secure_learning.models.secure_linear module

Implementation of Linear regression model.

class secure_learning.models.secure_linear.Linear(solver_type=SolverTypes.GD, penalty=PenaltyTypes.NONE, **penalty_args)

Bases: Model

Solver for Linear regression. Optimizes a model with objective function: $$frac{1}{{2n}_textrm{samples}} times ||y - Xw||^2_2$$

The gradient is given by: $$g(X, y, w) = frac{1}{{2n}_textrm{samples}} times X^T (Xw - y)$$

See secure_model.py docstrings for more information on solver types and penalties.

__init__(solver_type=SolverTypes.GD, penalty=PenaltyTypes.NONE, **penalty_args)

Constructor method.

Parameters:

• solver_type (SolverTypes) – Solver type to use (e.g. Gradient Descent aka GD)

• penalty (PenaltyTypes) – Choose whether using L1, L2 or no penalty

• penalty_args (float) – Necessary arguments for chosen penalty.

gradient_function(X, y, weights, grad_per_sample)

Evaluate the gradient from the given parameters.

Parameters:

• X (List[List[SecureFixedPoint]]) – Independent variables

• y (List[SecureFixedPoint]) – Dependent variables

• weights (List[SecureFixedPoint]) – Current weights vector

• grad_per_sample (bool) – Return a list with gradient per sample instead of aggregated (summed) gradient

Return type:

Union[List[List[SecureFixedPoint]], List[SecureFixedPoint]]

Returns:

Gradient of objective function as specified in class docstring, evaluated from the provided parameters

name = 'Linear regression'

static predict(X, weights, **_kwargs)

Predicts target values for input data to regression model.

Parameters:

• X (List[List[SecureFixedPoint]]) – Input data with all features

• weights (Union[List[float], List[SecureFixedPoint]]) – Weight vector of regression model

• _kwargs (None) – Not used

Return type:

List[SecureFixedPoint]

Returns:

Target values of regression model

score(X, y, weights)

Compute the coefficient of determination $R^2$ of the prediction.

Parameters:

• X (List[List[SecureFixedPoint]]) – Test data.

• y (List[SecureFixedPoint]) – True value for $X$.

• weights (Union[List[float], List[SecureFixedPoint]]) – Weight vector.

Return type:

SecureFixedPoint

Returns:

Score of the model prediction.