| Name | pyBregMan JSON |
| Version |
0.1.0
JSON |
| download |
| home_page | None |
| Summary | A Python library for geometric computing on BREGman MANifolds with applications. |
| upload_time | 2024-08-17 01:26:07 |
| maintainer | None |
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| author | None |
| requires_python | >=3.8 |
| license | Apache License Version 2.0, January 2004 http://www.apache.org/licenses/ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 1. Definitions. "License" shall mean the terms and conditions for use, reproduction, and distribution as defined by Sections 1 through 9 of this document. "Licensor" shall mean the copyright owner or entity authorized by the copyright owner that is granting the License. "Legal Entity" shall mean the union of the acting entity and all other entities that control, are controlled by, or are under common control with that entity. For the purposes of this definition, "control" means (i) the power, direct or indirect, to cause the direction or management of such entity, whether by contract or otherwise, or (ii) ownership of fifty percent (50%) or more of the outstanding shares, or (iii) beneficial ownership of such entity. "You" (or "Your") shall mean an individual or Legal Entity exercising permissions granted by this License. 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**pyBregMan**:
A Python library for geometric computing on BREGman MANifolds with applications.
The focus of the library is to provide a specialized framework for Bregman
manifolds: dually flat manifolds which consists of two convex generators
related via Legendre–Fenchel duality.
**Documentation** is available on [Read the Docs](https://pybregman.readthedocs.io/en/latest/).
# Installation
pyBregMan can be installed via `pip3` or `git`.
For the former (using `pip3`), one can call:
```
pip3 install pyBregMan
```
For `git` installation, one can directly clone from GitHub.
```
git clone https://github.com/alexandersoen/pyBregMan.git
cd pyBregMan
pip3 install .
```
# Getting Started
To use `pyBregMan`, a user can define `Point`s on a specified Bregman manifold, where additional geometric objects (Geodesics, notions of dissimilarities, etc) can be defined on.
Such a procedure consists of:
- defining a `BregmanManifold` object;
- specifying data via `Point` objects;
- defining additional objects which act on a manifold object and data.
In addition, we also provide an inbuilt visualization framework which calls `matplotlib`.
In the following code example, we define the manifold of bivariate Gaussian distribution. We then define and compute different types of centroids. Finally, we visualize the data and centroids.
Pre-defined manifolds can be found in the `bregman.application` submodule.
The following demonstrates how to define a manifold object for bivariate Gaussians. We additionally define two points.
```python
import numpy as np
from bregman.application.distribution.exponential_family.gaussian import GaussianManifold
from bregman.base import LAMBDA_COORDS, DualCoords, Point
# Define Bivariate Normal Manifold
manifold = GaussianManifold(input_dimension=2)
# Define data
to_vector = lambda mu, sigma: np.concatenate([mu, sigma.flatten()])
mu_1, sigma_1 = np.array([0.0, 1.0]), np.array([[1.0, 0.5], [0.5, 2.0]])
mu_2, sigma_2 = np.array([1.0, 2.0]), np.array([[2.0, 1.0], [1.0, 1.0]])
point_1 = Point(LAMBDA_COORDS, to_vector(mu_1, sigma_1))
point_2 = Point(LAMBDA_COORDS, to_vector(mu_2, sigma_2))
```
We note that the points are not specific to the Gaussian manifold.
However, given compatible dimensions, one can utilize manifold specific method. For instance, we can define the KL divergence between the two points.
```python
# KL divergence can be calculated
kl = manifold.kl_divergence(point_1, point_2)
rkl = manifold.kl_divergence(point_2, point_1)
print("KL(point_1 || point_2):", kl)
print("KL(point_2 || point_1):", rkl)
# >>> KL(point_1 || point_2): 0.9940936082534253
# >>> KL(point_2 || point_1): 1.2201921060322891
```
More complicated geometric objects can be imported from other submodules.
In this example, we will import various objects to allow us to compute a centroid of the two Gaussian distributions we have defined.
