R: The Jensen-Shannon Csiszar-function in log-space

vi_jensen_shannon {tfprobability}

R Documentation

The Jensen-Shannon Csiszar-function in log-space

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

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

`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.

When self_normalized = True, the Jensen-Shannon Csiszar-function is:

f(u) = u log(u) - (1 + u) log(1 + u) + (u + 1) log(2)

When self_normalized = False the ⁠(u + 1) log(2)⁠ term is omitted.

Observe that as an f-Divergence, this Csiszar-function implies:

D_f[p, q] = KL[p, m] + KL[q, m]
m(x) = 0.5 p(x) + 0.5 q(x)

In a sense, this divergence is the "reverse" of the Arithmetic-Geometric f-Divergence.

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.

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

Lin, J. "Divergence measures based on the Shannon entropy." IEEE Trans. Inf. Th., 37, 145-151, 1991.