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The log1p-abs Csiszar-function in log-space.
tfp.substrates.numpy.vi.log1p_abs(
logu, name=None
)
A Csiszar-function is a member of,
F = { f:R_+ to R : f convex }.
The Log1p-Abs Csiszar-function is:
f(u) = u**(sign(u-1)) - 1
This function is so-named because it was invented from the following recipe. Choose a convex function g such that g(0)=0 and solve for f:
log(1 + f(u)) = g(log(u)).
<=>
f(u) = exp(g(log(u))) - 1
That is, the graph is identically g
when y-axis is log1p
-domain and x-axis
is log
-domain.
Args | |
---|---|
logu
|
float -like Tensor representing log(u) from above.
|
name
|
Python str name prefixed to Ops created by this function.
|
Returns | |
---|---|
log1p_abs_of_u
|
float -like Tensor of the Csiszar-function evaluated
at u = exp(logu) .
|