Python implementation of block decomposition method for approximating algorithmic complexity.
Project description
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.
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 objectoriented approach and expects input represented as Numpy arrays of integer type.
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)
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)
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)
Nonbinary sequences (1D)
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 4symbols 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 makes it really easy to compute BDM for massive objects.
In this example we will slice a 1000x1000 dataset into 200x200 pieces compute socalled 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.
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.
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.
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)
Project details
Release history Release notifications
Download files
Download the file for your platform. If you're not sure which to choose, learn more about installing packages.
Filename, size  File type  Python version  Upload date  Hashes 

Filename, size pybdm0.1.0py2.py3noneany.whl (39.9 MB)  File type Wheel  Python version py2.py3  Upload date  Hashes View 
Filename, size pybdm0.1.0.tar.gz (39.9 MB)  File type Source  Python version None  Upload date  Hashes View 
Hashes for pybdm0.1.0py2.py3noneany.whl
Algorithm  Hash digest  

SHA256  28cec2b7263f4448ef9d62ae71bf84d1450b83d8a160a69779be0022959ce3c1 

MD5  9d181c541f5a56286c93ce3f2e38e58f 

BLAKE2256  b732fd74c068e07e1b91a732982125bd821af9fb144cd741d16ac0a607564538 