View source on GitHub
|
Cumulative estimates of variance.
tfp.substrates.numpy.stats.cumulative_variance(
x, sample_axis=0, name=None
)
Given N samples of a scalar-valued random variable X, we can compute
cumulative variance estimates
result[i] = variance(x[0:i+1])
in O(N) work and O(log(N)) depth (the length of the longest series
of operations that are performed sequentially), with O(1) TF kernel
invocations. This implementation also arranges to do so in a
numerically accurate manner, i.e., without incurring a subtraction
of floating-point numbers of size quadratic in the data x. The
underlying algorithm is from [1].
Args | |
|---|---|
x
|
A numeric Tensor holding samples.
|
sample_axis
|
Scalar Tensor designating the axis holding samples.
Other axes are treated in batch. Default value: 0 (leftmost
dimension).
|
name
|
Python str name prefixed to Ops created by this function.
Default value: None (i.e., 'cumulative_variance').
|
Returns | |
|---|---|
cum_var
|
A Tensor of same shape and dtype as x giving
cumulative variance estimates. The zeroth element is the
variance of a size-1 set of samples, so 0.
|
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