```python
from bregman.barycenter.bregman import BregmanBarycenter, SkewBurbeaRaoBarycenter
from bregman.application.distribution.exponential_family.gaussian.geodesic import FisherRaoKobayashiGeodesic
# We can define and calculate centroids
theta_barycenter = BregmanBarycenter(manifold, DualCoords.THETA)
eta_barycenter = BregmanBarycenter(manifold, DualCoords.ETA)
br_barycenter = SkewBurbeaRaoBarycenter(manifold)
dbr_barycenter = SkewBurbeaRaoBarycenter(manifold, DualCoords.ETA)
theta_centroid = theta_barycenter([point_1, point_2])
eta_centroid = eta_barycenter([point_1, point_2])
br_centroid = br_barycenter([point_1, point_2])
dbr_centroid = dbr_barycenter([point_1, point_2])
# Mid point of Fisher-Rao Geodesic is its corresponding centroid of two points
fr_geodesic = FisherRaoKobayashiGeodesic(manifold, point_1, point_2)
fr_centroid = fr_geodesic(t=0.5)
print("Right-Sided Centroid:", manifold.convert_to_display(theta_centroid))
print("Left-Sided Centroid:", manifold.convert_to_display(eta_centroid))
print("Bhattacharyya Centroid:", manifold.convert_to_display(br_centroid))
print("Fisher-Rao Centroid:", manifold.convert_to_display(fr_centroid))
# >>> Right-Sided Centroid: $\mu$ = [0.33333333 1.55555556]; $\Sigma$ = [[1.33333333 0.66666667]
# >>> [0.66666667 1.11111111]]
# >>> Left-Sided Centroid: $\mu$ = [0.5 1.5]; $\Sigma$ = [[1.75 1. ]
# >>> [1. 1.75]]
# >>> Bhattacharyya Centroid: $\mu$ = [0.41772374 1.53238683]; $\Sigma$ = [[1.53973074 0.82458984]
# >>> [0.82458984 1.40126629]]
# >>> Fisher-Rao Centroid: $\mu$ = [0.5326167 1.62759115]; $\Sigma$ = [[1.72908532 0.98542147]
# >>> [0.98542147 1.54545598]]
```
Finally, one can simply visualize the objects by using the inbuilt `matplotlib` visualizer.
```python
from bregman.visualizer.matplotlib.callback import VisualizeGaussian2DCovariancePoints
from bregman.visualizer.matplotlib.matplotlib import MatplotlibVisualizer
# These objects can be visualized through matplotlib
visualizer = MatplotlibVisualizer(manifold, (0, 1))
visualizer.plot_object(point_1, c="black")
visualizer.plot_object(point_2, c="black")
visualizer.plot_object(theta_centroid, c="red", label="Right-Sided Centroid")
visualizer.plot_object(eta_centroid, c="blue", label="Left-Sided Centroid")
visualizer.plot_object(br_centroid, c="purple", label="Bhattacharyya Centroid")
visualizer.plot_object(fr_centroid, c="pink", label="Fisher-Rao Centroid")
visualizer.add_callback(VisualizeGaussian2DCovariancePoints())
visualizer.visualize(LAMBDA_COORDS) # Display coordinate type
```
Code can be found in `examples/centroids.py`.
# Additional Links
## Tutorial: Data Representations on the Bregman Manifold
A tutorial published at the [ICML'24 GRAM workshop is available](https://colab.research.google.com/drive/14nf0w9b-SdgRGBrFstrKfHwToypO3_LP?usp=sharing) which explores different methods for summarizing data on a Bregman manifold.
## Technical Report
A preprint of the [technical report for pyBregMan is available on arXiv](https://arxiv.org/abs/2408.04175).
Raw data
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"description": "\n\n**pyBregMan**:\n\nA Python library for geometric computing on BREGman MANifolds with applications.\nThe focus of the library is to provide a specialized framework for Bregman\nmanifolds: dually flat manifolds which consists of two convex generators\nrelated via Legendre\u2013Fenchel duality.\n\n**Documentation** is available on [Read the Docs](https://pybregman.readthedocs.io/en/latest/).\n\n# Installation\n\npyBregMan can be installed via `pip3` or `git`.\n\nFor the former (using `pip3`), one can call:\n\n```\npip3 install pyBregMan\n```\n\nFor `git` installation, one can directly clone from GitHub.\n\n```\ngit clone https://github.com/alexandersoen/pyBregMan.git\ncd pyBregMan\npip3 install .\n```\n\n# Getting Started\n\nTo use `pyBregMan`, a user can define `Point`s on a specified Bregman manifold, where additional geometric objects (Geodesics, notions of dissimilarities, etc) can be defined on.\nSuch a procedure consists of:\n - defining a `BregmanManifold` object;\n - specifying data via `Point` objects;\n - defining additional objects which act on a manifold object and data.\n\nIn addition, we also provide an inbuilt visualization framework which calls `matplotlib`.\n\nIn the following code example, we define the manifold of bivariate Gaussian distribution. We then define and compute different types of centroids. Finally, we visualize the data and centroids.\n\nPre-defined manifolds can be found in the `bregman.application` submodule.\nThe following demonstrates how to define a manifold object for bivariate Gaussians. We additionally define two points.