Implementation of a basic regression decision tree. Input data set: The input data set must be 1dimensional with continuous labels. Output: The decision tree maps a real number input to a real number output. meansquarederror: param labels: a onedimensional numpy array param prediction: a floating point value return value: meansquarederror calculates the error if prediction is used to estimate the labels  tester  DecisionTree  testlabels  np.array1,2,3,4,5,6,7,8,9,10  testprediction  float6  tester.meansquarederrortestlabels, testprediction   ...     TestDecisionTree.helpermeansquarederrortesttestlabels, ...         testprediction True  testlabels  np.array1,2,3  testprediction  float2  tester.meansquarederrortestlabels, testprediction   ...     TestDecisionTree.helpermeansquarederrortesttestlabels, ...         testprediction True train: param x: a onedimensional numpy array param y: a onedimensional numpy array. The contents of y are the labels for the corresponding X values train does not have a return value Examples: 1. Try to train when x  y are of same length  1 dimensions No errors  dt  DecisionTree  dt.trainnp.array10,20,30,40,50,np.array0,0,0,1,1 2. Try to train when x is 2 dimensions  dt  DecisionTree  dt.trainnp.array1,2,3,4,5,1,2,3,4,5,np.array0,0,0,1,1 Traceback most recent call last: ... ValueError: Input data set must be onedimensional 3. Try to train when x and y are not of the same length  dt  DecisionTree  dt.trainnp.array1,2,3,4,5,np.array0,0,0,1,1,0,0,0,1,1 Traceback most recent call last: ... ValueError: x and y have different lengths 4. Try to train when x  y are of the same length but different dimensions  dt  DecisionTree  dt.trainnp.array1,2,3,4,5,np.array1,2,3,4,5 Traceback most recent call last: ... ValueError: Data set labels must be onedimensional This section is to check that the inputs conform to our dimensionality constraints 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 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 Decision Tres test class staticmethod def helpermeansquarederrortestlabels, prediction: squarederrorsum  float0 for label in labels: squarederrorsum  label  prediction  2 return floatsquarederrorsum  labels.size def main: x  np.arange1.0, 1.0, 0.005 y  np.sinx tree  DecisionTreedepth10, minleafsize10 tree.trainx, y testcases  np.random.rand10  2  1 predictions  np.arraytree.predictx for x in testcases avgerror  np.meanpredictions  testcases  2 printTest values:   strtestcases printPredictions:   strpredictions printAverage error:   stravgerror if name  main: main import doctest doctest.testmodnamemeansquarrederror, verboseTrue
import numpy as np


class DecisionTree:
    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
        >>> tester = DecisionTree()
        >>> test_labels = np.array([1,2,3,4,5,6,7,8,9,10])
        >>> test_prediction = float(6)
        >>> tester.mean_squared_error(test_labels, test_prediction) == (
        ...     TestDecisionTree.helper_mean_squared_error_test(test_labels,
        ...         test_prediction))
        True
        >>> test_labels = np.array([1,2,3])
        >>> test_prediction = float(2)
        >>> tester.mean_squared_error(test_labels, test_prediction) == (
        ...     TestDecisionTree.helper_mean_squared_error_test(test_labels,
        ...         test_prediction))
        True
        """
        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

        Examples:
        1. Try to train when x & y are of same length & 1 dimensions (No errors)
        >>> dt = DecisionTree()
        >>> dt.train(np.array([10,20,30,40,50]),np.array([0,0,0,1,1]))

        2. Try to train when x is 2 dimensions
        >>> dt = DecisionTree()
        >>> dt.train(np.array([[1,2,3,4,5],[1,2,3,4,5]]),np.array([0,0,0,1,1]))
        Traceback (most recent call last):
            ...
        ValueError: Input data set must be one-dimensional

        3. Try to train when x and y are not of the same length
        >>> dt = DecisionTree()
        >>> dt.train(np.array([1,2,3,4,5]),np.array([[0,0,0,1,1],[0,0,0,1,1]]))
        Traceback (most recent call last):
            ...
        ValueError: x and y have different lengths

        4. Try to train when x & y are of the same length but different dimensions
        >>> dt = DecisionTree()
        >>> dt.train(np.array([1,2,3,4,5]),np.array([[1],[2],[3],[4],[5]]))
        Traceback (most recent call last):
            ...
        ValueError: Data set labels must be one-dimensional

        This section is to check that the inputs conform to our dimensionality
        constraints
        """
        if x.ndim != 1:
            raise ValueError("Input data set must be one-dimensional")
        if len(x) != len(y):
            raise ValueError("x and y have different lengths")
        if y.ndim != 1:
            raise ValueError("Data set labels must be one-dimensional")

        if len(x) < 2 * self.min_leaf_size:
            self.prediction = np.mean(y)
            return

        if self.depth == 1:
            self.prediction = np.mean(y)
            return

        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 = DecisionTree(
                depth=self.depth - 1, min_leaf_size=self.min_leaf_size
            )
            self.right = DecisionTree(
                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


class TestDecisionTree:
    """Decision Tres test class"""

    @staticmethod
    def helper_mean_squared_error_test(labels, prediction):
        """
        helper_mean_squared_error_test:
        @param labels: a one dimensional numpy array
        @param prediction: a floating point value
        return value: helper_mean_squared_error_test calculates the mean squared error
        """
        squared_error_sum = float(0)
        for label in labels:
            squared_error_sum += (label - prediction) ** 2

        return float(squared_error_sum / labels.size)


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(-1.0, 1.0, 0.005)
    y = np.sin(x)

    tree = DecisionTree(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()
    import doctest

    doctest.testmod(name="mean_squarred_error", verbose=True)
