mygrad.nnet.losses.negative_log_likelihood#

mygrad.nnet.losses.negative_log_likelihood(x: ArrayLike, y_true: ArrayLike, *, weights: ArrayLike | None = None, constant: bool | None = None) → Tensor[source]#

Returns the (weighted) negative log-likelihood loss between log-probabilities and y_true.

Note that this does not compute a softmax, so you should input log-probabilities to this. See softmax_crossentropy if you need your loss to compute a softmax.

Parameters:

xArrayLike, shape=(N, C): The C log-probabilities for each of the N pieces of data.
y_trueArrayLike, shape=(N,): The correct class indices, in [0, C), for each datum.
weightsArrayLike, shape=(C,) optional (default=None): The weighting factor to use on each class, or None.
constantbool, optional(default=False): If True, the returned tensor is a constant (it does not back-propagate a gradient)

Returns:

mygrad.Tensor, shape=(): The average (weighted) negative log-likelihood loss.

Examples

>>> import mygrad as mg
>>> from mygrad.nnet import negative_log_likelihood

Let’s take a simple case where N=1, and C=3. We’ll thus make up classification scores for a single datum. Suppose the scores are identical for the three classes and that the true class is class-0, so that the log-probs are each 1/3:

>>> logprob = mg.log(1 / 3).item()
>>> x = mg.Tensor([[logprob, logprob, logprob]])  # a shape-(1, 3) tensor of log-probabilities
>>> y_true = mg.Tensor([0])  # the correct class for this datum is class-0
>>> negative_log_likelihood(x, y_true)
Tensor(1.09861229)

Log-probabilities where the prediction is highly-confident and correct:

>>> x = mg.Tensor([[0, -20, -20]])
>>> negative_log_likelihood(x, y_true)
Tensor(0.)

Adding a class-weighting:

>>> x = mg.Tensor([[-4.6, -4.6, -0.02]])
>>> weights = mg.Tensor([2, 1, 1])
>>> negative_log_likelihood(x, y_true, weights=weights)
Tensor(9.2)