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https://github.com/asnelt/mixedvines

Python package for canonical vine copula trees with mixed continuous and discrete marginals
https://github.com/asnelt/mixedvines

c-vines copula copula-models copulae copulas data-analysis dependency-analysis dependency-modeling modeling python regular-vines statistics

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Python package for canonical vine copula trees with mixed continuous and discrete marginals

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README 

        
=============================

mixedvines Package for Python

=============================



Package for canonical vine copula trees with mixed continuous and discrete

marginals.  If you use this software for publication, please cite

[ONKEN2016]_.



Description

-----------



This package contains a complete framework based on canonical vine copulas for

modeling multivariate data that are partly discrete and partly continuous.

The resulting multivariate distributions are flexible with rich dependence

structures and marginals.



For continuous marginals, implementations of the normal and the gamma

distributions are provided.  For discrete marginals, Poisson, binomial and

negative binomial distributions are provided.  As bivariate copula building

blocks, the Gaussian, Frank and Clayton families as well as rotation

transformed families are provided.  Additional marginal and pair-copula

distributions can be added easily.



The package includes methods for sampling, likelihood calculation and

inference, all of which have quadratic complexity.  These procedures are

combined to estimate entropy by means of Monte Carlo integration.



Please see [ONKEN2016]_ for a more detailed description of the framework.



Documentation

-------------



The full documentation for the mixedvines package is available at

`Read the Docs

`_.



Requirements

------------



The package requires Python 3.10 or greater and additionally requires

`NumPy and SciPy

`_.



Installation

------------



To install the mixedvines package, run::



    pip install mixedvines



Usage

-----



Suppose that data are given in a NumPy array ``samples`` with shape

``(n, d)``, where ``n`` is the number of samples and ``d`` is the number of

elements per sample.  First, specify which of the elements are continuous.

If, for instance, the distribution has three elements and the first and last

elements are continuous whereas the second element is discrete:



.. code-block:: python



    is_continuous = [True, False, True]



To fit a mixed vine to the samples:



.. code-block:: python



    from mixedvines.mixedvine import MixedVine

    vine = MixedVine.fit(samples, is_continuous)



``vine`` is now a ``MixedVine`` object.  To draw samples from the

distribution, calculate their density and estimate the distribution entropy in

units of bits:



.. code-block:: python



    samples = vine.rvs(size=100)

    logpdf = vine.logpdf(samples)

    entropy, standard_error_mean = vine.entropy(sem_tol=1e-2)



To manually construct and visualize a simple mixed vine model:



.. code-block:: python



    from scipy.stats import norm, gamma, poisson

    import numpy as np

    from mixedvines.copula import GaussianCopula, ClaytonCopula, FrankCopula

    from mixedvines.mixedvine import MixedVine

    import matplotlib.pyplot as plt

    import itertools

    # Manually construct mixed vine

    dim = 3  # Dimension

    vine = MixedVine(dim)

    # Specify marginals

    vine.set_marginal(0, norm(0, 1))

    vine.set_marginal(1, poisson(5))

    vine.set_marginal(2, gamma(2, 0, 4))

    # Specify pair-copulas

    vine.set_copula(1, 0, GaussianCopula(0.5))

    vine.set_copula(1, 1, FrankCopula(4))

    vine.set_copula(2, 0, ClaytonCopula(5))

    # Calculate probability density function on lattice

    bnds = np.empty((3), dtype=object)

    bnds[0] = [-3, 3]

    bnds[1] = [0, 15]

    bnds[2] = [0.5, 25]

    x0, x1, x2 = np.mgrid[bnds[0][0]:bnds[0][1]:0.05, bnds[1][0]:bnds[1][1],

                          bnds[2][0]:bnds[2][1]:0.1]

    points = np.array([x0.ravel(), x1.ravel(), x2.ravel()]).T

    pdf = vine.pdf(points)

    pdf = np.reshape(pdf, x1.shape)

    # Generate random variates

    size = 100

    samples = vine.rvs(size)

    # Visualize 2d marginals and samples

    comb = list(itertools.combinations(range(dim), 2))

    for i, cmb in enumerate(comb):

        # Sum over all axes not in cmb

        cmb_inv = tuple(set(range(dim)) - set(cmb))

        margin = np.sum(pdf, axis=cmb_inv).T

        plt.subplot(2, len(comb), i + 1)

        plt.imshow(margin, aspect='auto', interpolation='none', cmap='hot',

                   origin='lower', extent=[bnds[cmb[0]][0], bnds[cmb[0]][1],

                                           bnds[cmb[1]][0], bnds[cmb[1]][1]])

        plt.ylabel('$x_' + str(cmb[1]) + '$')

        plt.subplot(2, len(comb), len(comb) + i + 1)

        plt.scatter(samples[:, cmb[0]], samples[:, cmb[1]], s=1)

        plt.xlim(bnds[cmb[0]][0], bnds[cmb[0]][1])

        plt.ylim(bnds[cmb[1]][0], bnds[cmb[1]][1])

        plt.xlabel('$x_' + str(cmb[0]) + '$')

        plt.ylabel('$x_' + str(cmb[1]) + '$')

    plt.tight_layout()

    plt.show()



This code shows the 2d marginals and 100 samples of a 3d mixed vine.



Source code

-----------



The source code of the mixedvines package is hosted on

`GitHub

`_.



References

----------



.. [ONKEN2016] A. Onken and S. Panzeri (2016).  Mixed vine copulas as joint

   models of spike counts and local field potentials.  In D. D. Lee,

   M. Sugiyama, U. V. Luxburg, I. Guyon and R. Garnett, editors, Advances in

   Neural Information Processing Systems 29 (NIPS 2016), pages 1325-1333.



License

-------



Copyright (C) 2017-2019, 2021-2023 Arno Onken



This file is part of the mixedvines package.



The mixedvines package is free software: you can redistribute it and/or modify

it under the terms of the GNU General Public License as published by the Free

Software Foundation, version 3.



The mixedvines package is distributed in the hope that it will be useful, but

WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or

FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more

details.



You should have received a copy of the GNU General Public License along with

this program; if not, see .