\n```python\nimport numpy as np\n\nfrom bregman.application.distribution.exponential_family.gaussian import GaussianManifold\nfrom bregman.base import LAMBDA_COORDS, DualCoords, Point\n\n# Define Bivariate Normal Manifold\nmanifold = GaussianManifold(input_dimension=2)\n\n# Define data\nto_vector = lambda mu, sigma: np.concatenate([mu, sigma.flatten()])\nmu_1, sigma_1 = np.array([0.0, 1.0]), np.array([[1.0, 0.5], [0.5, 2.0]])\nmu_2, sigma_2 = np.array([1.0, 2.0]), np.array([[2.0, 1.0], [1.0, 1.0]])\n\npoint_1 = Point(LAMBDA_COORDS, to_vector(mu_1, sigma_1))\npoint_2 = Point(LAMBDA_COORDS, to_vector(mu_2, sigma_2))\n```\n\nWe note that the points are not specific to the Gaussian manifold.\nHowever, given compatible dimensions, one can utilize manifold specific method. For instance, we can define the KL divergence between the two points.\n\n```python\n# KL divergence can be calculated\nkl = manifold.kl_divergence(point_1, point_2)\nrkl = manifold.kl_divergence(point_2, point_1)\n\nprint(\"KL(point_1 || point_2):\", kl)\nprint(\"KL(point_2 || point_1):\", rkl)\n\n# >>> KL(point_1 || point_2): 0.9940936082534253\n# >>> KL(point_2 || point_1): 1.2201921060322891\n```\n\nMore complicated geometric objects can be imported from other submodules.\nIn this example, we will import various objects to allow us to compute a centroid of the two Gaussian distributions we have defined.\n\n```python\nfrom bregman.barycenter.bregman import BregmanBarycenter, SkewBurbeaRaoBarycenter\nfrom bregman.application.distribution.exponential_family.gaussian.geodesic import FisherRaoKobayashiGeodesic\n\n# We can define and calculate centroids\ntheta_barycenter = BregmanBarycenter(manifold, DualCoords.THETA)\neta_barycenter = BregmanBarycenter(manifold, DualCoords.ETA)\nbr_barycenter = SkewBurbeaRaoBarycenter(manifold)\ndbr_barycenter = SkewBurbeaRaoBarycenter(manifold, DualCoords.ETA)\n\ntheta_centroid = theta_barycenter([point_1, point_2])\neta_centroid = eta_barycenter([point_1, point_2])\nbr_centroid = br_barycenter([point_1, point_2])\ndbr_centroid = dbr_barycenter([point_1, point_2])\n\n# Mid point of Fisher-Rao Geodesic is its corresponding centroid of two points\nfr_geodesic = FisherRaoKobayashiGeodesic(manifold, point_1, point_2)\nfr_centroid = fr_geodesic(t=0.5)\n\nprint(\"Right-Sided Centroid:\", manifold.convert_to_display(theta_centroid))\nprint(\"Left-Sided Centroid:\", manifold.convert_to_display(eta_centroid))\nprint(\"Bhattacharyya Centroid:\", manifold.convert_to_display(br_centroid))\nprint(\"Fisher-Rao Centroid:\", manifold.convert_to_display(fr_centroid))\n\n# >>> Right-Sided Centroid: $\\mu$ = [0.33333333 1.55555556]; $\\Sigma$ = [[1.33333333 0.66666667]\n# >>> [0.66666667 1.11111111]]\n# >>> Left-Sided Centroid: $\\mu$ = [0.5 1.5]; $\\Sigma$ = [[1.75 1. ]\n# >>> [1. 1.75]]\n# >>> Bhattacharyya Centroid: $\\mu$ = [0.41772374 1.53238683]; $\\Sigma$ = [[1.53973074 0.82458984]\n# >>> [0.82458984 1.40126629]]\n# >>> Fisher-Rao Centroid: $\\mu$ = [0.5326167 1.62759115]; $\\Sigma$ = [[1.72908532 0.98542147]\n# >>> [0.98542147 1.54545598]]\n```\n\nFinally, one can simply visualize the objects by using the inbuilt `matplotlib` visualizer.\n\n```python\nfrom bregman.visualizer.matplotlib.callback import VisualizeGaussian2DCovariancePoints\nfrom bregman.visualizer.matplotlib.matplotlib import MatplotlibVisualizer\n\n# These objects can be visualized through matplotlib\nvisualizer = MatplotlibVisualizer(manifold, (0, 1))\nvisualizer.plot_object(point_1, c=\"black\")\nvisualizer.plot_object(point_2, c=\"black\")\nvisualizer.plot_object(theta_centroid, c=\"red\", label=\"Right-Sided Centroid\")\nvisualizer.plot_object(eta_centroid, c=\"blue\", label=\"Left-Sided Centroid\")\nvisualizer.plot_object(br_centroid, c=\"purple\", label=\"Bhattacharyya Centroid\")\nvisualizer.plot_object(fr_centroid, c=\"pink\", label=\"Fisher-Rao Centroid\")\nvisualizer.add_callback(VisualizeGaussian2DCovariancePoints())\n\nvisualizer.visualize(LAMBDA_COORDS) # Display coordinate type\n```\n\n\n\nCode can be found in `examples/centroids.py`.\n\n# Additional Links\n\n## Tutorial: Data Representations on the Bregman Manifold\n\nA tutorial published at the [ICML'24 GRAM workshop is available](https://colab.research.google.com/drive/14nf0w9b-SdgRGBrFstrKfHwToypO3_LP?usp=sharing) which explores different methods for summarizing data on a Bregman manifold.\n\n## Technical Report\n\nA preprint of the [technical report for pyBregMan is available on arXiv](https://arxiv.org/abs/2408.04175).\n",
"bugtrack_url": null,
