vi_t_power {tfprobability}

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()