# pycopent

**Repository Path**: android_fen/pycopent

## Basic Information

- **Project Name**: pycopent
- **Description**: No description available
- **Primary Language**: Python
- **License**: GPL-3.0
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 0
- **Forks**: 0
- **Created**: 2021-11-10
- **Last Updated**: 2021-11-10

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README

[![PyPI version](https://badge.fury.io/py/copent.svg)](https://pypi.org/project/copent)
# copent
Estimating Copula Entropy and Transfer Entropy

#### Introduction
The nonparametric methods for estimating copula entropy and transfer entropy are implemented. 

The method for estimating copula entropy composes of two simple steps: estimating empirical copula by rank statistic and estimating copula entropy with k-Nearest-Neighbour method. Copula Entropy is a mathematical concept for multivariate statistical independence measuring and testing, and proved to be equivalent to mutual information. Different from Pearson Correlation Coefficient, Copula Entropy is defined for non-linear, high-order and multivariate cases, which makes it universally applicable. Estimating copula entropy can be applied to many cases, including but not limited to variable selection [2] and causal discovery (by estimating transfer entropy) [3]. Please refer to Ma and Sun (2011) <[doi:10.1016/S1007-0214(11)70008-6](http://www.doi.org/10.1016/S1007-0214(11)70008-6)> for more information. For more information in Chinese, please follow [this link](http://blog.sciencenet.cn/blog-3018268-978326.html).

The nonparametric method for estimating transfer entropy composes of two steps: estimating three copula entropy and calculating transfer entropy from the estimated copula entropy. A function for conditional independence testing is also provided. Please refer to Ma (2019) <[arXiv:1910.04375](https://arxiv.org/abs/1910.04375)> for more information.

#### Functions
* copent -- estimating copula entropy;
* construct_empirical_copula -- the first step of the copent function, which estimates empirical copula for data by rank statistics;
* entknn -- the second step of the copent function, which estimates copula entropy from empirical copula with kNN method;
* ci -- conditional independence testing based on copula entropy 
* transent -- estimating transfer entropy via copula entropy

#### Installation
The package can be installed from PyPI directly:
```
pip install copent
```
The package can be installed from Github:
```
pip install git+https://github.com/majianthu/pycopent.git
```
#### Usage Example
##### estimating copula entropy 
```
from numpy.random import multivariate_normal as mnorm
import copent
rho = 0.6
mean1 = [0,0]
cov1 = [ [1,rho],[rho,1] ]
x = mnorm(mean1,cov1,200) # bivariate gaussian 
ce1 = copent.copent(x) # estimated copula entropy
```

##### estimating transfer entropy 
```
from copent import transent
from pandas import read_csv
import numpy as np
url = "https://archive.ics.uci.edu/ml/machine-learning-databases/00381/PRSA_data_2010.1.1-2014.12.31.csv"
prsa2010 = read_csv(url)
# index: 5(PM2.5),6(Dew Point),7(Temperature),8(Pressure),10(Cumulative Wind Speed)
data = prsa2010.iloc[2200:2700,[5,8]].values
te = np.zeros(24)
for lag in range(1,25):
	te[lag-1] = transent(data[:,0],data[:,1],lag)
	str = "TE from pressure to PM2.5 at %d hours lag : %f" %(lag,te[lag-1])
	print(str)
```

#### References
1. Ma Jian, Sun Zengqi. Mutual information is copula entropy. Tsinghua Science & Technology, 2011, 16(1): 51-54. See also arXiv preprint, arXiv:0808.0845, 2008.
2. Ma Jian. Variable Selection with Copula Entropy. arXiv preprint arXiv:1910.12389, 2019.
3. Ma Jian. Estimating Transfer Entropy via Copula Entropy. arXiv preprint arXiv:1910.04375, 2019.