Pinball loss¶

pinball loss in Quantile Regression¶

• https://mindfulmodeler.substack.com/p/how-i-made-peace-with-quantile-regression

  diff = y_true - y_pred
  pinball_loss = np.maximum(quantile * diff, (quantile - 1) * diff).mean()
  

• assume quantile = 0.1 and y_true = 100

• if y_pred = 97 (y_pred < y_true, underpredict): loss = 0.1 * (100 - 97) = 3 * 0.1

• if y_pred = 103 (y_pred > y_true, overpredict): loss = (1 - 0.1) * (103 - 100) = 3 * 0.9

• loss is asymmetric, more penalty for overpredict

• expect the model to underpredict 90% of the time and overpredict 10% of the time

• the predict mean is below the true - equivalent to the 10% quantile