tf.nn.log_poisson_loss

Computes log Poisson loss given log_input.

tf.nn.log_poisson_loss(
    targets, log_input, compute_full_loss=False, name=None
)

Gives the log-likelihood loss between the prediction and the target under the assumption that the target has a Poisson distribution. Caveat: By default, this is not the exact loss, but the loss minus a constant term [log(z!)]. That has no effect for optimization, but does not play well with relative loss comparisons. To compute an approximation of the log factorial term, specify compute_full_loss=True to enable Stirling's Approximation.

For brevity, let c = log(x) = log_input, z = targets. The log Poisson loss is

  -log(exp(-x) * (x^z) / z!)
= -log(exp(-x) * (x^z)) + log(z!)
~ -log(exp(-x)) - log(x^z) [+ z * log(z) - z + 0.5 * log(2 * pi * z)]
    [ Note the second term is the Stirling's Approximation for log(z!).
      It is invariant to x and does not affect optimization, though
      important for correct relative loss comparisons. It is only
      computed when compute_full_loss == True. ]
= x - z * log(x) [+ z * log(z) - z + 0.5 * log(2 * pi * z)]
= exp(c) - z * c [+ z * log(z) - z + 0.5 * log(2 * pi * z)]

targets A Tensor of the same type and shape as log_input.
log_input A Tensor of type float32 or float64.
compute_full_loss whether to compute the full loss. If false, a constant term is dropped in favor of more efficient optimization.
name A name for the operation (optional).

A Tensor of the same shape as log_input with the componentwise logistic losses.

ValueError If log_input and targets do not have the same shape.