MultivariateGaussian¶

Multivariate normal distribution with parameters mu and var.

Parameters¶

seed

Default → None

Random number generator seed for reproducibility.

Attributes¶

mode

The most likely value in the distribution.
mu

The mean value of the distribution.
n_samples

The number of observed samples.
sigma

The standard deviation of the distribution.
var

The variance of the distribution.

Examples¶

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

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

p = proba.MultivariateGaussian(seed=42)
p.n_samples

0.0

for x in X.to_dict(orient="records"):
    p.update(x)
p.var

           blue     green       red
blue   0.076119  0.020292 -0.010128
green  0.020292  0.112931 -0.053268
red   -0.010128 -0.053268  0.078961

Retrieving current state in nice format is simple

𝒩(
    μ=(0.518, 0.387, 0.416),
    σ^2=(
        [ 0.076  0.020 -0.010]
        [ 0.020  0.113 -0.053]
        [-0.010 -0.053  0.079]
    )
)

To retrieve number of samples and mode:

p.n_samples

8.0

p.mode

{'blue': 0.5179..., 'green': 0.3866..., 'red': 0.4158...}

To retrieve the PDF and CDF:

p(x)

0.97967...

p.cdf(x)

0.00787...

To sample data from distribution:

p.sample()

{'blue': -0.179..., 'green': -0.051..., 'red': 0.376...}

MultivariateGaussian works with utils.Rolling:

from river import utils

p = utils.Rolling(MultivariateGaussian(), window_size=5)
for x in X.to_dict(orient="records"):
    p.update(x)
p.var

           blue     green       red
blue   0.087062 -0.022873  0.007765
green -0.022873  0.014279 -0.025181
red    0.007765 -0.025181  0.095066

MultivariateGaussian works with utils.TimeRolling:

from datetime import datetime as dt, timedelta as td
X.index = [dt(2023, 3, 28, 0, 0, 0) + td(seconds=x) for x in range(8)]
p = utils.TimeRolling(MultivariateGaussian(), period=td(seconds=5))
for t, x in X.iterrows():
    p.update(x.to_dict(), t=t)
p.var

           blue     green       red
blue   0.087062 -0.022873  0.007765
green -0.022873  0.014279 -0.025181
red    0.007765 -0.025181  0.095066

Variance on diagonal is consistent with proba.Gaussian.

multi = proba.MultivariateGaussian()
single = proba.Gaussian()
for x in X.to_dict(orient='records'):
    multi.update(x)
    single.update(x['blue'])
multi.mu['blue'] == single.mu

True

multi.sigma['blue']['blue'] == single.sigma

True

Methods¶

call

PDF(x) method.

Parameters

x — 'dict[str, float]'

cdf

Cumulative density function, i.e. P(X <= x).

Parameters

x — 'dict[str, float]'

revert

Reverts the parameters of the distribution for a given observation.

Parameters

x — 'dict[str, float]'

sample

Sample a random value from the distribution.

update

Updates the parameters of the distribution given a new observation.

Parameters

x — 'dict[str, float]'