The log1p-abs Csiszar-function in log-space

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

vi_log1p_abs(logu, name = NULL)

Arguments

logu	float-like Tensor representing log(u) from above.
name	name prefixed to Ops created by this function.

Value

log1p_abs_of_u: float-like Tensor of the Csiszar-function evaluated at u = exp(logu).

Details

The Log1p-Abs Csiszar-function is:

f(u) = u**(sign(u-1)) - 1

This function is so-named because it was invented from the following recipe. Choose a convex function g such that g(0)=0 and solve for f:

log(1 + f(u)) = g(log(u)).
<=>
f(u) = exp(g(log(u))) - 1

That is, the graph is identically g when y-axis is log1p-domain and x-axis is log-domain.

Warning: this function makes non-log-space calculations and may therefore be numerically unstable for |logu| >> 0.

See also

Other vi-functions: vi_amari_alpha(), vi_arithmetic_geometric(), vi_chi_square(), vi_csiszar_vimco(), vi_dual_csiszar_function(), vi_fit_surrogate_posterior(), vi_jeffreys(), vi_jensen_shannon(), vi_kl_forward(), vi_kl_reverse(), vi_modified_gan(), vi_monte_carlo_variational_loss(), vi_pearson(), vi_squared_hellinger(), vi_symmetrized_csiszar_function()