which quantile value is good for prediction ?

Hello,

Quantile random forest model is used to predict 1 year solar radiation.

Question : which quantile value should i use to have accurate forecasts ?

Thank you.

[Adam Danz]

d) none of the above.

Just kidding. This sounds like homework. You could reframe your question showing that you've tried to find a solution, got stuck, or need some help with something specific.

[Hamza Ali]

Thank you for your answer.

Comparaison between QRF and RF has been carried out. for QRF algorithm, different quantile values were tested, and i found that the 50th percentile is the best quantile.

Question : This comparaison, between different values of quantiles, is sufficient to prove that 50th quantile should be used to have accurate forecasts ?

[Adam Danz]

I'm not familiar with RF or QRF but in terms of expected values from a distribution, the 50 quantile is the median and if the distribution is even remotely normal, then the median is the expected value. If the distribution is not approximately normal then more info is needed in terms of estimating the expected value.

I agree with the cyclist that such a comparison is certainly not a proof in the formal definition of the term. For random processes, bootstrapping is often a good approach at computing expected value and it's error (confidence intervals). But I have no idea if this suggestion is applicable to your project.

[Hamza Ali]

Thank you for your answer.

I think that the distribution is non-parametric distribution (see the figure below). In fact, the recent litterature in this field, shows the superiority of QRF compared to RF in terms of forecasting accuracy.

I wanted to say that if it is a proof in the experimental sense, because i found in research articles that authors try different values of quantiles (0.1: 0.1: 0.9), anf they choose the quantile that gives small error.

I wonder if this experimental technique is valid to demonstrate why we have choosen the quantile value ?

Answer 1

[the cyclist]

The usual random forest (RF) algorithm gives a point estimate for each set of input values. It predicts one value.

The point of quantile random forest (QRF) is to provide an estimate of the dispersion of observations around the predicted value.

So, if all you care about is the prediction value, you don't really need to use QRF; you could just use RF. That being said, I expect the 50th percentile gives the best average prediction.

[Hamza Ali]

Thank you for your answer.

In fact, i have compred between RF and QRF(0.5) algorithms, and the result shows that QRF model outperforms RF in term of mse. In addition, different values of quantiles [0.05 0.1 0.25 0.5 0.75 0.9 0.95] have been used to determine the best quantile. the best quantile that gives low error is the 50th percentile as you said.

Question : This comparaison, between different values of quantiles, is sufficient to prove that 50th quantile (or other quantile) should be used to have accurate forecasts ?

Thank you.

[the cyclist]

It is certainly not proof (in the mathematical sense). I suppose it is evidence.

I am not an expert in QRF, but my understanding is that its primary purpose is to get a sense of variability around the point estimate. So, I am not really sure of what you are trying to do here. (Unless it is just a homework problem, as Adam has speculated.)