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Module « scipy.special »

Fonction xlogy - module scipy.special

Signature de la fonction xlogy

def xlogy(*args, **kwargs) 

Description

help(scipy.special.xlogy)

xlogy(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

xlogy(x, y, out=None)

Compute ``x*log(y)`` so that the result is 0 if ``x = 0``.

Parameters
----------
x : array_like
    Multiplier
y : array_like
    Argument
out : ndarray, optional
    Optional output array for the function results

Returns
-------
z : scalar or ndarray
    Computed x*log(y)

Notes
-----
The log function used in the computation is the natural log.

.. versionadded:: 0.13.0

Examples
--------
We can use this function to calculate the binary logistic loss also
known as the binary cross entropy. This loss function is used for
binary classification problems and is defined as:

.. math::
    L = 1/n * \sum_{i=0}^n -(y_i*log(y\_pred_i) + (1-y_i)*log(1-y\_pred_i))

We can define the parameters `x` and `y` as y and y_pred respectively.
y is the array of the actual labels which over here can be either 0 or 1.
y_pred is the array of the predicted probabilities with respect to
the positive class (1).

>>> import numpy as np
>>> from scipy.special import xlogy
>>> y = np.array([0, 1, 0, 1, 1, 0])
>>> y_pred = np.array([0.3, 0.8, 0.4, 0.7, 0.9, 0.2])
>>> n = len(y)
>>> loss = -(xlogy(y, y_pred) + xlogy(1 - y, 1 - y_pred)).sum()
>>> loss /= n
>>> loss
0.29597052165495025

A lower loss is usually better as it indicates that the predictions are
similar to the actual labels. In this example since our predicted
probabilities are close to the actual labels, we get an overall loss
that is reasonably low and appropriate.

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