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I am working on adding prediction intervals for each prediction value of new input samples.
Do prediction intervals for Random Forest predictions are average of prediction intervals of trees being Random Forest estimators? Since predictions of Random Forest is an average of predictions of each tree that is Random Forest's estimator
No, prediction intervals for Random Forest predictions are not simply the average of prediction intervals of individual trees. The reason is that Random Forest is an ensemble method, which means it combines the predictions of multiple decision trees to make a final prediction. This process reduces the variance of the predictions, which in turn affects the prediction intervals.
The prediction interval for a Random Forest model is typically calculated by generating predictions for each tree in the forest, then calculating the desired percentile of these predictions. For example, a 95% prediction interval might be calculated by taking the 2.5th and 97.5th percentiles of the predictions.
This method takes into account the variability between the trees in the Random Forest, which is not captured if you simply average the prediction intervals of individual trees. It's also worth noting that this method assumes that the predictions of the trees are approximately normally distributed, which may not always be the case.
In addition, it's important to remember that prediction intervals are a measure of uncertainty in the predictions. They do not guarantee that future observations will fall within the interval, but rather give an indication of the likely range of values.
