| vi_dual_csiszar_function {tfprobability} | R Documentation |
Calculates the dual Csiszar-function in log-space
Description
A Csiszar-function is a member of F = { f:R_+ to R : f convex }.
Usage
vi_dual_csiszar_function(logu, csiszar_function, name = NULL)
Arguments
logu |
|
csiszar_function |
function representing a Csiszar-function over log-domain. |
name |
name prefixed to Ops created by this function. |
Details
The Csiszar-dual is defined as:
f^*(u) = u f(1 / u)
where f is some other Csiszar-function.
For example, the dual of kl_reverse is kl_forward, i.e.,
f(u) = -log(u) f^*(u) = u f(1 / u) = -u log(1 / u) = u log(u)
The dual of the dual is the original function:
f^**(u) = {u f(1/u)}^*(u) = u (1/u) f(1/(1/u)) = f(u)
Warning: this function makes non-log-space calculations and may therefore be
numerically unstable for |logu| >> 0.
Value
dual_f_of_u float-like Tensor of the result of calculating the dual of
f at u = exp(logu).
See Also
Other vi-functions:
vi_amari_alpha(),
vi_arithmetic_geometric(),
vi_chi_square(),
vi_csiszar_vimco(),
vi_fit_surrogate_posterior(),
vi_jeffreys(),
vi_jensen_shannon(),
vi_kl_forward(),
vi_kl_reverse(),
vi_log1p_abs(),
vi_modified_gan(),
vi_monte_carlo_variational_loss(),
vi_pearson(),
vi_squared_hellinger(),
vi_symmetrized_csiszar_function()