vi_t_power: The T-Power Csiszar-function in log-space

In tfprobability: Interface to 'TensorFlow Probability'

The T-Power Csiszar-function in log-space

Description

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

Usage

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

Arguments

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.

Details

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'.

Value

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

See Also

Other vi-functions#': vi_total_variation(), vi_triangular()

tfprobability documentation built on Sept. 1, 2022, 5:07 p.m.