View source on GitHub |
The Arithmetic-Geometric Csiszar-function in log-space.
tfp.substrates.numpy.vi.arithmetic_geometric(
logu, self_normalized=False, name=None
)
A Csiszar-function is a member of,
F = { f:R_+ to R : f convex }.
When self_normalized = True
the Arithmetic-Geometric Csiszar-function is:
f(u) = (1 + u) log( (1 + u) / sqrt(u) ) - (1 + u) log(2)
When self_normalized = False
the (1 + u) log(2)
term is omitted.
Observe that as an f-Divergence, this Csiszar-function implies:
D_f[p, q] = KL[m, p] + KL[m, q]
m(x) = 0.5 p(x) + 0.5 q(x)
In a sense, this divergence is the "reverse" of the Jensen-Shannon f-Divergence.
This Csiszar-function induces a symmetric f-Divergence, i.e.,
D_f[p, q] = D_f[q, p]
.
Returns | |
---|---|
arithmetic_geometric_of_u
|
float -like Tensor of the
Csiszar-function evaluated at u = exp(logu) .
|