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Computes running central moments.

Inherits From: AutoCompositeTensor

RunningCentralMoments will compute arbitrary central moments in streaming fashion following the formula proposed by Philippe Pebay (2008) [1]. For reference, the formula we refer to is the incremental version of arbitrary moments (equation 2.9). Since the algorithm computes moments as a function of lower ones, even if not requested, all lower moments will be computed as well. The moments that are actually returned is specified by the moment parameter at initialization. Note, while any arbitrarily high central moment is theoretically supported, RunningCentralMoments cannot guarantee numerical stability for all moments.


[1]: Philippe Pebay. Formulas for Robust, One-Pass Parallel Computation of Covariances and Arbitrary-Order Statistical Moments. Technical Report SAND2008-6212, 2008.

mean_state A RunningMean carrying the running mean estimate.
exponentiated_residuals A Tensor representing the sum of exponentiated residuals. This is a Tensor of shape [max_moment - 1] + mean_state.mean.shape, which contains the sum of the residuals raised to the kth power, for all 2 <= k <= max_moment.
desired_moments A Python list of integers giving the moments to return. The maximum element of this list gives the number of moments that will be computed.



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Returns an empty RunningCentralMoments.

shape Python Tuple or TensorShape representing the shape of incoming samples.
moment Integer or iterable of integers that represent the desired moments to return.
dtype Dtype of incoming samples and the resulting statistics. By default, the dtype is tf.float32. Any integer dtypes will be cast to corresponding floats (i.e. tf.int32 will be cast to tf.float32), as intermediate calculations should be performing floating-point division.

state RunningCentralMoments representing a stream of no inputs.


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Returns the central moments represented by this RunningCentralMoments.

all_moments A Tensor representing estimates of the requested central moments. Its leading dimension indexes the moment, in order of those requested (i.e. in order of self.desired_moments).


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Update with a new sample.

new_sample Incoming Tensor sample with shape and dtype compatible with those used to form the RunningCentralMoments.

state RunningCentralMoments updated to include the new sample.