# tfp.vi.kl_reverse

The reverse Kullback-Leibler Csiszar-function in log-space.

A Csiszar-function is a member of,

``````F = { f:R_+ to R : f convex }.
``````

When `self_normalized = True`, the KL-reverse Csiszar-function is:

``````f(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 "reverse" because in maximum likelihood we think of minimizing `q` as in `KL[p, q]`.

`logu` `float`-like `Tensor` representing `log(u)` from above.
`self_normalized` Python `bool` 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` Python `str` name prefixed to Ops created by this function.

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

`TypeError` if `self_normalized` is `None` or a `Tensor`.

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