Implementation of a regression tree in python

I've implemented a basic decision tree in python as an example of how they work. Although the class I've created only works on one dimensional data sets, the reader should be able to generalize it to higher dimensions should they need to.

machine_learning/decision_tree.py

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+"""
+Implementation of a basic regression decision tree.
+Input data set: The input data set must be 1-dimensional with continuous labels.
+Output: The decision tree maps a real number input to a real number output. 
+"""
+
+import numpy as np
+
+class Decision_Tree:
+    def __init__(self, depth = 5, min_leaf_size = 5):
+        self.depth = depth
+        self.decision_boundary = 0
+        self.left = None
+        self.right = None
+        self.min_leaf_size = min_leaf_size
+        self.prediction = None
+
+    def mean_squared_error(self, labels, prediction):
+        """
+        mean_squared_error:
+        @param labels: a one dimensional numpy array 
+        @param prediction: a floating point value
+        return value: mean_squared_error calculates the error if prediction is used to estimate the labels
+        """
+        if labels.ndim != 1:
+            print("Error: Input labels must be one dimensional")
+
+        return np.mean((labels - prediction) ** 2)
+
+    def train(self, X, y):
+        """
+        train:
+        @param X: a one dimensional numpy array
+        @param y: a one dimensional numpy array. 
+        The contents of y are the labels for the corresponding X values
+
+        train does not have a return value
+        """
+
+        """
+        this section is to check that the inputs conform to our dimensionality constraints
+        """
+        if X.ndim != 1:
+            print("Error: Input data set must be one dimensional")
+            return
+        if len(X) != len(y):
+            print("Error: X and y have different lengths")
+            return
+        if y.ndim != 1:
+            print("Error: Data set labels must be one dimensional")
+
+        if len(X) < 2 * self.min_leaf_size:
+            self.prediction = np.mean(y)
+
+        if self.depth == 1:
+            self.prediction = np.mean(y)
+
+        best_split = 0
+        min_error = self.mean_squared_error(X,np.mean(y)) * 2
+
+
+        """
+        loop over all possible splits for the decision tree. find the best split.
+        if no split exists that is less than 2 * error for the entire array
+        then the data set is not split and the average for the entire array is used as the predictor
+        """
+        for i in range(len(X)):
+            if len(X[:i]) < self.min_leaf_size:
+                continue
+            elif len(X[i:]) < self.min_leaf_size:
+                continue
+            else:
+                error_left = self.mean_squared_error(X[:i], np.mean(y[:i]))
+                error_right = self.mean_squared_error(X[i:], np.mean(y[i:]))
+                error = error_left + error_right
+                if error < min_error:
+                    best_split = i
+                    min_error = error
+
+        if best_split != 0:
+            left_X = X[:best_split]
+            left_y = y[:best_split]
+            right_X = X[best_split:]
+            right_y = y[best_split:]
+
+            self.decision_boundary = X[best_split]
+            self.left = Decision_Tree(depth = self.depth - 1, min_leaf_size = self.min_leaf_size)
+            self.right = Decision_Tree(depth = self.depth - 1, min_leaf_size = self.min_leaf_size)
+            self.left.train(left_X, left_y)
+            self.right.train(right_X, right_y)
+        else:
+            self.prediction = np.mean(y)
+
+        return
+
+    def predict(self, x):
+        """
+        predict:
+        @param x: a floating point value to predict the label of
+        the prediction function works by recursively calling the predict function
+        of the appropriate subtrees based on the tree's decision boundary
+        """
+        if self.prediction is not None:
+            return self.prediction
+        elif self.left or self.right is not None:
+            if x >= self.decision_boundary:
+                return self.right.predict(x)
+            else:
+                return self.left.predict(x)
+        else:
+            print("Error: Decision tree not yet trained")
+            return None
+
+def main():
+    """
+    In this demonstration we're generating a sample data set from the sin function in numpy.
+    We then train a decision tree on the data set and use the decision tree to predict the
+    label of 10 different test values. Then the mean squared error over this test is displayed.
+    """
+    X = np.arange(-1., 1., 0.005)
+    y = np.sin(X)
+
+    tree = Decision_Tree(depth = 10, min_leaf_size = 10)
+    tree.train(X,y)
+
+    test_cases = (np.random.rand(10) * 2) - 1
+    predictions = np.array([tree.predict(x) for x in test_cases])
+    avg_error = np.mean((predictions - test_cases) ** 2)
+
+    print("Test values: " + str(test_cases))
+    print("Predictions: " + str(predictions))
+    print("Average error: " + str(avg_error))
+
+
+if __name__ == '__main__':
+    main()