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# tfp.substrates.numpy.stats.assign_log_moving_mean_exp

Compute the log of the exponentially weighted moving mean of the exp.

If `log_value` is a draw from a stationary random variable, this function approximates `log(E[exp(log_value)])`, i.e., a weighted log-sum-exp. More precisely, a `tf.Variable`, `moving_log_mean_exp`, is updated by `log_value` using the following identity:

``````moving_log_mean_exp =
= log(decay exp(moving_log_mean_exp) + (1 - decay) exp(log_value))
= log(exp(moving_log_mean_exp + log(decay)) + exp(log_value + log1p(-decay)))
= moving_log_mean_exp

+ log(  exp(moving_log_mean_exp   - moving_log_mean_exp + log(decay))
+ exp(log_value - moving_log_mean_exp + log1p(-decay)))
= moving_log_mean_exp
+ log_sum_exp([log(decay), log_value - moving_log_mean_exp +
log1p(-decay)]).
``````

In addition to numerical stability, this formulation is advantageous because `moving_log_mean_exp` can be updated in a lock-free manner, i.e., using `assign_add`. (Note: the updates are not thread-safe; it's just that the update to the tf.Variable is presumed efficient due to being lock-free.)

`log_value` `float`-like `Tensor` representing a new (streaming) observation. Same shape as `moving_log_mean_exp`.
`moving_log_mean_exp` `float`-like `Variable` representing the log of the exponentially weighted moving mean of the exp. Same shape as `log_value`.
`zero_debias_count` `int`-like `tf.Variable` representing the number of times this function has been called on streaming input (not the number of reduced values used in this functions computation). When not `None` (the default) the returned values for `moving_mean` and `moving_variance` are "zero debiased", i.e., corrected for their presumed all zeros intialization. Note: the `tf.Variable`s `moving_mean` and `moving_variance` always store the unbiased calculation, regardless of setting this argument. To obtain unbiased calculations from these `tf.Variable`s, see `tfp.stats.moving_mean_variance_zero_debiased`. Default value: `None` (i.e., no zero debiasing calculation is made).
`decay` A `float`-like `Tensor` representing the moving mean decay. Typically close to `1.`, e.g., `0.99`. Default value: `0.99`.
`name` Python `str` prepended to op names created by this function. Default value: `None` (i.e., 'assign_log_moving_mean_exp').

`moving_log_mean_exp` A reference to the input 'Variable' tensor with the `log_value`-updated log of the exponentially weighted moving mean of exp.

`TypeError` if `moving_log_mean_exp` does not have float type `dtype`.
`TypeError` if `moving_log_mean_exp`, `log_value`, `decay` have different `base_dtype`.