|---| | [ View source on GitHub](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/stats/moving_stats.py#L32-L209) | Compute one update to the exponentially weighted moving mean and variance. tfp.stats.assign_moving_mean_variance( value, moving_mean, moving_variance=None, zero_debias_count=None, decay=0.99, axis=(), name=None ) The `value` updated exponentially weighted moving `moving_mean` and `moving_variance` are conceptually given by the following recurrence relations (\[Welford (1962)\]\[1\]): new_mean = old_mean + (1 - decay) * (value - old_mean) new_var = old_var + (1 - decay) * (value - old_mean) * (value - new_mean) This function implements the above recurrences in a numerically stable manner and also uses the `assign_add` op to allow concurrent lockless updates to the supplied variables. For additional references see [John D. Cook's Blog](https://www.johndcook.com/blog/standard_deviation), whereas we use `1 - decay = 1 / k`, and \[Finch (2009; Eq. 143)\]\[2\], whereas we use `1 - decay = alpha`. Since variables that are initialized to a `0` value will be `0` biased, providing `zero_debias_count` triggers scaling the `moving_mean` and `moving_variance` by the factor of `1 - decay ** (zero_debias_count + 1)`. For more details, see [`tfp.stats.moving_mean_variance_zero_debiased`](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/moving_mean_variance_zero_debiased).


| ## Args || |---|---| | `value` | `float`-like `Tensor` representing one or more streaming observations. When `axis` is non-empty `value` is reduced (by mean) for updated `moving_mean` and `moving-variance`. Presumed to have same shape as `moving_mean` and `moving_variance`. | | `moving_mean` | `float`-like [`tf.Variable`](https://www.tensorflow.org/api_docs/python/tf/Variable) representing the exponentially weighted moving mean. Same shape as `moving_variance` and `value`. This function presumes the [`tf.Variable`](https://www.tensorflow.org/api_docs/python/tf/Variable) was created with all zero initial value(s). | | `moving_variance` | `float`-like [`tf.Variable`](https://www.tensorflow.org/api_docs/python/tf/Variable) representing the exponentially weighted moving variance. Same shape as `moving_mean` and `value`. This function presumes the [`tf.Variable`](https://www.tensorflow.org/api_docs/python/tf/Variable) was created with all zero initial value(s). Default value: `None` (i.e., no moving variance is computed). | | `zero_debias_count` | `int`-like [`tf.Variable`](https://www.tensorflow.org/api_docs/python/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`](https://www.tensorflow.org/api_docs/python/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`](https://www.tensorflow.org/api_docs/python/tf/Variable)s, see [`tfp.stats.moving_mean_variance_zero_debiased`](https://www.tensorflow.org/probability/api_docs/python/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`. | | `axis` | The dimensions to reduce. If `()` (the default) no dimensions are reduced. If `None` all dimensions are reduced. Must be in the range `[-rank(value), rank(value))`. Default value: `()` (i.e., no reduction is made). | | `name` | Python `str` prepended to op names created by this function. Default value: `None` (i.e., 'assign_moving_mean_variance'). |



| ## Returns || |---|---| | `moving_mean` | The `value`-updated exponentially weighted moving mean. Debiased if `zero_debias_count is not None`. | | `moving_variance` | The `value`-updated exponentially weighted moving variance. Debiased if `zero_debias_count is not None`. |



| ## Raises || |---|---| | `TypeError` | if `moving_mean` does not have float type `dtype`. | | `TypeError` | if `moving_mean`, `moving_variance`, `value`, `decay` have different `base_dtype`. |
#### Examples import tensorflow as tf import tensorflow_probability as tfp tfd = tfp.distributions d = tfd.MultivariateNormalTriL( loc=[-1., 1.], scale_tril=tf.linalg.cholesky([[0.75, 0.05], [0.05, 0.5]])) d.mean() # ==> [-1., 1.] d.variance() # ==> [0.75, 0.5] moving_mean = tf.Variable(tf.zeros(2)) moving_variance = tf.Variable(tf.zeros(2)) zero_debias_count = tf.Variable(0) for _ in range(100): m, v = tfp.stats.assign_moving_mean_variance( value=d.sample(3), moving_mean=moving_mean, moving_variance=moving_variance, zero_debias_count=zero_debias_count, decay=0.99, axis=-2) print(m.numpy(), v.numpy()) # ==> [-1.0334632 0.9545268] [0.8126194 0.5118788] # ==> [-1.0293456 0.96070296] [0.8115873 0.50947404] # ... # ==> [-1.025172 0.96351 ] [0.7142789 0.48570773] m1, v1 = tfp.stats.moving_mean_variance_zero_debiased( moving_mean, moving_variance, zero_debias_count, decay=0.99) print(m.numpy(), v.numpy()) # ==> [-1.025172 0.96351 ] [0.7142789 0.48570773] assert(all(m == m1)) assert(all(v == v1)) #### References \[1\] B. P. Welford. Note on a Method for Calculating Corrected Sums of Squares and Products. Technometrics, Vol. 4, No. 3 (Aug., 1962), p419-20. [http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.302.7503\&rep=rep1\&type=pdf](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.302.7503&rep=rep1&type=pdf) \[2\]: Tony Finch. Incremental calculation of weighted mean and variance. *Technical Report* , 2009.