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linear_regression.py
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/
linear_regression.py
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"""Linear Regression Module"""
# Import dependencies.
import numpy as np
from ..utils.features import prepare_for_training
class LinearRegression:
# pylint: disable=too-many-instance-attributes
"""Linear Regression Class"""
def __init__(self, data, labels, polynomial_degree=0, sinusoid_degree=0, normalize_data=True):
# pylint: disable=too-many-arguments
"""Linear regression constructor.
:param data: training set.
:param labels: training set outputs (correct values).
:param polynomial_degree: degree of additional polynomial features.
:param sinusoid_degree: multipliers for sinusoidal features.
:param normalize_data: flag that indicates that features should be normalized.
"""
# Normalize features and add ones column.
(
data_processed,
features_mean,
features_deviation
) = prepare_for_training(data, polynomial_degree, sinusoid_degree, normalize_data)
self.data = data_processed
self.labels = labels
self.features_mean = features_mean
self.features_deviation = features_deviation
self.polynomial_degree = polynomial_degree
self.sinusoid_degree = sinusoid_degree
self.normalize_data = normalize_data
# Initialize model parameters.
num_features = self.data.shape[1]
self.theta = np.zeros((num_features, 1))
def train(self, alpha, lambda_param=0, num_iterations=500):
"""Trains linear regression.
:param alpha: learning rate (the size of the step for gradient descent)
:param lambda_param: regularization parameter
:param num_iterations: number of gradient descent iterations.
"""
# Run gradient descent.
cost_history = self.gradient_descent(alpha, lambda_param, num_iterations)
return self.theta, cost_history
def gradient_descent(self, alpha, lambda_param, num_iterations):
"""Gradient descent.
It calculates what steps (deltas) should be taken for each theta parameter in
order to minimize the cost function.
:param alpha: learning rate (the size of the step for gradient descent)
:param lambda_param: regularization parameter
:param num_iterations: number of gradient descent iterations.
"""
# Initialize J_history with zeros.
cost_history = []
for _ in range(num_iterations):
# Perform a single gradient step on the parameter vector theta.
self.gradient_step(alpha, lambda_param)
# Save the cost J in every iteration.
cost_history.append(self.cost_function(self.data, self.labels, lambda_param))
return cost_history
def gradient_step(self, alpha, lambda_param):
"""Gradient step.
Function performs one step of gradient descent for theta parameters.
:param alpha: learning rate (the size of the step for gradient descent)
:param lambda_param: regularization parameter
"""
# Calculate the number of training examples.
num_examples = self.data.shape[0]
# Predictions of hypothesis on all m examples.
predictions = LinearRegression.hypothesis(self.data, self.theta)
# The difference between predictions and actual values for all m examples.
delta = predictions - self.labels
# Calculate regularization parameter.
reg_param = 1 - alpha * lambda_param / num_examples
# Create theta shortcut.
theta = self.theta
# Vectorized version of gradient descent.
theta = theta * reg_param - alpha * (1 / num_examples) * (delta.T @ self.data).T
# We should NOT regularize the parameter theta_zero.
theta[0] = theta[0] - alpha * (1 / num_examples) * (self.data[:, 0].T @ delta).T
self.theta = theta
def get_cost(self, data, labels, lambda_param):
"""Get the cost value for specific data set.
:param data: the set of training or test data.
:param labels: training set outputs (correct values).
:param lambda_param: regularization parameter
"""
data_processed = prepare_for_training(
data,
self.polynomial_degree,
self.sinusoid_degree,
self.normalize_data,
)[0]
return self.cost_function(data_processed, labels, lambda_param)
def cost_function(self, data, labels, lambda_param):
"""Cost function.
It shows how accurate our model is based on current model parameters.
:param data: the set of training or test data.
:param labels: training set outputs (correct values).
:param lambda_param: regularization parameter
"""
# Calculate the number of training examples and features.
num_examples = data.shape[0]
# Get the difference between predictions and correct output values.
delta = LinearRegression.hypothesis(data, self.theta) - labels
# Calculate regularization parameter.
# Remember that we should not regularize the parameter theta_zero.
theta_cut = self.theta[1:, 0]
reg_param = lambda_param * (theta_cut.T @ theta_cut)
# Calculate current predictions cost.
cost = (1 / 2 * num_examples) * (delta.T @ delta + reg_param)
# Let's extract cost value from the one and only cost numpy matrix cell.
return cost[0][0]
def predict(self, data):
"""Predict the output for data_set input based on trained theta values
:param data: training set of features.
"""
# Normalize features and add ones column.
data_processed = prepare_for_training(
data,
self.polynomial_degree,
self.sinusoid_degree,
self.normalize_data,
)[0]
# Do predictions using model hypothesis.
predictions = LinearRegression.hypothesis(data_processed, self.theta)
return predictions
@staticmethod
def hypothesis(data, theta):
"""Hypothesis function.
It predicts the output values y based on the input values X and model parameters.
:param data: data set for what the predictions will be calculated.
:param theta: model params.
:return: predictions made by model based on provided theta.
"""
predictions = data @ theta
return predictions