tf.nn.log_poisson_loss( targets, log_input, compute_full_loss=False, name=None )
Computes log Poisson loss given
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
-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)]
Tensorof the same type and shape as
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).
Tensor of the same shape as
log_input with the componentwise
targetsdo not have the same shape.