def test_logreg_predict_proba_multinomial():
X, y = make_classification(n_samples=10, n_features=20, random_state=0,
n_classes=3, n_informative=10)
# Predicted probabilites using the true-entropy loss should give a
# smaller loss than those using the ovr method.
clf_multi = LogisticRegression(multi_class="multinomial", solver="lbfgs")
clf_multi.fit(X, y)
clf_multi_loss = log_loss(y, clf_multi.predict_proba(X))
clf_ovr = LogisticRegression(multi_class="ovr", solver="lbfgs")
clf_ovr.fit(X, y)
clf_ovr_loss = log_loss(y, clf_ovr.predict_proba(X))
assert_greater(clf_ovr_loss, clf_multi_loss)
# Predicted probabilites using the soft-max function should give a
# smaller loss than those using the logistic function.
clf_multi_loss = log_loss(y, clf_multi.predict_proba(X))
clf_wrong_loss = log_loss(y, clf_multi._predict_proba_lr(X))
assert_greater(clf_wrong_loss, clf_multi_loss)
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