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
)

Defined in python/vi/csiszar_divergence.py.

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.