"license": " Apache License Version 2.0, January 2004 http://www.apache.org/licenses/ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 1. Definitions. \"License\" shall mean the terms and conditions for use, reproduction, and distribution as defined by Sections 1 through 9 of this document. \"Licensor\" shall mean the copyright owner or entity authorized by the copyright owner that is granting the License. \"Legal Entity\" shall mean the union of the acting entity and all other entities that control, are controlled by, or are under common control with that entity. For the purposes of this definition, \"control\" means (i) the power, direct or indirect, to cause the direction or management of such entity, whether by contract or otherwise, or (ii) ownership of fifty percent (50%) or more of the outstanding shares, or (iii) beneficial ownership of such entity. \"You\" (or \"Your\") shall mean an individual or Legal Entity exercising permissions granted by this License. \"Source\" form shall mean the preferred form for making modifications, including but not limited to software source code, documentation source, and configuration files. \"Object\" form shall mean any form resulting from mechanical transformation or translation of a Source form, including but not limited to compiled object code, generated documentation, and conversions to other media types. \"Work\" shall mean the work of authorship, whether in Source or Object form, made available under the License, as indicated by a copyright notice that is included in or attached to the work (an example is provided in the Appendix below). \"Derivative Works\" shall mean any work, whether in Source or Object form, that is based on (or derived from) the Work and for which the editorial revisions, annotations, elaborations, or other modifications represent, as a whole, an original work of authorship. For the purposes of this License, Derivative Works shall not include works that remain separable from, or merely link (or bind by name) to the interfaces of, the Work and Derivative Works thereof. \"Contribution\" shall mean any work of authorship, including the original version of the Work and any modifications or additions to that Work or Derivative Works thereof, that is intentionally submitted to Licensor for inclusion in the Work by the copyright owner or by an individual or Legal Entity authorized to submit on behalf of the copyright owner. For the purposes of this definition, \"submitted\" means any form of electronic, verbal, or written communication sent to the Licensor or its representatives, including but not limited to communication on electronic mailing lists, source code control systems, and issue tracking systems that are managed by, or on behalf of, the Licensor for the purpose of discussing and improving the Work, but excluding communication that is conspicuously marked or otherwise designated in writing by the copyright owner as \"Not a Contribution.\" \"Contributor\" shall mean Licensor and any individual or Legal Entity on behalf of whom a Contribution has been received by Licensor and subsequently incorporated within the Work. 2. Grant of Copyright License. Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable copyright license to reproduce, prepare Derivative Works of, publicly display, publicly perform, sublicense, and distribute the Work and such Derivative Works in Source or Object form. 3. Grant of Patent License. Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable (except as stated in this section) patent license to make, have made, use, offer to sell, sell, import, and otherwise transfer the Work, where such license applies only to those patent claims licensable by such Contributor that are necessarily infringed by their Contribution(s) alone or by combination of their Contribution(s) with the Work to which such Contribution(s) was submitted. If You institute patent litigation against any entity (including a cross-claim or counterclaim in a lawsuit) alleging that the Work or a Contribution incorporated within the Work constitutes direct or contributory patent infringement, then any patent licenses granted to You under this License for that Work shall terminate as of the date such litigation is filed. 4. Redistribution. You may reproduce and distribute copies of the Work or Derivative Works thereof in any medium, with or without modifications, and in Source or Object form, provided that You meet the following conditions: (a) You must give any other recipients of the Work or Derivative Works a copy of this License; and (b) You must cause any modified files to carry prominent notices stating that You changed the files; and (c) You must retain, in the Source form of any Derivative Works that You distribute, all copyright, patent, trademark, and attribution notices from the Source form of the Work, excluding those notices that do not pertain to any part of the Derivative Works; and (d) If the Work includes a \"NOTICE\" text file as part of its distribution, then any Derivative Works that You distribute must include a readable copy of the attribution notices contained within such NOTICE file, excluding those notices that do not pertain to any part of the Derivative Works, in at least one of the following places: within a NOTICE text file distributed as part of the Derivative Works; within the Source form or documentation, if provided along with the Derivative Works; or, within a display generated by the Derivative Works, if and wherever such third-party notices normally appear. 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