The Jeffreys Csiszar-function in log-space

Source: R/vi-functions.R

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

vi_jeffreys(logu, name = NULL)

Arguments

logu

float-like Tensor representing log(u) from above.
name

name prefixed to Ops created by this function.

Value

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

Details

The Jeffreys Csiszar-function is:

f(u) = 0.5 ( u log(u) - log(u))
= 0.5 kl_forward + 0.5 kl_reverse
= symmetrized_csiszar_function(kl_reverse)
= symmetrized_csiszar_function(kl_forward)

This Csiszar-function induces a symmetric f-Divergence, i.e., D_f[p, q] = D_f[q, p].

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_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()