vi_t_power: The T-Power Csiszar-function in log-space
In rstudio/tfprobability: Interface to 'TensorFlow Probability'

vi_t_power

R Documentation

The T-Power Csiszar-function in log-space

A Csiszar-function is a member of F = { f:R_+ to R : f convex }.

vi_t_power(logu, t, self_normalized = FALSE, name = NULL)

`logu`	`float`-like `Tensor` representing `log(u)` from above.
`t`	`Tensor` of same `dtype` as `logu` and broadcastable shape.
`self_normalized`	`logical` 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`	name prefixed to Ops created by this function.

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.

Warning: when self_normalized = Truethis function makes non-log-space calculations and may therefore be numerically unstable for|logu| >> 0'.

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