Slightly-known approach for turning quantile regression predictions right into a likelihood distribution.
Once we practice regressive fashions, we get hold of level predictions. Nonetheless, in apply we are sometimes occupied with estimating the uncertainty related to every prediction. To realize that, we assume that the worth we are attempting to foretell is a random variable, and the objective is to estimate its distribution.
There are numerous strategies out there to estimate uncertainty from predictions, equivalent to variance estimation, Bayesian methods, conformal predictions, and so forth. Quantile regression is one in all these well-known strategies.
Quantile regression consists in estimating one mannequin for every quantile you have an interest in. This may be achieved by means of an uneven loss perform, generally known as pinball loss. Quantile regression is straightforward, simple to grasp, and available in excessive performing libraries equivalent to LightGBM. Nonetheless, quantile regression presents some points:
- There is no such thing as a assure that the order of the quantiles can be right. For instance, your prediction for the 50% quantile may very well be larger than the one you get for the 60% quantile, which is absurd.
- To acquire an estimate of the complete distribution, it’s essential practice many fashions. As an illustration, for those who want an estimate for every level % quantile, you need to practice 99 fashions.
Right here’s how quantile matching will help.
The objective of quantile matching is to suit a distribution perform given a pattern of quantile estimates. We will body this as a regression downside, so the curve doesn’t must completely match the quantiles. As a substitute, it needs to be “as shut as potential”, whereas protecting the properties which make it a distribution perform.
Particularly, we’re occupied with estimating the inverse cumulative distribution perform: given a…
