The Modified-GAN Csiszar-function in log-space

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

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.

Value

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

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.

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()