class RidgeRegression():
"""Linear regression model with a regularization factor.
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.
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,
reg_factor,
n_iterations=100,
learning_rate=0.001,
gradient_descent=True):
self.w = None
self.n_iterations = n_iterations
self.learning_rate = learning_rate
self.gradient_descent = gradient_descent
self.reg_factor = reg_factor
self.square_loss = SquareLoss()
def fit(self, X, y):
# Insert dummy ones for bias weights
X = np.insert(X, 0, 1, axis=1)
n_features = np.shape(X)[1]
# Get weights by gradient descent opt.
if self.gradient_descent:
# Initial weights randomly [0, 1]
self.w = np.random.random((n_features, ))
# Do gradient descent for n_iterations
for _ in range(self.n_iterations):
grad_w = self.square_loss.gradient(
y, X, self.w) + self.reg_factor * self.w
self.w -= self.learning_rate * grad_w
# Get weights by least squares (by pseudoinverse)
else:
U, S, V = np.linalg.svd(
X.T.dot(X) + self.reg_factor * np.identity(n_features))
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)
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():
"""Linear model for doing regression.
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.
momentum: float
A momentum term that helps accelerate SGD by adding a fraction of the previous
weight update to the current update.
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, momentum=0.3, gradient_descent=True):
self.w = None
self.n_iterations = n_iterations
self.learning_rate = learning_rate
self.momentum = momentum
self.gradient_descent = gradient_descent # Opt. method. If False => Least squares
self.square_loss = SquareLoss()
def fit(self, X, y):
# Insert constant ones as first column (for bias weights)
X = np.insert(X, 0, 1, axis=1)
w_gradient = np.zeros(np.shape(self.w))
# Get weights by gradient descent opt.
if self.gradient_descent:
n_features = np.shape(X)[1]
# Initial weights randomly [0, 1]
self.w = np.random.random((n_features, ))
# Do gradient descent for n_iterations
for _ in range(self.n_iterations):
# Gradient of squared loss w.r.t the weights
w_gradient = self.momentum*w_gradient + self.square_loss.gradient(y, X, self.w)
# Move against the gradient to minimize loss
self.w -= self.learning_rate * w_gradient
# Get weights by least squares (by pseudoinverse)
else:
U, S, V = np.linalg.svd(X.T.dot(X))
S = np.diag(S)
X_sq_inv = V.dot(np.linalg.pinv(S)).dot(U.T)
self.w = X_sq_inv.dot(X.T).dot(y)
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