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MultivariateGaussian

Multivariate normal distribution with parameters mu and var.

Parameters

  • seed

    DefaultNone

    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 = 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

p
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 = 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 = 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 = multi.update(x)
    single = 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]'