omoment 0.1.1

Estimates statistical moments in online or distributed settings.

OMoment: Efficient online calculation of statistical moments

OMoment package calculates moments of statistical distributions (mean and variance) in online or distributed settings.

• Suitable for large data – works well with numpy and Pandas and in distributed setting.

• Moments calculated from different parts of data can be easily combined or updated for new data (supports addition of results).

• Objects are lightweight, calculation is done in numpy if possible.

• Weights for data can be provided.

• Invalid values (NaNs, infinities are omitted by default).

Typical application is calculation of means and variances of many chunks of data (corresponding to different groups or to different parts of the distributed data), the results can be analyzed on level of the groups or easily combined to get exact moments for the full dataset.

Basic example

from omoment import OMeanVar
import numpy as np
import pandas as pd

rng = np.random.default_rng(12354)
g = rng.integers(low=0, high=10, size=1000)
x = g + rng.normal(loc=0, scale=10, size=1000)
w = rng.exponential(scale=1, size=1000)

# calculate overall moments
OMeanVar(x, weight=w)
# should give: OMeanVar(mean=4.6, var=108, weight=1.08e+03)

# or calculate moments for every group
df = pd.DataFrame({'g': g, 'x': x, 'w': w})
omvs = df.groupby('g').apply(OMeanVar.of_frame, x='x', w='w')

# and combine group moments to obtain the same overall results
OMeanVar.combine(omvs)

# addition is also supported
omvs.loc[0] + omvs.loc[1]

At the moment, only univariate distributions are supported. Bivariate or even multivariate distributions can be efficiently processed in a similar fashion, so the support for them might be added in the future. Moments of multivariate distributions would also allow for linear regression estimation and other statistical methods (such as PCA or regularized regression) to be calculated in a single pass through large distributed datasets.

Documentation

• https://protivinsky.github.io/omoment/index.html