Linear Regression¶

Single Parameter¶

class touvlo.lin_rg.AbstractLinearRegression(theta=None)[source]¶

Represents the definitons common to all Linear Regressions.

Parameters:	theta (numpy.array) – Column vector of model’s parameters. Defaults to None

theta¶

Column vector of model’s parameters.

Type:	numpy.array

fit(X, y, strategy='BGD', alpha=0.1, num_iters=100, **kwargs)[source]¶

Adjusts model parameters to training data.

Parameters:

X (numpy.array) – Features’ dataset.
y (numpy.array) – Column vector of expected values.
strategy (str) –
Which optimization strategy should be employed:
- ’BGD’: Performs Batch Gradient Descent
- ’SGD’: Performs Stochastic Gradient Descent
- ’MBGD’: Performs Mini-Batch Gradient Descent
- ’normal_equation’: Employs Normal Equation
alpha (float) – Learning rate or _step size of the optimization.
num_iters (int) – Number of times the optimization will be performed.

Returns:

None

predict(X)[source]¶

Computes prediction vector.

Parameters:	X (numpy.array) – Features’ dataset.
Returns:	vector with a prediction for each example.
Return type:	numpy.array

class touvlo.lin_rg.LinearRegression(theta=None)[source]¶

Represents an Unregularized Linear Regression model

Parameters:	theta (numpy.array) – Column vector of model’s parameters. Defaults to None

theta¶

Column vector of model’s parameters.

Type:	numpy.array

cost(X, y)[source]¶

Computes the cost function J for Linear Regression.

Parameters:	X (numpy.array) – Features’ dataset plus bias column. y (numpy.array) – Column vector of expected values.
Returns:	Computed cost.
Return type:	float

class touvlo.lin_rg.RidgeLinearRegression(theta=None, _lambda=0)[source]¶

Represents a Ridge Linear Regression model

Parameters:	theta (numpy.array) – Column vector of model’s parameters. Defaults to None _lambda (float) – The regularization hyperparameter.

theta¶

Column vector of model’s parameters.

Type:	numpy.array

_lambda¶

The regularization hyperparameter.

Type:	float

cost(X, y, **kwargs)[source]¶

Computes the regularized cost function J for: Ridge Linear Regression.

Parameters:	X (numpy.array) – Features’ dataset plus bias column. y (numpy.array) – Column vector of expected values.
Returns:	Computed cost.
Return type:	float

touvlo.lin_rg.cost_func(X, y, theta)[source]¶

Computes the cost function J for Linear Regression.

Parameters:	X (numpy.array) – Features’ dataset plus bias column. y (numpy.array) – Column vector of expected values. theta (numpy.array) – Column vector of model’s parameters.
Returns:	Computed cost.
Return type:	float

touvlo.lin_rg.grad(X, y, theta)[source]¶

Computes the gradient for Linear Regression.

Parameters:	X (numpy.array) – Features’ dataset plus bias column. y (numpy.array) – Column vector of expected values. theta (numpy.array) – Column vector of model’s parameters.
Returns:	Gradient column vector.
Return type:	numpy.array

touvlo.lin_rg.h(X, theta)[source]¶

Linear regression hypothesis.

Parameters:	X (numpy.array) – Features’ dataset plus bias column. theta (numpy.array) – Column vector of model’s parameters.
Returns:	The projected value for each line of the dataset.
Return type:	numpy.array

touvlo.lin_rg.normal_eqn(X, y)[source]¶

Produces optimal theta via normal equation.

Parameters:	X (numpy.array) – Features’ dataset plus bias column. y (numpy.array) – Column vector of expected values.
Raises:	`LinAlgError`
Returns:	Optimized model parameters theta.
Return type:	numpy.array

touvlo.lin_rg.predict(X, theta)[source]¶

Computes prediction vector.

Parameters:	X (numpy.array) – Features’ dataset plus bias column. theta (numpy.array) – Column vector of model’s parameters.
Returns:	vector with predictions for each input line.
Return type:	numpy.array

touvlo.lin_rg.reg_cost_func(X, y, theta, _lambda)[source]¶

Computes the regularized cost function J for Linear Regression.

Parameters:	X (numpy.array) – Features’ dataset plus bias column. y (numpy.array) – Column vector of expected values. theta (numpy.array) – Column vector of model’s parameters. _lambda (float) – The regularization hyperparameter.
Returns:	Computed cost with regularization.
Return type:	float

touvlo.lin_rg.reg_grad(X, y, theta, _lambda)[source]¶

Computes the regularized gradient for Linear Regression.

Parameters:	X (numpy.array) – Features’ dataset plus bias column. y (numpy.array) – Column vector of expected values. theta (numpy.array) – Column vector of model’s parameters. _lambda (float) – The regularization hyperparameter.
Returns:	Regularized gradient column vector.
Return type:	numpy.array

touvlo.lin_rg.reg_normal_eqn(X, y, _lambda)[source]¶

Produces optimal theta via normal equation.

Parameters:	X (numpy.array) – Features’ dataset plus bias column. y (numpy.array) – Column vector of expected values. _lambda (float) – The regularization hyperparameter.
Returns:	Optimized model parameters theta.
Return type:	numpy.array