vi_kl_forward {tfprobability}

The forward Kullback-Leibler Csiszar-function in log-space

Description

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

Usage

vi_kl_forward(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 KL-reverse Csiszar-function is ⁠f(u) = u log(u) - (u - 1)⁠. When self_normalized = FALSE the (u - 1) term is omitted. Observe that as an f-Divergence, this Csiszar-function implies: D_f[p, q] = KL[q, p]

The KL is "forward" because in maximum likelihood we think of minimizing q as in KL[p, q].

Warning: when self_normalized = True⁠this function makes non-log-space calculations and may therefore be numerically unstable for⁠|logu| >> 0'.

Value

kl_forward_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_reverse(), vi_log1p_abs(), vi_modified_gan(), vi_monte_carlo_variational_loss(), vi_pearson(), vi_squared_hellinger(), vi_symmetrized_csiszar_function()