86 lines
2.8 KiB
Python
86 lines
2.8 KiB
Python
"""Determination of parameter bounds"""
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# Author: Paolo Losi
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# License: BSD 3 clause
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from numbers import Real
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import numpy as np
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from ..preprocessing import LabelBinarizer
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from ..utils.validation import check_consistent_length, check_array
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from ..utils.extmath import safe_sparse_dot
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from ..utils._param_validation import StrOptions, Interval, validate_params
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@validate_params(
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{
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"X": ["array-like", "sparse matrix"],
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"y": ["array-like"],
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"loss": [StrOptions({"squared_hinge", "log"})],
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"fit_intercept": ["boolean"],
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"intercept_scaling": [Interval(Real, 0, None, closed="neither")],
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}
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)
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def l1_min_c(X, y, *, loss="squared_hinge", fit_intercept=True, intercept_scaling=1.0):
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"""Return the lowest bound for C.
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The lower bound for C is computed such that for C in (l1_min_C, infinity)
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the model is guaranteed not to be empty. This applies to l1 penalized
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classifiers, such as LinearSVC with penalty='l1' and
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linear_model.LogisticRegression with penalty='l1'.
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This value is valid if class_weight parameter in fit() is not set.
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Parameters
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----------
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X : {array-like, sparse matrix} of shape (n_samples, n_features)
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Training vector, where `n_samples` is the number of samples and
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`n_features` is the number of features.
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y : array-like of shape (n_samples,)
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Target vector relative to X.
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loss : {'squared_hinge', 'log'}, default='squared_hinge'
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Specifies the loss function.
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With 'squared_hinge' it is the squared hinge loss (a.k.a. L2 loss).
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With 'log' it is the loss of logistic regression models.
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fit_intercept : bool, default=True
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Specifies if the intercept should be fitted by the model.
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It must match the fit() method parameter.
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intercept_scaling : float, default=1.0
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When fit_intercept is True, instance vector x becomes
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[x, intercept_scaling],
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i.e. a "synthetic" feature with constant value equals to
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intercept_scaling is appended to the instance vector.
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It must match the fit() method parameter.
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Returns
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-------
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l1_min_c : float
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Minimum value for C.
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"""
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X = check_array(X, accept_sparse="csc")
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check_consistent_length(X, y)
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Y = LabelBinarizer(neg_label=-1).fit_transform(y).T
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# maximum absolute value over classes and features
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den = np.max(np.abs(safe_sparse_dot(Y, X)))
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if fit_intercept:
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bias = np.full(
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(np.size(y), 1), intercept_scaling, dtype=np.array(intercept_scaling).dtype
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)
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den = max(den, abs(np.dot(Y, bias)).max())
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if den == 0.0:
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raise ValueError(
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"Ill-posed l1_min_c calculation: l1 will always "
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"select zero coefficients for this data"
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)
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if loss == "squared_hinge":
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return 0.5 / den
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else: # loss == 'log':
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return 2.0 / den
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