzes
067.1-quiz-definition-and-units.md to
067.9-quiz-reporting-mae.md