Help protect the Great Barrier Reef with TensorFlow on Kaggle

# tfp.vi.symmetrized_csiszar_function

Symmetrizes a Csiszar-function in log-space.

A Csiszar-function is a member of,

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

The symmetrized Csiszar-function is defined as:

``````f_g(u) = 0.5 g(u) + 0.5 u g (1 / u)
``````

where `g` is some other Csiszar-function.

We say the function is "symmetrized" because:

``````D_{f_g}[p, q] = D_{f_g}[q, p]
``````

for all `p << >> q` (i.e., `support(p) = support(q)`).

There exists alternatives for symmetrizing a Csiszar-function. For example,

``````f_g(u) = max(f(u), f^*(u)),
``````

where `f^*` is the dual Csiszar-function, also implies a symmetric f-Divergence.

#### Example:

When either of the following functions are symmetrized, we obtain the Jensen-Shannon Csiszar-function, i.e.,

``````g(u) = -log(u) - (1 + u) log((1 + u) / 2) + u - 1
h(u) = log(4) + 2 u log(u / (1 + u))
``````

implies,

``````f_g(u) = f_h(u) = u log(u) - (1 + u) log((1 + u) / 2)
= jensen_shannon(log(u)).
``````

`logu` `float`-like `Tensor` representing `log(u)` from above.
`csiszar_function` Python `callable` representing a Csiszar-function over log-domain.
`name` Python `str` name prefixed to Ops created by this function.

`symmetrized_g_of_u` `float`-like `Tensor` of the result of applying the symmetrization of `g` evaluated at `u = exp(logu)`.

[{ "type": "thumb-down", "id": "missingTheInformationINeed", "label":"Missing the information I need" },{ "type": "thumb-down", "id": "tooComplicatedTooManySteps", "label":"Too complicated / too many steps" },{ "type": "thumb-down", "id": "outOfDate", "label":"Out of date" },{ "type": "thumb-down", "id": "samplesCodeIssue", "label":"Samples / code issue" },{ "type": "thumb-down", "id": "otherDown", "label":"Other" }]
[{ "type": "thumb-up", "id": "easyToUnderstand", "label":"Easy to understand" },{ "type": "thumb-up", "id": "solvedMyProblem", "label":"Solved my problem" },{ "type": "thumb-up", "id": "otherUp", "label":"Other" }]