online-stats — Online algorithm for mean, variance, and covariance

The online-stats Python package contains a single function online_stats.add_sample() which updates a sample mean given a new sample, as well as optionally the sample variance and the sample covariance matrix.

The package has no dependencies, as the online_stats.add_sample() function works with any input data type that supports in-place addition and fancy slicing.

Usage

>>> import numpy as np
>>>
>>> # the package
>>> import online_stats
>>>
>>> # online algorithm for the mean
>>> # start from zero
>>> mu = np.zeros(4)
>>>
>>> # generate samples and compute their mean
>>> for i in range(1000):
...     x = np.random.normal([0.1, 0.3, 0.5, 0.7])
...     online_stats.add_sample(i, x, mu)
...
>>> # the mean is computed in place
>>> print(mu)
[0.08804402 0.25896929 0.44891264 0.73418769]
>>>
>>> # compute the variance
>>> mu = np.zeros(4)
>>> var = np.zeros(4)
>>> for i in range(1000):
...     x = np.random.normal([0.1, 0.3, 0.5, 0.7], [0.2, 0.4, 0.6, 0.8])
...     online_stats.add_sample(i, x, mu, var=var)
...
>>> print(mu)
[0.09854301 0.29509305 0.4777673  0.70008311]
>>> print(var**0.5)
[0.19900518 0.4012857  0.59267129 0.81856542]
>>>
>>> # compute the covariance matrix
>>> mu = np.zeros(4)
>>> cov = np.zeros((4, 4))
>>> for i in range(100_000):
...     x = np.random.multivariate_normal([0.1, 0.3, 0.5, 0.7],
...             [[0.2, 0.02, 0.04, 0.06],
...              [0.02, 0.4, 0.06, 0.08],
...              [0.04, 0.06, 0.6, 0.10],
...              [0.06, 0.08, 0.10, 0.8]])
...     online_stats.add_sample(i, x, mu, cov=cov)
...
>>> print(mu)
[0.10095607 0.30486108 0.50113141 0.69912377]
>>> print(cov)
[[0.20101406 0.02105503 0.0382198  0.06220174]
 [0.02105503 0.39909545 0.06192678 0.0791239 ]
 [0.0382198  0.06192678 0.59960537 0.1082596 ]
 [0.06220174 0.0791239  0.1082596  0.80071002]]