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The Amari-alpha Csiszar-function in log-space.
tfp.substrates.jax.vi.amari_alpha(
logu, alpha=1.0, self_normalized=False, name=None
)
A Csiszar-function is a member of,
F = { f:R_+ to R : f convex }.
When self_normalized = True
, the Amari-alpha Csiszar-function is:
f(u) = { -log(u) + (u - 1), alpha = 0
{ u log(u) - (u - 1), alpha = 1
{ [(u**alpha - 1) - alpha (u - 1)] / (alpha (alpha - 1)), otherwise
When self_normalized = False
the (u - 1)
terms are omitted.
For more information, see: A. Cichocki and S. Amari. "Families of Alpha-Beta-and GammaDivergences: Flexible and Robust Measures of Similarities." Entropy, vol. 12, no. 6, pp. 1532-1568, 2010.
Returns | |
---|---|
amari_alpha_of_u
|
float -like Tensor of the Csiszar-function evaluated
at u = exp(logu) .
|
Raises | |
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TypeError
|
if alpha is None or a Tensor .
|
TypeError
|
if self_normalized is None or a Tensor .
|