secure_learning.models.secure_svm module

Implementation of Support Vector Machine regression model.

class secure_learning.models.secure_svm.SVM(solver_type=SolverTypes.GD, penalty=PenaltyTypes.L2, **penalty_args)

Bases: Model

Solver for support vector machine. Optimizes a model with objective function: $$frac{1}{n_{textrm{samples}}} sum_{i=1}^{n_{textrm{samples}}} h_w(x_i, y_i).$$

Here, $h_w(x, y)$ is the hinge loss, defined as: $$max(0, 1 - y times (w^T x))$$

Labels $y_i$ are assumed to obtain values $-1$ and $1$.

__init__(solver_type=SolverTypes.GD, penalty=PenaltyTypes.L2, **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, coef_, grad_per_sample)

This function calculates the gradient as if the input data consists out of all data samples. That is, it does not incorporate coefficients for gradients of partial input data.

The gradient itself is given by $$1 / n * sum_{i=1} [0 if y times (w^T X_i) geq 1 else y_i * X_i]$$

Parameters:

• X (List[List[SecureFixedPoint]]) – Input matrix

• y (List[SecureFixedPoint]) – Dependent variable

• coef – Current coefficients vector

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

Return type:

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

Returns:

Gradient of SVM objective function.

name = 'SVM'

static predict(X, coef_, **_kwargs)

Predicts labels for input data to classification model. Label $-1$ is assigned of the predicted probability is less then prob, otherwise label $+1$ is assigned.

Parameters:

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

• coef – Coefficient vector of classification model

• _kwargs (None) – Not used

Return type:

List[SecureFixedPoint]

Returns:

Target labels of classification model

score(X, y, coef_)

Compute the mean accuracy of the prediction.

Parameters:

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

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

• coef – Coefficient vector.

Return type:

SecureFixedPoint

Returns:

Score of the model prediction.