The loss used to predict a quantile instead of a mean: for quantile τ, an under-prediction costs τ × error and an over-prediction costs (1 − τ) × error. Minimizing it with τ = 0.9 gives a forecast that actual values fall below 90% of the time.
Card 1 of 259. Answer: The loss used to predict a quantile instead of a mean: for quantile τ, an under-prediction costs τ × error and an over-prediction costs (1 − τ) × error. Minimizing it with τ = 0.9 gives a forecast that actual values fall below 90% of the time.
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Pinball loss, also called quantile loss, is max(τ(y − ŷ), (τ − 1)(y − ŷ)). Its asymmetry moves the optimal prediction from the mean to the τ-th quantile; with τ = 0.5 it is half the absolute error, and the optimum is the median. It is the loss behind quantile regression (Koenker and Bassett, 1978), and gradient boosting libraries offer it as an objective.
Example with τ = 0.9 and actual demand of 100 units: a forecast of 80 is short by 20 and costs 0.9 × 20 = 18, while a forecast of 120 is over by 20 and costs 0.1 × 20 = 2. Running short is nine times as expensive, so the model learns to aim high, which is right for stock where an empty shelf costs more than a spare unit.
The common use is a prediction interval: train for τ = 0.05 and τ = 0.95 and you get a 90% interval that can widen and narrow with the inputs, unlike a fixed ± 2σ around a mean forecast. Check its coverage on held-out data, since nominal 90% often isn't, and watch for quantile crossing, where separately trained quantiles come out in the wrong order.
