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What does the quantile (pinball) loss measure?

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Answer

  • For quantile tau in (0, 1), pinball loss(r) = tau * r if r > 0 else (tau - 1) * r, where r  =  y  −  yhatr\; = \;y\; - \;y_{\mathrm{hat}}.
  • Minimizing it fits the conditional tau-quantile of y given x. τ  =  0.5\tau\; = \;0.5 → median (equivalent to MAE). τ  =  0.9\tau\; = \;0.9 → 90th percentile prediction — great for delivery-time SLAs, inventory sizing, risk quantiles.
  • Fit multiple quantiles to construct prediction intervals: e.g., 0.05 and 0.95 give a 90% interval.
  • Used by quantile regression, LightGBM's quantile objective, and neural nets with pinball loss.
Check yourself — multiple choice
  • Same as MSE
  • Asymmetric loss that fits the τ-quantile of the conditional distribution
  • Only defined for τ = 0.5
  • Not related to quantile regression

Pinball loss fits any conditional quantile — median at τ=0.5, tails at τ=0.05/0.95.

#metrics-regression#regression

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