skwdro.linear_models.LogisticRegression#

class skwdro.linear_models.LogisticRegression(rho: float = 0.01, l2_reg: float = 0.0, fit_intercept: bool = True, cost: str = 't-NLC-2-2', solver='entropic_torch', solver_reg: float | None = None, sampler_reg: float | None = None, learning_rate: float | None = None, n_zeta_samples: int = 10, random_state: int = 0, n_iter: int | ~typing.Tuple[int, int] | None=None, opt_cond: OptCondTorch | None = <skwdro.solvers.optim_cond.OptCondTorch object>)[source]#

A Wasserstein Distributionally Robust logistic regression classifier.

The cost function is

\[\ell(\theta,\xi=(x,y)) = \log(1+e^{-y\langle \theta,x \rangle})\]

The WDRO problem solved at fitting is

\[\min_{\theta} \max_{\mathbb{Q} | W(\mathbb{P}^n,\mathbb{Q}) \le\rho} \mathbb{E}_{\zeta\sim\mathbb{Q}} \ell(\theta,\zeta=(x,y))\]

Parameters:

rho: float, default=1e-2

Robustness radius

l2_reg: float, default=None

l2 regularization

fit_intercept: boolean, default=True

Determines if an intercept is fit or not

cost: str, default=”n-NC-1-2”

Tiret-separated code to define the transport cost:: “<engine>-<cost id>-<k-norm type>-<power>” for \(c(x, y):=\|x-y\|_k^p\)

solver: str, default=’entropic_torch’

Solver to be used: ‘entropic’, ‘entropic_torch’ (_pre or _post) or ‘dedicated’

solver_reg: float | None, default=None

regularization value for the entropic solver, has a default heuristic

sampler_reg: float | None, default=None

standard deviation of the regularization distribution \(\pi_0\), has a default heuristic

learning_rate: float | None, default=None

if not set, use a default value depending on the problem, else specifies the stepsize of the gradient descent algorithm

n_zeta_samples: int, default=10

number of adversarial samples to draw

opt_cond: Optional[OptCondTorch]

optimality condition, see OptCondTorch

Attributes:

coef_array, shape (n_features,): parameter vector (\(w\) in the cost function formula)
intercept_float: constant term in decision function.

Examples

>>> import numpy as np
>>> from skwdro.linear_models import LogisticRegression
>>> from sklearn.datasets import make_blobs
>>> from sklearn.model_selection import train_test_split
>>> X, y = make_blobs(n_samples=100, centers=2, n_features=2, random_state=0)
>>> y = np.sign(y-0.5)
>>> X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)
>>> estimator = LogisticRegression()
>>> estimator.fit(X_train,y_train)
LogisticRegression()
>>> estimator.predict(X_test)
array([-1., -1., -1.,  1., -1.,  1.,  1., -1., -1.,  1.,  1.,  1., -1.,
        1.,  1.,  1.,  1.,  1., -1., -1., -1.,  1.,  1., -1., -1.,  1.,
       -1.,  1.,  1.,  1.,  1.,  1., -1.])
>>> estimator.score(X_test,y_test)
0.9393939393939394