secure_learning.models.secure_logistic

Implementation of Logistic regression model.

Classes

ExponentiationTypes	Class to store whether exponentations are approximated
Logistic	Solver for logistic regression. Optimizes a model with objective function

Module Contents

class secure_learning.models.secure_logistic.ExponentiationTypes(*args, **kwds)

Class to store whether exponentations are approximated or calculated exactly.

NONE

APPROX

EXACT

class secure_learning.models.secure_logistic.Logistic(solver_type: tno.mpc.mpyc.secure_learning.models.secure_model.SolverTypes = SolverTypes.GD, exponentiation: ExponentiationTypes = ExponentiationTypes.EXACT, penalty: tno.mpc.mpyc.secure_learning.models.secure_model.PenaltyTypes = PenaltyTypes.NONE, **penalty_args: float)

Solver for logistic regression. Optimizes a model with objective function $$left(frac{1}{2{n}_{textrm{samples}}}right) sum_{i=1}^{{n}_{textrm{samples}}}left(textrm{-}(1+y_i) log(h_w(x_i)) - (1-y_i) log(1-h_w(x_i))right)$$

Here, $$h_w(x) = frac{1}{(1 + e^{-w^T x}}$$

Labels $y_i$ are assumed to have value $-1$ or $1$.

The gradient is given by: $$g(X, y, w) = left(frac{1}{2} times {n}_{textrm{samples}}right) sum_{i=1}^{{n}_textrm{samples}} x_i^T left( (2h_w(x_i) - 1) - y right)$$

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

name = 'Logistic regression'

gradient_function(X: tno.mpc.mpyc.secure_learning.utils.Matrix[mpyc.sectypes.SecureFixedPoint], y: tno.mpc.mpyc.secure_learning.utils.Vector[mpyc.sectypes.SecureFixedPoint], weights: tno.mpc.mpyc.secure_learning.utils.Vector[mpyc.sectypes.SecureFixedPoint], grad_per_sample: False) → tno.mpc.mpyc.secure_learning.utils.Vector[mpyc.sectypes.SecureFixedPoint]

gradient_function(X: tno.mpc.mpyc.secure_learning.utils.Matrix[mpyc.sectypes.SecureFixedPoint], y: tno.mpc.mpyc.secure_learning.utils.Vector[mpyc.sectypes.SecureFixedPoint], weights: tno.mpc.mpyc.secure_learning.utils.Vector[mpyc.sectypes.SecureFixedPoint], grad_per_sample: True) → List[tno.mpc.mpyc.secure_learning.utils.Vector[mpyc.sectypes.SecureFixedPoint]]

gradient_function(X: tno.mpc.mpyc.secure_learning.utils.Matrix[mpyc.sectypes.SecureFixedPoint], y: tno.mpc.mpyc.secure_learning.utils.Vector[mpyc.sectypes.SecureFixedPoint], weights: tno.mpc.mpyc.secure_learning.utils.Vector[mpyc.sectypes.SecureFixedPoint], grad_per_sample: bool) → tno.mpc.mpyc.secure_learning.utils.Vector[mpyc.sectypes.SecureFixedPoint] | List[tno.mpc.mpyc.secure_learning.utils.Vector[mpyc.sectypes.SecureFixedPoint]]

Evaluate the gradient from the given parameters.

Parameters:

• X – Independent variables

• y – Dependent variables

• weights – Current weights vector

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

Returns:

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

score(X: tno.mpc.mpyc.secure_learning.utils.Matrix[mpyc.sectypes.SecureFixedPoint], y: tno.mpc.mpyc.secure_learning.utils.Vector[mpyc.sectypes.SecureFixedPoint], weights: tno.mpc.mpyc.secure_learning.utils.Vector[float] | tno.mpc.mpyc.secure_learning.utils.Vector[mpyc.sectypes.SecureFixedPoint]) → mpyc.sectypes.SecureFixedPoint

Compute the mean accuracy of the prediction.

Parameters:

• X – Test data.

• y – True label for $X$.

• weights – Weight vector.

Returns:

Score of the model prediction.

static predict(X: tno.mpc.mpyc.secure_learning.utils.Matrix[mpyc.sectypes.SecureFixedPoint], weights: tno.mpc.mpyc.secure_learning.utils.Vector[float] | tno.mpc.mpyc.secure_learning.utils.Vector[mpyc.sectypes.SecureFixedPoint], prob: float = 0.5, **_kwargs: None) → tno.mpc.mpyc.secure_learning.utils.Vector[mpyc.sectypes.SecureFixedPoint]

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 – Input data with all features

• weights – Weight vector of classification model

• prob – Threshold for labelling. Defaults to $0.5$.

• _kwargs – Not used

Returns:

Target labels of classification model