decision_tree.py

"""
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 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
 """

 """
 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")
 return

 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)