log_loss

sklearn.metrics.log_loss(y_true, y_pred, *, normalize=True, sample_weight=None, labels=None)[source]

Log loss, aka logistic loss or cross-entropy loss.

This is the loss function used in (multinomial) logistic regression and extensions of it such as neural networks, defined as the negative log-likelihood of a logistic model that returns y_pred probabilities for its training data y_true. The log loss is only defined for two or more labels. For a single sample with true label \(y \in \{0,1\}\) and a probability estimate \(p = \operatorname{Pr}(y = 1)\), the log loss is:

\[L_{\log}(y, p) = -(y \log (p) + (1 - y) \log (1 - p))\]

Read more in the User Guide.

Parameters:

y_truearray-like or label indicator matrix

Ground truth (correct) labels for n_samples samples.

y_predarray-like of float, shape = (n_samples, n_classes) or (n_samples,)

Predicted probabilities, as returned by a classifier’s predict_proba method. If y_pred.shape = (n_samples,) the probabilities provided are assumed to be that of the positive class. The labels in y_pred are assumed to be ordered alphabetically, as done by LabelBinarizer.

y_pred values are clipped to [eps, 1-eps] where eps is the machine precision for y_pred’s dtype.

normalizebool, default=True

If true, return the mean loss per sample. Otherwise, return the sum of the per-sample losses.

sample_weightarray-like of shape (n_samples,), default=None

Sample weights.

labelsarray-like, default=None

If not provided, labels will be inferred from y_true. If labels is None and y_pred has shape (n_samples,) the labels are assumed to be binary and are inferred from y_true.

Added in version 0.18.

Returns:

lossfloat

Log loss, aka logistic loss or cross-entropy loss.

Notes

The logarithm used is the natural logarithm (base-e).

References

C.M. Bishop (2006). Pattern Recognition and Machine Learning. Springer, p. 209.

Examples

>>> from sklearn.metrics import log_loss
>>> log_loss(["spam", "ham", "ham", "spam"],
...          [[.1, .9], [.9, .1], [.8, .2], [.35, .65]])
0.21616...

Gallery examples

Probability Calibration curves

Probability Calibration for 3-class classification

Gradient Boosting Out-of-Bag estimates

Gradient Boosting regularization

Probabilistic predictions with Gaussian process classification (GPC)

Importance of Feature Scaling