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from __future__ import print_function, division
import numpy as np
import math
from mlfromscratch.utils import normalize, polynomial_features
class l1_regularization():
""" Regularization for Lasso Regression """
def __init__(self, alpha):
self.alpha = alpha
def __call__(self, w):
return self.alpha * np.linalg.norm(w)
def grad(self, w):
return self.alpha * np.sign(w)
class l2_regularization():
""" Regularization for Ridge Regression """
def __init__(self, alpha):
self.alpha = alpha
def __call__(self, w):
return self.alpha * 0.5 * w.T.dot(w)
def grad(self, w):
return self.alpha * w
class l1_l2_regularization():
""" Regularization for Elastic Net Regression """
def __init__(self, alpha, l1_ratio=0.5):
self.alpha = alpha
self.l1_ratio = l1_ratio
def __call__(self, w):
l1_contr = self.l1_ratio * np.linalg.norm(w)
l2_contr = (1 - self.l1_ratio) * 0.5 * w.T.dot(w)
return self.alpha * (l1_contr + l2_contr)
def grad(self, w):
l1_contr = self.l1_ratio * np.sign(w)
l2_contr = (1 - self.l1_ratio) * w
return self.alpha * (l1_contr + l2_contr)
class Regression(object):
""" Base regression model. Models the relationship between a scalar dependent variable y and the independent
variables X.
Parameters:
-----------
n_iterations: float
The number of training iterations the algorithm will tune the weights for.
learning_rate: float
The step length that will be used when updating the weights.
"""
def __init__(self, n_iterations, learning_rate):
self.n_iterations = n_iterations
self.learning_rate = learning_rate
def initialize_weights(self, n_features):
""" Initialize weights randomly [-1/N, 1/N] """
limit = 1 / math.sqrt(n_features)
self.w = np.random.uniform(-limit, limit, (n_features, ))
def fit(self, X, y):
# Insert constant ones for bias weights
X = np.insert(X, 0, 1, axis=1)
self.training_errors = []
self.initialize_weights(n_features=X.shape[1])
# Do gradient descent for n_iterations
for i in range(self.n_iterations):
y_pred = X.dot(self.w)
# Calculate l2 loss
mse = np.mean(0.5 * (y - y_pred)**2 + self.regularization(self.w))
self.training_errors.append(mse)
# Gradient of l2 loss w.r.t w
grad_w = -(y - y_pred).dot(X) + self.regularization.grad(self.w)
# Update the weights
self.w -= self.learning_rate * grad_w
def predict(self, X):
# Insert constant ones for bias weights
X = np.insert(X, 0, 1, axis=1)
y_pred = X.dot(self.w)
return y_pred
class LinearRegression(Regression):
"""Linear model.
Parameters:
-----------
n_iterations: float
The number of training iterations the algorithm will tune the weights for.
learning_rate: float
The step length that will be used when updating the weights.
gradient_descent: boolean
True or false depending if gradient descent should be used when training. If
false then we use batch optimization by least squares.
"""
def __init__(self, n_iterations=100, learning_rate=0.001, gradient_descent=True):
self.gradient_descent = gradient_descent
# No regularization
self.regularization = lambda x: 0
self.regularization.grad = lambda x: 0
super(LinearRegression, self).__init__(n_iterations=n_iterations,
learning_rate=learning_rate)
def fit(self, X, y):
# If not gradient descent => Least squares approximation of w
if not self.gradient_descent:
# Insert constant ones for bias weights
X = np.insert(X, 0, 1, axis=1)
# Calculate weights by least squares (using Moore-Penrose pseudoinverse)
U, S, V = np.linalg.svd(X.T.dot(X))
S = np.diag(S)
X_sq_reg_inv = V.dot(np.linalg.pinv(S)).dot(U.T)
self.w = X_sq_reg_inv.dot(X.T).dot(y)
else:
super(LinearRegression, self).fit(X, y)
class LassoRegression(Regression):
"""Linear regression model with a regularization factor which does both variable selection
and regularization. Model that tries to balance the fit of the model with respect to the training
data and the complexity of the model. A large regularization factor with decreases the variance of
the model and do para.
Parameters:
-----------
degree: int
The degree of the polynomial that the independent variable X will be transformed to.
reg_factor: float
The factor that will determine the amount of regularization and feature
shrinkage.
n_iterations: float
The number of training iterations the algorithm will tune the weights for.
learning_rate: float
The step length that will be used when updating the weights.
