And the loss function weights the values larger than this number at only a third of the weight given to values less than it. Thus, it's sort of intuitive that the scales are balanced when the $\tau$ th quantile is used as the inflection point for the loss function.

2019年12月10日 · I'm not sure the above sentence is true, but I read it here, here and here that quantile loss function percentile 0.5 is MAE (mean absolute error).

2023年9月14日 · $\begingroup$ (1) I hope you plan on evaluating the loss with different predicitions for your two $\alpha$ levels, since a useful 20% quantile prediction should be quite different from a good 80% quantile prediction.

2024年1月16日 · $\begingroup$ I am a demand forecaster, and I approve this message. Seriously, "real" costs are likely quite nonlinear, but they are extremely hard to pin down to any degree of precision (what is the "real" cost of a stockout when you can't observe demand?), and finance "costs" (including costs of capital tied up in inventory, e.g. WACC) are often …

2020年6月9日 · Meanwhile, quantile loss is characterized by different angles (as in the picture below) for all quantiles except the median. On the other hand, the image of the ball hitting a pin instead of the wall is not a very helpful analogy to the picture of the quantile loss function either.

2018年6月24日 · How does quantile regression work here i.e. how is the model trained? When creating the classifier, you've passed loss='quantile' along with alpha=0.95. You are optimizing quantile loss for 95th percentile in this situation. You can read up …

2019年11月30日 · This is the result one step ahead (here QS stands for quantile score, which is just twice the pinball loss): And 10 steps ahead: We can see that the AR(1) model dominates the white noise process in the short term but not the long term, and that the degenerate point forecast is worse in the tails but not too bad as an estimate in the 50-85% ...

If you fit a quantile regression for the 5th and 95th percentile this is often described as an estimate of a 90% prediction interval. This is the most prevalent it seems in the machine learning domain where random forests has been adapted to predict the quantiles of each leaf node or GBM with a quantile loss function.

2022年10月22日 · This implies the sample quantile is consistent if the data distribution has a non-zero density at the quantile (which is what gives a unique population minimum). It's also consistent if there is non-zero point mass at the quantile. It's not consistent if the quantile is the middle of a gap in the distribution.

In view of $(1)$, the $\tau$-th sample quantile receives a new interpretation as the minimizer of some loss function which is determined by the check function $\rho_\tau(\cdot)$. This is in agreement with more standardized results for the least-squares estimate and the least-absolute-deviation estimate, as the following chart shows: