EmpiricalCovariance

Empirical covariance matrix.

Parameters

• ddof

  Default → 1

  Delta Degrees of Freedom.

Attributes

• matrix

Examples

import numpy as np
import pandas as pd
from river import covariance

np.random.seed(42)
X = pd.DataFrame(np.random.random((8, 3)), columns=["red", "green", "blue"])
X

        red     green      blue
0  0.374540  0.950714  0.731994
1  0.598658  0.156019  0.155995
2  0.058084  0.866176  0.601115
3  0.708073  0.020584  0.969910
4  0.832443  0.212339  0.181825
5  0.183405  0.304242  0.524756
6  0.431945  0.291229  0.611853
7  0.139494  0.292145  0.366362

cov = covariance.EmpiricalCovariance()
for x in X.to_dict(orient="records"):
    cov = cov.update(x)
cov

        blue     green    red
 blue    0.076    0.020   -0.010
green    0.020    0.113   -0.053
  red   -0.010   -0.053    0.079

There is also an update_many method to process mini-batches. The results are identical.

cov = covariance.EmpiricalCovariance()
cov = cov.update_many(X)
cov

        blue     green    red
 blue    0.076    0.020   -0.010
green    0.020    0.113   -0.053
  red   -0.010   -0.053    0.079

The covariances are stored in a dictionary, meaning any one of them can be accessed as such:

cov["blue", "green"]

Cov: 0.020292

Diagonal entries are variances:

cov["blue", "blue"]

Var: 0.076119

Start from a state:

n = 8
mean = {'red': 0.416, 'green': 0.387, 'blue': 0.518}
cov_ = {('red', 'red'): 0.079,
    ('red', 'green'): -0.053,
    ('red', 'blue'): -0.010,
    ('green', 'green'): 0.113,
    ('green', 'blue'): 0.020,
    ('blue', 'blue'): 0.076}
cov = covariance.EmpiricalCovariance._from_state(
   n=n, mean=mean, cov=cov_, ddof=1)
cov

        blue     green    red
 blue    0.076    0.020   -0.010
green    0.020    0.113   -0.053
  red   -0.010   -0.053    0.079

Methods

revert

Downdate with a single sample.

Parameters

• x — 'dict'

update

Update with a single sample.

Parameters

• x — 'dict'

update_many

Update with a dataframe of samples.

Parameters

• X — 'pd.DataFrame'