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# tfp.stats.log_soosum_exp

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Computes the log-swap-one-out-sum of `exp(logx)`.

The swapped out element `logx[i]` is replaced with the log-leave-`i`-out geometric mean of `logx`.

`logx` Floating-type `Tensor` representing `log(x)` where `x` is some positive value.
`axis` The dimensions to sum across. If `None` (the default), reduces all dimensions. Must be in the range `[-rank(logx), rank(logx)]`. Default value: `None` (i.e., reduce over all dims).
`keepdims` If true, retains reduced dimensions with length 1. Default value: `False` (i.e., keep all dims in `log_mean_x`).
`name` Python `str` name prefixed to Ops created by this function. Default value: `None` (i.e., `"log_soomean_exp"`).

`log_soomean_x` `logx.dtype` `Tensor` characterized by the natural-log of the sum of `x``except that the element`logx[i]```is replaced with the log of the leave-```i`-out Geometric-average. The sum of the gradient of`log_soosum_x`is`n```, i.e., the number of reduced elements. Mathematically```log_soomean_x` is,

``````log_soomean_x[i] = log(Avg{h[j ; i] : j=0, ..., m-1})
h[j ; i] = { u[j]                              j!=i
{ GeometricAverage{u[k] : k != i}   j==i
``````

`log_sum_x` `logx.dtype` `Tensor` corresponding to the natural-log of the average of `x`. The sum of the gradient of `log_mean_x` is `1`. Has reduced shape of `logx` (per `axis` and `keepdims`).

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