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tfp.vi.t_power

tfp.vi.t_power(
    logu,
    t,
    self_normalized=False,
    name=None
)

The T-Power Csiszar-function in log-space.

A Csiszar-function is a member of,

F = { f:R_+ to R : f convex }.

When self_normalized = True the T-Power Csiszar-function is:

f(u) = s [ u**t - 1 - t(u - 1) ]
s = { -1   0 < t < 1
    { +1   otherwise

When self_normalized = False the - t(u - 1) term is omitted.

This is similar to the amari_alpha Csiszar-function, with the associated divergence being the same up to factors depending only on t.

Args:

  • logu: float-like Tensor representing log(u) from above.
  • t: Tensor of same dtype as logu and broadcastable shape.
  • self_normalized: Python bool indicating whether f'(u=1)=0.
  • name: Python str name prefixed to Ops created by this function.

Returns:

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