113 lines
3.7 KiB
Python
113 lines
3.7 KiB
Python
# Sebastian Raschka 2014-2020
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# mlxtend Machine Learning Library Extensions
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#
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# Author: Sebastian Raschka <sebastianraschka.com>
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#
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# License: BSD 3 clause
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from scipy.optimize import minimize
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import warnings
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import numpy as np
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def create_counterfactual(x_reference, y_desired, model, X_dataset,
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y_desired_proba=None, lammbda=0.1, random_seed=None):
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"""
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Implementation of the counterfactual method by Wachter et al. 2017
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References:
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- Wachter, S., Mittelstadt, B., & Russell, C. (2017).
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Counterfactual explanations without opening the black box:
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Automated decisions and the GDPR. Harv. JL & Tech., 31, 841.,
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https://arxiv.org/abs/1711.00399
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Parameters
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----------
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x_reference : array-like, shape=[m_features]
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The data instance (training example) to be explained.
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y_desired : int
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The desired class label for `x_reference`.
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model : estimator
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A (scikit-learn) estimator implementing `.predict()` and/or
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`predict_proba()`.
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- If `model` supports `predict_proba()`, then this is used by
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default for the first loss term,
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`(lambda * model.predict[_proba](x_counterfact) - y_desired[_proba])^2`
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- Otherwise, method will fall back to `predict`.
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X_dataset : array-like, shape=[n_examples, m_features]
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A (training) dataset for picking the initial counterfactual
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as initial value for starting the optimization procedure.
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y_desired_proba : float (default: None)
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A float within the range [0, 1] designating the desired
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class probability for `y_desired`.
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- If `y_desired_proba=None` (default), the first loss term
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is `(lambda * model(x_counterfact) - y_desired)^2` where `y_desired`
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is a class label
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- If `y_desired_proba` is not None, the first loss term
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is `(lambda * model(x_counterfact) - y_desired_proba)^2`
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lammbda : Weighting parameter for the first loss term,
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`(lambda * model(x_counterfact) - y_desired[_proba])^2`
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random_seed : int (default=None)
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If int, random_seed is the seed used by
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the random number generator for selecting the inital counterfactual
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from `X_dataset`.
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"""
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if y_desired_proba is not None:
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use_proba = True
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if not hasattr(model, "predict_proba"):
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raise AttributeError("Your `model` does not support "
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"`predict_proba`. Set `y_desired_proba` "
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" to `None` to use `predict`instead.")
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else:
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use_proba = False
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if y_desired_proba is None:
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# class label
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y_to_be_annealed_to = y_desired
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else:
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# class proba corresponding to class label y_desired
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y_to_be_annealed_to = y_desired_proba
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# start with random counterfactual
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rng = np.random.RandomState(random_seed)
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x_counterfact = X_dataset[rng.randint(X_dataset.shape[0])]
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# compute median absolute deviation
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mad = np.abs(np.median(X_dataset, axis=0) - x_reference)
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def dist(x_reference, x_counterfact):
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numerator = np.abs(x_reference - x_counterfact)
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return np.sum(numerator/mad)
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def loss(x_counterfact, lammbda):
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if use_proba:
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y_predict = model.predict_proba(
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x_counterfact.reshape(1, -1)).flatten()[y_desired]
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else:
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y_predict = model.predict(x_counterfact.reshape(1, -1))
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diff = lammbda*(y_predict - y_to_be_annealed_to)**2
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return diff + dist(x_reference, x_counterfact)
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res = minimize(loss, x_counterfact, args=(lammbda), method='Nelder-Mead')
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if not res['success']:
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warnings.warn(res['message'])
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x_counterfact = res['x']
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return x_counterfact
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