vi_modified_gan {tfprobability}

The Modified-GAN Csiszar-function in log-space

Description

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

Usage

vi_modified_gan(logu, self_normalized = FALSE, name = NULL)

Arguments

logu

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

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 modified-GAN (Generative/Adversarial Network) Csiszar-function is:

f(u) = log(1 + u) - log(u) + 0.5 (u - 1)

When self_normalized = False the 0.5 (u - 1) is omitted.

The unmodified GAN Csiszar-function is identical to Jensen-Shannon (with self_normalized = False).

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

Value

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

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_log1p_abs(), vi_monte_carlo_variational_loss(), vi_pearson(), vi_squared_hellinger(), vi_symmetrized_csiszar_function()