Decision Tree Regression (using DecisionTrees.jl)

Adapted from http://scikit-learn.org/stable/auto_examples/tree/plot_tree_regression.html

A 1D regression with decision tree.

The decision trees is used to fit a sine curve with addition noisy observation. As a result, it learns local linear regressions approximating the sine curve.

We can see that if the maximum depth of the tree (controlled by the max_depth parameter) is set too high, the decision trees learn too fine details of the training data and learn from the noise, i.e. they overfit.

using DecisionTree
using ScikitLearn
using PyPlot

# Create a random dataset
srand(42)
X = sort(5 * rand(80))
XX = reshape(X, 80, 1)
y = sin(X)
y[1:5:end] += 3 * (0.5 - rand(16))

# Fit regression model
regr_1 = DecisionTreeRegressor()
regr_2 = DecisionTreeRegressor(pruning_purity_threshold=0.05)
regr_3 = RandomForestRegressor(ntrees=20)
fit!(regr_1, XX, y)
fit!(regr_2, XX, y)
fit!(regr_3, XX, y)

# Predict
X_test = 0:0.01:5.0
y_1 = predict(regr_1, hcat(X_test))
y_2 = predict(regr_2, hcat(X_test))
y_3 = predict(regr_3, hcat(X_test))

# Plot the results
scatter(X, y, c="k", label="data")
plot(X_test, y_1, c="g", label="no pruning", linewidth=2)
plot(X_test, y_2, c="r", label="pruning_purity_threshold=0.05", linewidth=2)
plot(X_test, y_3, c="b", label="RandomForestClassifier", linewidth=2)
xlabel("data")
ylabel("target")
title("Decision Tree Regression")
legend(prop=Dict("size"=>10));