tfp.experimental.stats.RunningCovariance

Holds metadata for and facilitates covariance computation.

RunningCovariance objects do not hold state information. That information, which includes intermediate calculations, are held in a RunningCovarianceState as returned via initialize and update method calls.

The running covariance computation supports batching. The event_ndims parameter indicates the number of trailing dimensions to treat as part of the event, and to compute covariance across. The leading dimensions, if any, are treated as batch shape, and no cross terms are computed.

For example, if the incoming samples have shape [5, 7], the event_ndims selects among three different covariance computations:

  • event_ndims=0 treats the samples as a [5, 7] batch of scalar random variables, and computes their variances in batch. The shape of the result is [5, 7].
  • event_ndims=1 treats the samples as a [5] batch of vector random variables of shape [7], and computes their covariances in batch. The shape of the result is [5, 7, 7].
  • event_ndims=2 treats the samples as a single random variable of shape [5, 7] and computes its covariance. The shape of the result is [5, 7, 5, 7].

RunningCovariance is meant to serve general streaming covariance needs. For a specialized version that fits streaming over MCMC samples, see CovarianceReducer in tfp.experimental.mcmc.

shape Python Tuple or TensorShape representing the shape of incoming samples.
event_ndims Number of dimensions that specify the event shape, from the inner-most dimensions. Specifying None returns all cross product terms (no batching) and is the default.
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.

ValueError if event_ndims is greater than the rank of the intended incoming samples (operation is extraneous).

Methods

finalize

View source

Finalizes running covariance computation for the state.

Args
state RunningCovarianceState that represents the current state of running statistics.
ddof Requested dynamic degrees of freedom for the covariance calculation. For example, use ddof=0 for population covariance and ddof=1 for sample covariance. Defaults to the population covariance.

Returns
covariance An estimate of the covariance.

initialize

View source

Initializes a RunningCovarianceState using previously defined metadata.

Returns
state RunningCovarianceState representing a stream of no inputs.

update

View source

Update the RunningCovarianceState with a new sample.

The update formula is from Philippe Pebay (2008) [1]. This implementation supports both batched and chunked covariance computation. A "batch" is the usual parallel computation, namely a batch of size N implies N independent covariance computations, each stepping one sample (or chunk) at a time. A "chunk" of size M implies incorporating M samples into a single covariance computation at once, which is more efficient than one by one.

To further illustrate the difference between batching and chunking, consider the following example:

# treat as 3 samples from each of 5 independent vector random variables of
# shape (2,)
sample = tf.ones((3, 5, 2))
running_cov = tfp.experimental.stats.RunningCovariance(
    (5, 2), event_ndims=1)
state = running_cov.initialize()
state = running_cov.update(state, sample, axis=0)
final_cov = running_cov.finalize(state)
final_cov.shape # (5, 2, 2)

Args
state RunningCovarianceState that represents the current state of running statistics.
new_sample Incoming sample with shape and dtype compatible with those used to form the RunningCovarianceState.
axis If chunking is desired, this is an integer that specifies the axis with chunked samples. For individual samples, set this to None. By default, samples are not chunked (axis is None).

Returns
state RunningCovarianceState with updated calculations.

References

[1]: Philippe Pebay. Formulas for Robust, One-Pass Parallel Computation of Covariances and Arbitrary-Order Statistical Moments. Technical Report SAND2008-6212, 2008. https://prod-ng.sandia.gov/techlib-noauth/access-control.cgi/2008/086212.pdf