AI-IRW: Affine-Invariant Integrated Rank-Weighted depth

This repository hosts Python code of the Affine-Invariant Integrated Rank-Weighted depth introduced in https://arxiv.org/abs/2106.11068. If one want the code to be able to reproduce experiments in the paper, send me an email.

Algorithm

The AI-IRW depth belong to the family of data depth. It provides a score in [0,1] reflecting how deep (resp. far) an observation is w.r.t. a probability distribution. When computed on the entire dataset, it provides an ordering of the dataset.

Some parameters have to be set by the user:

                                - X: Array of shape (n_samples, n_features): the training set.
                                
                                - AI: bool
                                      if True, the affine-invariant version of irw is computed. 
                                      If False, the original irw is computed.

                                - robust: bool, default=False
                                      if robust is true, the MCD estimator of the covariance matrix
                                      is performed.

                                - n_dirs: int | None
                                      The number of random directions needed to approximate 
                                      the integral over the unit sphere.
                                      If None, n_dirs is set as 100 * n_features.

                                - X_test: Array of shape (n_samples_test, n_features): the testing set. 
                                      If None, return the score of the training sample.

                                                               

Quick Start :

Create toy training and testing datasets:

.. code:: python

import numpy as np import matplotlib.pyplot as plt from aiirw import AI_IRW

np.random.seed(0)
n_samples = 1000 n_samples_test = 1000 dim = 2 mu = np.zeros(dim) sigma = np.identity(dim)

X_train = np.random.multivariate_normal(mu, sigma, n_samples) X_test = np.random.multivariate_normal(mu, sigma, n_samples_test)

And then use AI-IRW to sort the dataset :

.. code:: python

score_aiirw = AI_IRW(X, AI=True, robust=True, X_test=Y, n_dirs=1000) rank_aiirw = np.argsort(score_aiirw) colors = [cm.viridis_r(x) for x in np.linspace(0, 1, n_samples_test)] plt.scatter(Y[rank_aiirw, 0], Y[rank_aiirw, 1], s=10, c=colors, cmap='viridis') plt.show()

The sorted simulated dataset, the darker the color, the deeper it is considered in the distribution.

.. image:: AI-IRW_example.png

Dependencies

These are the dependencies to use AI-IRW:

• numpy
• sklearn

Cite

If you use this code in your project, please cite::

@article{staerman2021affine, title={Affine-Invariant Integrated Rank-Weighted Depth: Definition, Properties and Finite Sample Analysis}, author={Staerman, Guillaume and Mozharovskyi, Pavlo and Cl{'e}men{\c{c}}on, St{'e}phan}, journal={arXiv preprint arXiv:2106.11068}, year={2021} }