mars.learn.metrics.log_loss#

mars.learn.metrics.log_loss(y_true, y_pred, *, eps=1e-15, 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 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_true (array-like or label indicator matrix) – Ground truth (correct) labels for n_samples samples.

  • y_pred (array-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 preprocessing.LabelBinarizer.

  • eps (float, default=1e-15) – Log loss is undefined for p=0 or p=1, so probabilities are clipped to max(eps, min(1 - eps, p)).

  • normalize (bool, default=True) – If true, return the mean loss per sample. Otherwise, return the sum of the per-sample losses.

  • sample_weight (array-like of shape (n_samples,), default=None) – Sample weights.

  • labels (array-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.

Returns

loss

Return type

float

Notes

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

Examples

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

References

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