tfp.substrates.numpy.vi.t_power

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

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

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.

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.

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