# tfp.vi.amari_alpha

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

``````tfp.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.

#### Args:

• `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.

#### Returns:

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

#### Raises:

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