kjella / copulas

A library to model multivariate data using copulas.

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 [email protected]: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
Variable name: feature_01
Mean: 5.843333333333334
Standard deviation: 0.8253012917851409

Once you fit the distribution, you can get the pdf or cdf of data points and you can sample from the distribution.

>>> gu.probability_density(5)
0.2867858505472377
>>> gu.cumulative_distribution(5)
0.15342617720079227
>>> 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

feature_02
===============
Distribution Type: Gaussian
Variable name: feature_02
Mean: 3.0540000000000003
Standard deviation: 0.4321465800705435

feature_03
===============
Distribution Type: Gaussian
Variable name: feature_03
Mean: 3.758666666666666
Standard deviation: 1.7585291834055212

feature_04
===============
Distribution Type: Gaussian
Variable name: feature_04
Mean: 1.1986666666666668
Standard deviation: 0.7606126185881716

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]]

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