"""
def __init__(self, degree, reg_factor, n_iterations=3000, learning_rate=0.01):
self.degree = degree
self.regularization = l1_regularization(alpha=reg_factor)
super(LassoRegression, self).__init__(n_iterations,
learning_rate)
def fit(self, X, y):
X = normalize(polynomial_features(X, degree=self.degree))
super(LassoRegression, self).fit(X, y)
def predict(self, X):
X = normalize(polynomial_features(X, degree=self.degree))
return super(LassoRegression, self).predict(X)
class PolynomialRegression(Regression):
"""Performs a non-linear transformation of the data before fitting the model
and doing predictions which allows for doing non-linear regression.
Parameters:
-----------
degree: int
The degree of the polynomial that the independent variable X will be transformed to.
n_iterations: float
The number of training iterations the algorithm will tune the weights for.
learning_rate: float
The step length that will be used when updating the weights.
"""
def __init__(self, degree, n_iterations=3000, learning_rate=0.001):
self.degree = degree
# No regularization
self.regularization = lambda x: 0
self.regularization.grad = lambda x: 0
super(PolynomialRegression, self).__init__(n_iterations=n_iterations,
learning_rate=learning_rate)
def fit(self, X, y):
X = polynomial_features(X, degree=self.degree)
super(PolynomialRegression, self).fit(X, y)
def predict(self, X):
X = polynomial_features(X, degree=self.degree)
return super(PolynomialRegression, self).predict(X)
class RidgeRegression(Regression):
"""Also referred to as Tikhonov regularization. Linear regression model with a regularization factor.
Model that tries to balance the fit of the model with respect to the training data and the complexity
of the model. A large regularization factor with decreases the variance of the model.
Parameters:
-----------
reg_factor: float
The factor that will determine the amount of regularization and feature
shrinkage.
n_iterations: float
The number of training iterations the algorithm will tune the weights for.
learning_rate: float
The step length that will be used when updating the weights.
"""
def __init__(self, reg_factor, n_iterations=1000, learning_rate=0.001):
self.regularization = l2_regularization(alpha=reg_factor)
super(RidgeRegression, self).__init__(n_iterations,
learning_rate)
class PolynomialRidgeRegression(Regression):
"""Similar to regular ridge regression except that the data is transformed to allow
for polynomial regression.
Parameters:
-----------
degree: int
The degree of the polynomial that the independent variable X will be transformed to.
reg_factor: float
The factor that will determine the amount of regularization and feature
shrinkage.
n_iterations: float
The number of training iterations the algorithm will tune the weights for.
learning_rate: float
The step length that will be used when updating the weights.
"""
def __init__(self, degree, reg_factor, n_iterations=3000, learning_rate=0.01, gradient_descent=True):
self.degree = degree
self.regularization = l2_regularization(alpha=reg_factor)
super(PolynomialRidgeRegression, self).__init__(n_iterations,
learning_rate)
def fit(self, X, y):
X = normalize(polynomial_features(X, degree=self.degree))
super(PolynomialRidgeRegression, self).fit(X, y)
def predict(self, X):
X = normalize(polynomial_features(X, degree=self.degree))
return super(PolynomialRidgeRegression, self).predict(X)
class ElasticNet(Regression):
""" Regression where a combination of l1 and l2 regularization are used. The
ratio of their contributions are set with the 'l1_ratio' parameter.
Parameters:
-----------
degree: int
The degree of the polynomial that the independent variable X will be transformed to.
reg_factor: float
The factor that will determine the amount of regularization and feature
shrinkage.
l1_ration: float
Weighs the contribution of l1 and l2 regularization.
n_iterations: float
The number of training iterations the algorithm will tune the weights for.
learning_rate: float
The step length that will be used when updating the weights.
"""
def __init__(self, degree=1, reg_factor=0.05, l1_ratio=0.5, n_iterations=3000,
learning_rate=0.01):
self.degree = degree
self.regularization = l1_l2_regularization(alpha=reg_factor, l1_ratio=l1_ratio)
super(ElasticNet, self).__init__(n_iterations,
learning_rate)
def fit(self, X, y):
X = normalize(polynomial_features(X, degree=self.degree))
super(ElasticNet, self).fit(X, y)
def predict(self, X):
X = normalize(polynomial_features(X, degree=self.degree))
return super(ElasticNet, self).predict(X)
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