10/2/2023 0 Comments Random forest prediction![]() Let’s compute 90% prediction intervals and test how many observations in the test set fall into the interval.Įrr_down, err_up = pred_ints(rf, X], percentile=90) We can now define a function to calculate prediction intervals for every prediction:Įrr_down.append(np.percentile(preds, (100 - percentile) / 2. Rf = RandomForestRegressor(n_estimators=1000, min_samples_leaf=1) The size of the forest should be relatively large, so let’s use 1000 trees. We’ll use 400 samples for training, leaving 106 samples for test. Let’s look at the well-known Boston housing dataset and try to create prediction intervals using vanilla random forest from scikit-learn:įrom sklearn.ensemble import RandomForestRegressor The nice thing is that just like accuracy and precision, the intervals can be cross-validated. One caveat is that expanding the tree fully can overfit: if that does happen, the intervals will be useless, just as the predictions. (And expanding the trees fully is in fact what Breiman suggested in his original random forest paper.) Then a prediction trivially returns individual response variables from which the distribution can be built if the forest is large enough. Random forests as quantile regression forestsīut here’s a nice thing: one can use a random forest as quantile regression forest simply by expanding the tree fully so that each leaf has exactly one value. While it is available in R’s quantreg packages, most machine learning packages do not seem to include the method. Unfortunately, quantile regression forests do not enjoy too wild of a popularity. And of course one could calculate other estimates on the distribution, such as median, standard deviation etc. For example, the 95% prediction intervals would be the range between 2.5 and 97.5 percentiles of the distribution of the response variables in the leaves. Using the distribution, it is trivial to create prediction intervals for new instances simply by using the appropriate percentiles of the distribution. The prediction can then return not just the mean of the response variables, but the full conditional distribution \(P(Y \leq y \mid X = x)\) of response values for every \(x\). The idea behind quantile regression forests is simple: instead of recording the mean value of response variables in each tree leaf in the forest, record all observed responses in the leaf. Unlike confidence intervals from classical statistics, which are about a parameter of population (such as the mean), prediction intervals are about individual predictions.įor linear regression, calculating the predictions intervals is straightforward (under certain assumptions like the normal distribution of the residuals) and included in most libraries, such as R’s predict method for linear models.īut how to calculate the intervals for tree based methods such as random forests? Quantile regression forestsĪ general method for finding confidence intervals for decision tree based methods is Quantile Regression Forests. In other words, it can quantify our confidence or certainty in the prediction. A prediction interval is an estimate of an interval into which the future observations will fall with a given probability. But while the model predictions would be similar, confidence in them would be quite different for obvious reasons: we have much less and more spread out data in the second case.Ī useful concept for quantifying the latter issue is prediction intervals. Looking at the following plots, both the left and right plot represent similar, learned models for predicting Y from X. Or it could be that we have a lot of data, and the response is fundamentally uncertain, like flipping a coin.įor regression, a prediction returning a single value (typically meant to minimize the squared error) likewise does not relay any information about the underlying distribution of the data or the range of response values we might later see in the test data. A prediction of 0.5 could mean that we have learned very little about a given instance, due to observing no or only a few data points about it. But there are two concepts being mixed up here. ![]() For classification tasks, beginning practitioners quite often conflate probability with confidence: probability of 0.5 is taken to mean that we are uncertain about the prediction, while a prediction of 1.0 means we are absolutely certain in the outcome. An aspect that is important but often overlooked in applied machine learning is intervals for predictions, be it confidence or prediction intervals.
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