pybdm 0.1.0
Python implementation of block decomposition method for approximating algorithmic complexity.
License: MIT
Keywords: bdm,ctm,aid,algorithmic information,algorithmic information dynamics,algorithmic complexity,kolmogorov complexity,k-complexity,description length,block decomposition method,coding theorem method,algorithmic information theory

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PyBDM: Python interface to the *Block Decomposition Method*
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The Block Decomposition Method (BDM) approximates algorithmic complexity
of a dataset of arbitrary size, that is, the length of the shortest computer
program that generates it. This is not trivial as algorithmic complexity
is not a computable quantity in the general case and estimation of
algorithmic complexity of a dataset can be very useful as it points to
mechanistic connections between elements of a system, even such that
do not yield any regular statistical patterns that can be captured with
more traditional tools based on probability theory and information theory.

Currently 1D and 2D binary arrays are supported, as well as 1D arrays
with 4, 5, 6 and 9 discrete symbols.

BDM and the necessary parts of the algorithmic information theory
it is based on are described in `this article <https://www.mdpi.com/1099-4300/20/8/605>`_.

See the official documentation_ for more information.


Installation
============

Standard installation (stable)::

    pip install pybdm

Development version installation::

    pip install git+https://github.com/sztal/pybdm.git

Local development::

    git clone https://github.com/sztal/pybdm
    cd pybdm
    pip install --editable .


Supported versions
------------------

Python3.5+ is supported. Tests are run against Linux, but
Windows and OSX should work as well.


Usage
=====

The BDM is implemented using the object-oriented approach and expects
input represented as `Numpy <http://www.numpy.org/>`__ arrays of integer type.

.. highlights::

   ``BDM`` objects operate exclusively on **integer arrays**.
   Hence, any alphabet must be first mapped to a set of integers ranging
   from ``0`` to ``k``.

Detailed usage examples can be found in the official documentation_.


Binary sequences (1D)
---------------------

.. code-block:: python

    import numpy as np
    from pybdm import BDM

    # Create a dataset (must be of integer type)
    X = np.ones((100,), dtype=int)

    # Initialize BDM object
    # ndim argument specifies dimensionality of BDM
    bdm = BDM(ndim=1)

    # Compute BDM
    bdm.bdm(X)

    # BDM objects may also compute standard Shannon entropy in base 2
    bdm.ent(X)


Binary matrices (2D)
--------------------

.. code-block:: python

    import numpy as np
    from pybdm import BDM

    # Create a dataset (must be of integer type)
    X = np.ones((100, 100), dtype=int)

    # Initialize BDM object
    bdm = BDM(ndim=2)

    # Compute BDM
    bdm.bdm(X)

    # BDM objects may also compute standard Shannon entropy in base 2
    bdm.ent(X)

Non-binary sequences (1D)
-------------------------

.. code-block:: python

    import numpy as np
    from pybdm import BDM

    # Create a dataset (4 discrete symbols)
    np.random.seed(303)
    X = np.random.randint(0, 4, (100,))

    # Initialize BDM object with 4-symbols alphabet
    bdm = BDM(ndim=1, nsymbols=4)

    # Compute BDM
    bdm.bdm(X)



Parallel processing
-------------------

*PyBDM* was designed with parallel processing in mind.
Using modern packages for parallelization such as
`joblib <https://joblib.readthedocs.io/en/latest/parallel.html>`__
makes it really easy to compute BDM for massive objects.

In this example we will slice a 1000x1000 dataset into 200x200 pieces
compute so-called counter objects (final BDM computation operates on such objects)
in parallel in 4 independent processes, and aggregate the results
into a single BDM approximation of the algorithmic complexity of the dataset.

.. highlights::

    Remember that data has to be sliced correctly during parallelization
    in order to ensure fully correct BDM computations. That is, all slices
    except lower and right boundaries have to be decomposable without
    any boundary leftovers by the selected decomposition algorithm.

.. code-block:: python

    import numpy as np
    from joblib import Parallel, delayed
    from pybdm import BDM
    from pybdm.utils import decompose_dataset

    # Create a dataset (must be of integer type)
    X = np.ones((1000, 1000), dtype=int)

    # Initialize BDM object
    bdm = BDM(ndim=2)

    # Compute counter objects in parallel
    counters = Parallel(n_jobs=4) \
        (delayed(bdm.decompose_and_count)(d) for d in decompose_dataset(X, (200, 200)))

    # Compute BDM
    bdm.compute_bdm(*counters)


Perturbation analysis
---------------------

Besides the main *Block Decomposition Method* implementation *PyBDM* provides
also an efficient algorithm for perturbation analysis based on *BDM*
(or standard Shannon entropy).

A perturbation experiment studies change of *BDM* / entropy under changes
applied to the underlying dataset. This is the main tool for detecting
parts of a system having some causal significance as opposed
to noise parts.

Parts which after yield negative contribution to the overall
complexity after change are likely to be important for the system,
since their removal make it more noisy. On the other hand parts that yield
positive contribution to the overall complexity after change are likely
to be noise since they extend the system's description length.

.. code-block:: python

    import numpy as np
    from pybdm import BDM
    from pybdm.algorithms import PerturbationExperiment

    # Create a dataset (must be of integer type)
    X = np.ones((100, 100), dtype=int)

    # Initialize BDM object
    bdm = BDM(ndim=2)

    # Initialize perturbation experiment object
    # (may be run for both bdm or entropy)
    perturbation = PerturbationExperiment(bdm, X, metric='bdm')

    # Compute BDM change for all data points
    delta_bdm = perturbation.run()

    # Compute BDM change for selected data points and keep the changes while running
    # One array provide indices of elements that are to be change.
    idx = np.array([[0, 0], [10, 10]], dtype=int)
    # Another array provide new values to assign.
    # Negative values mean that new values will be selected
    # randomly from the set of other possible values from the alphabet.
    values = np.array([-1, -1], dtype=int)
    delta_bdm = perturbation.run(idx, values, keep_changes=True)


Authors & Contact
=================

* Szymon Talaga <stalaga@protonmail.com>
* Kostas Tsampourakis <kostas.tsampourakis@gmail.com>


.. _documentation: http://pybdm-docs.rtfd.org



Documentation
-------------

The full documentation is at http://pybdm-docs.rtfd.org.



History
-------

0.1.0 (2019-09-22)
++++++++++++++++++

* First release on PyPI.