Demo: RF CIs

[swo]

• Very simple: make a single y=x line with some noise, then try to predict a value inside it
• A bootstrap over trees gives a decent interval
• A boostrap over forests gives a somewhat smaller interval (although as @Fuhan-Yang points out it doesn't shrink that fast with increasing trees; although that might have to do with my very small dataset here)

It's fairly straightforward to take a quantile over the predictions of trees in a forest, since RandomForestRegressor() has attribute .estimators_, which can be used to .predict() on the data.

[Fuhan-Yang]

The change seems to be the Option 1 we have talked about: bootstrap individual trees to get the interval. It is great to see that the manual bootstrapping over 100 individual trees has the same intervals with the random forest with 100 trees! Sounds good to me moving forward with this method. But hyperparameter tuning may not be avoidable when the prediction mean doesn't fit well, while a good thing is that we don't need to tune for intervals in this case.

Let me open a PR using this method on NIS data!

[swo]

We agreed to do an interval over trees' prediction