Fast-TMFG

Fast_TMFG is an ultra-fast implementation of the Triangulated Maximally Fileterd Graph (TMFG). It is based on the work by Guido Previde Massara and is fully implemented by Antonio Briola and Tong Zheng.

The interface is fully scikit-learn compatible. Consequently, it has three main methods:

• fit(weights, cov, output): Fits the model to the input matrix weights (e.g. a squared correlation matrix) and input matrix cov (e.g. covariance matrix). This method computes the Triangulated Maximal Filtered Graph (TMFG) based on the input weight matrix. The output parameter specifies what is the nature of the desired output:
  • sparse inverse covariance matrix (output = 'logo')
  • sparse unweighted weights matrix (output = 'unweighted_sparse_W_matrix')
  • sparse weighted weights matrix (output = 'weighted_sparse_W_matrix')
• transform(): Returns the computed cliques and separators set of the model. The method also returns the TMFG adjacency matrix.
• fit_transform(weights, cov, output): Fits the model to the input matrix weights (e.g. a squared correlation matrix) and input matrix cov (e.g. covariance matrix), and returns the computed cliques and separators set and the TMFG adjacency matrix over the covariance matrix input. The output parameter specifies what is the nature of the desired output:
  • sparse inverse covariance matrix (output = 'logo')
  • sparse unweighted weights matrix (output = 'unweighted_sparse_W_matrix')
  • sparse weighted weights matrix (output = 'weighted_sparse_W_matrix')

We provide a detailed explanation of each function/method. Such an explanation is entirely generated through ChatGPT.

For a full understanding of the TMFG, we refer the interested reader to the following papers:

• Parsimonious modelling with information filtering networks
• Network filtering for big data: Triangulated maximally filtered graph
• Dependency structures in cryptocurrency market from high to low frequency

For the use of the TMFG as a topological regularization tool for the covariance selection problem, we further refer the interested reader to the following paper:

• Topological regularization with information filtering networks

Installation

Install the latest version of the package using PyPI: pip3 install fast-tmfg

Usage Example

import numpy as np
import pandas as pd

from fast_tmfg import *

def generate_random_df(num_rows, num_columns):
  data = np.random.randint(0, 100, size=(num_rows, num_columns))
  df = pd.DataFrame(data, columns=['col_{}'.format(i) for i in range(num_columns)])
  return df

df = generate_random_df(100, 50)
corr = np.square(df.corr())
cov = df.cov()
model = TMFG()
cliques, seps, adj_matrix = model.fit_transform(weights=corr, cov=cov, output='logo')

How to cite us

If you use TMFG in a scientific publication, we would appreciate citations to the following paper:

@article{briola2022dependency,
  title={Dependency structures in cryptocurrency market from high to low frequency},
  author={Briola, Antonio and Aste, Tomaso},
  journal={arXiv preprint arXiv:2206.03386},
  year={2022}
}