如何使用随机森林 model 反向计算给定因变量的预测变量？

Question

Given a random forest model y ~ x1 + x2 , is there a possibility to hand the model a value for y and get possible results of x1 and x2 back?

To give a short random example:

require(randomForest)
mydf <- data.frame(y =  c(1, 5, 6, 8, -1, -4), x1 = c(2, 8, 7, 10, 3, 0), x2 = c(18, 24, 26, 30, 15, 12))
myrf <- randomForest(y ~ ., data = mydf)

Is there a way to reverse calculate the predictors with the random forest model?

Answer 1

No. Such functionality does not exist, and I cannot see why it would exist. You are trying to do something Random Forest is not designed to do. But if you wanted to, and I don't think you should, you could generate an ND space, in this case for x1 and x2, which has all predictions and then subset the regions that are sufficiently close to the value of y.

Answer 2

Long story short: no in most cases.

Without going too much into the details, a random forest is more or less the average between several decision trees. In most cases, it's not possible to reverse a decision tree. For instance in the following:

If the prediction is 4.5, your original data could be any value inferior to 10.5 (eg Alcohol level=0 and Alcohol level=3 would have 4.5 as predicted value).

The only way you would be able to reverse a tree would be if you happen to create a bijection between the cartesian product of your input data and your predicted value; but that would be quite seldom (and it would probably overfit)