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# tfp.vi.amari_alpha

The Amari-alpha Csiszar-function in log-space.

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.

`logu` `float`-like `Tensor` representing `log(u)` from above.
`alpha` `float`-like Python scalar. (See Mathematical Details for meaning.)
`self_normalized` Python `bool` indicating whether `f'(u=1)=0`. When `f'(u=1)=0` the implied Csiszar f-Divergence remains non-negative even when `p, q` are unnormalized measures.
`name` Python `str` name prefixed to Ops created by this function.

`amari_alpha_of_u` `float`-like `Tensor` of the Csiszar-function evaluated at `u = exp(logu)`.

`TypeError` if `alpha` is `None` or a `Tensor`.
`TypeError` if `self_normalized` is `None` or a `Tensor`.

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