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123 lines
4.2 KiB
Python
123 lines
4.2 KiB
Python
"""
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Implementation of gradient descent algorithm for minimizing cost of a linear hypothesis function.
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"""
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from __future__ import print_function
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import numpy
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# List of input, output pairs
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train_data = (((5, 2, 3), 15), ((6, 5, 9), 25),
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((11, 12, 13), 41), ((1, 1, 1), 8), ((11, 12, 13), 41))
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test_data = (((515, 22, 13), 555), ((61, 35, 49), 150))
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parameter_vector = [2, 4, 1, 5]
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m = len(train_data)
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LEARNING_RATE = 0.009
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def _error(example_no, data_set='train'):
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"""
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:param data_set: train data or test data
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:param example_no: example number whose error has to be checked
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:return: error in example pointed by example number.
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"""
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return calculate_hypothesis_value(example_no, data_set) - output(example_no, data_set)
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def _hypothesis_value(data_input_tuple):
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"""
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Calculates hypothesis function value for a given input
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:param data_input_tuple: Input tuple of a particular example
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:return: Value of hypothesis function at that point.
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Note that there is an 'biased input' whose value is fixed as 1.
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It is not explicitly mentioned in input data.. But, ML hypothesis functions use it.
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So, we have to take care of it separately. Line 36 takes care of it.
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"""
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hyp_val = 0
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for i in range(len(parameter_vector) - 1):
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hyp_val += data_input_tuple[i]*parameter_vector[i+1]
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hyp_val += parameter_vector[0]
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return hyp_val
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def output(example_no, data_set):
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"""
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:param data_set: test data or train data
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:param example_no: example whose output is to be fetched
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:return: output for that example
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"""
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if data_set == 'train':
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return train_data[example_no][1]
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elif data_set == 'test':
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return test_data[example_no][1]
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def calculate_hypothesis_value(example_no, data_set):
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"""
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Calculates hypothesis value for a given example
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:param data_set: test data or train_data
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:param example_no: example whose hypothesis value is to be calculated
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:return: hypothesis value for that example
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"""
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if data_set == "train":
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return _hypothesis_value(train_data[example_no][0])
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elif data_set == "test":
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return _hypothesis_value(test_data[example_no][0])
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def summation_of_cost_derivative(index, end=m):
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"""
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Calculates the sum of cost function derivative
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:param index: index wrt derivative is being calculated
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:param end: value where summation ends, default is m, number of examples
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:return: Returns the summation of cost derivative
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Note: If index is -1, this means we are calculating summation wrt to biased parameter.
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"""
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summation_value = 0
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for i in range(end):
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if index == -1:
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summation_value += _error(i)
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else:
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summation_value += _error(i)*train_data[i][0][index]
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return summation_value
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def get_cost_derivative(index):
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"""
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:param index: index of the parameter vector wrt to derivative is to be calculated
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:return: derivative wrt to that index
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Note: If index is -1, this means we are calculating summation wrt to biased parameter.
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"""
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cost_derivative_value = summation_of_cost_derivative(index, m)/m
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return cost_derivative_value
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def run_gradient_descent():
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global parameter_vector
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# Tune these values to set a tolerance value for predicted output
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absolute_error_limit = 0.000002
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relative_error_limit = 0
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j = 0
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while True:
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j += 1
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temp_parameter_vector = [0, 0, 0, 0]
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for i in range(0, len(parameter_vector)):
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cost_derivative = get_cost_derivative(i-1)
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temp_parameter_vector[i] = parameter_vector[i] - \
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LEARNING_RATE*cost_derivative
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if numpy.allclose(parameter_vector, temp_parameter_vector,
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atol=absolute_error_limit, rtol=relative_error_limit):
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break
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parameter_vector = temp_parameter_vector
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print(("Number of iterations:", j))
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def test_gradient_descent():
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for i in range(len(test_data)):
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print(("Actual output value:", output(i, 'test')))
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print(("Hypothesis output:", calculate_hypothesis_value(i, 'test')))
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if __name__ == '__main__':
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run_gradient_descent()
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print("\nTesting gradient descent for a linear hypothesis function.\n")
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test_gradient_descent()
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