A python library for building different types of copulas and using them for sampling.
Project description
An open source project from Data to AI Lab at MIT.
Copulas
Overview
A python library for building different types of copulas and using them for sampling.
- Free software: MIT license
- Documentation: https://DAI-Lab.github.io/Copulas
Supported Copulas
Bivariate
- Clayton
- Frank
- Gumbel
Accesible from copulas.bivariate.copulas.Copula
Multivariate
- Gaussian [+ info]
Accesible from copulas.multivariate.models.CopulaModel
Installation
Install with pip
The easiest way to install Copulas is using pip
pip install copulas
Install from sources
You can also clone the repository and install it from sources
git clone git@github.com:DAI-Lab/Copulas.git
cd Copulas
python setup.py install
Data Requirements
This package works under the assumption that the data is perfectly clean, that means that:
- There are no missing values.
- All values are numerical
Usage
In this library you can model univariate distributions and create copulas from a numeric dataset. For this example, we will use the iris dataset in the data folder.
Creating Univariate Distribution
First we will retrieve the data from the data folder and create a univariate distribution. For this example, we will create a normal distribution. First type the following commands on a python terminal.
>>> from copulas.univariate.gaussian import GaussianUnivariate
>>> import pandas as pd
>>> data = pd.read_csv('data/iris.data.csv')
>>> data.head()
feature_01 feature_02 feature_03 feature_04
0 5.1 3.5 1.4 0.2
1 4.9 3.0 1.4 0.2
2 4.7 3.2 1.3 0.2
3 4.6 3.1 1.5 0.2
4 5.0 3.6 1.4 0.2
Once we have the data, we can pass it into the GaussianUnivariate class.
>>> feature1 = data['feature_01']
>>> gu = GaussianUnivariate()
>>> gu.fit(feature1)
>>> print(gu)
Distribution Type: Gaussian
mean = 5.843333333333335
standard deviation = 0.8253012917851409
max = 7.9
min = 4.3
Once you fit the distribution, you can get the pdf or cdf of data points and you can sample from the distribution.
>>> gu.get_pdf(5)
0.28678585054723732
>>> gu.get_cdf(5)
0.15342617720079199
>>> gu.sample(1)
array([ 6.14745446])
Creating a Gaussian Copula
When you have a numeric data table, you can also create a copula and use it to sample from the multivariate distribution. In this example, we will use a Gaussian Copula.
>>> from copulas.multivariate.gaussian import GaussianMultivariate
>>> gc = GaussianMultivariate()
>>> gc.fit(data)
>>> print(gc)
feature_01
===============
Distribution Type: Gaussian
Variable name: feature_01
Mean: 5.843333333333334
Standard deviation: 0.8253012917851409
Max: 7.9
Min: 4.3
feature_02
===============
Distribution Type: Gaussian
Variable name: feature_02
Mean: 3.0540000000000003
Standard deviation: 0.4321465800705435
Max: 4.4
Min: 2.0
feature_03
===============
Distribution Type: Gaussian
Variable name: feature_03
Mean: 3.758666666666666
Standard deviation: 1.7585291834055212
Max: 6.9
Min: 1.0
feature_04
===============
Distribution Type: Gaussian
Variable name: feature_04
Mean: 1.1986666666666668
Standard deviation: 0.7606126185881716
Max: 2.5
Min: 0.1
Copula Distribution:
feature_01 feature_02 feature_03 feature_04
0 -0.900681 1.032057 -1.341272 -1.312977
1 -1.143017 -0.124958 -1.341272 -1.312977
2 -1.385353 0.337848 -1.398138 -1.312977
3 -1.506521 0.106445 -1.284407 -1.312977
4 -1.021849 1.263460 -1.341272 -1.312977
5 -0.537178 1.957669 -1.170675 -1.050031
...
[150 rows x 4 columns]
Covariance matrix:
[[ 1.26935536 0.64987728 0.94166734 ... -0.57458312 -0.14548004
-0.43589371]
[ 0.64987728 0.33302068 0.4849735 ... -0.29401609 -0.06772633
-0.21867228]
[ 0.94166734 0.4849735 0.72674568 ... -0.42778472 -0.04608618
-0.27836438]
...
[-0.57458312 -0.29401609 -0.42778472 ... 0.2708685 0.0786054
0.19208669]
[-0.14548004 -0.06772633 -0.04608618 ... 0.0786054 0.17668562
0.14455133]
[-0.43589371 -0.21867228 -0.27836438 ... 0.19208669 0.14455133
0.22229033]]
Means:
[-3.315866100213801e-16, -7.815970093361102e-16, 2.842170943040401e-16, -2.3684757858670006e-16]
Once you have fit the copula, you can sample from it.
gc.sample(5)
feature_01 feature_02 feature_03 feature_04
0 5.529610 2.966947 3.162891 0.974260
1 5.708827 3.011078 3.407812 1.149803
2 4.623795 2.712284 1.283194 0.213796
3 5.952688 3.086259 4.088219 1.382523
4 5.360256 2.920929 2.844729 0.826919
History
0.1.1 - Minor Improvements
- Different Copula types separated in subclasses
- Extensive Unit Testing
- More pythonic names in the public API.
- Stop using third party elements that will be deprected soon.
- Add methods to sample new data on bivariate copulas.
- New KDE Univariate copula
- Improved examples with additional demo data.
0.1.0 - First Release
- First release on PyPI.
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