choix

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choix is a Python library that provides inference algorithms for models based on Luce's choice axiom. These probabilistic models can be used to explain and predict outcomes of comparisons between items.

• Pairwise comparisons: when the data consists of comparisons between two items, the model variant is usually referred to as the Bradley-Terry model. It is closely related to the Elo rating system used to rank chess players.
• Partial rankings: when the data consists of rankings over (a subset of) the items, the model variant is usually referred to as the Plackett-Luce model.
• Top-1 lists: another variation of the model arises when the data consists of discrete choices, i.e., we observe the selection of one item out of a subset of items.
• Choices in a network: when the data consists of counts of the number of visits to each node in a network, the model is known as the Network Choice Model.

choix makes it easy to infer model parameters from these different types of data, using a variety of algorithms:

• Luce Spectral Ranking
• Minorization-Maximization
• Rank Centrality
• Approximate Bayesian inference with expectation propagation

Getting started

To install the latest release directly from PyPI, simply type::

pip install choix

To get started, you might want to explore one of these notebooks:

• Introduction using pairwise-comparison data <https://github.com/lucasmaystre/choix/blob/master/notebooks/intro-pairwise.ipynb>_
• Case study: analyzing the GIFGIF dataset <https://github.com/lucasmaystre/choix/blob/master/notebooks/gifgif-dataset.ipynb>_
• Using ChoiceRank to understand traffic on a network <https://github.com/lucasmaystre/choix/blob/master/notebooks/choicerank-tutorial.ipynb>_
• Approximate Bayesian inference using EP <https://github.com/lucasmaystre/choix/blob/master/notebooks/ep-example.ipynb>_

You can also find more information on the official documentation <http://choix.lum.li/en/latest/>. In particular, the API reference <http://choix.lum.li/en/latest/api.html> contains a good summary of the library's features.

References

• Hossein Azari Soufiani, William Z. Chen, David C. Parkes, and Lirong Xia, Generalized Method-of-Moments for Rank Aggregation_, NIPS 2013
• François Caron and Arnaud Doucet. Efficient Bayesian Inference for Generalized Bradley-Terry models_. Journal of Computational and Graphical Statistics, 21(1):174-196, 2012.
• Wei Chu and Zoubin Ghahramani, Extensions of Gaussian processes for ranking\: semi-supervised and active learning_, NIPS 2005 Workshop on Learning to Rank.
• David R. Hunter. MM algorithms for generalized Bradley-Terry models_, The Annals of Statistics 32(1):384-406, 2004.
• Ravi Kumar, Andrew Tomkins, Sergei Vassilvitskii and Erik Vee, Inverting a Steady-State_, WSDM 2015.
• Lucas Maystre and Matthias Grossglauser, Fast and Accurate Inference of Plackett-Luce Models_, NIPS, 2015.
• Lucas Maystre and M. Grossglauser, ChoiceRank\: Identifying Preferences from Node Traffic in Networks_, ICML 2017.
• Sahand Negahban, Sewoong Oh, and Devavrat Shah, Iterative Ranking from Pair-wise Comparison_, NIPS 2012.

.. _Generalized Method-of-Moments for Rank Aggregation: https://papers.nips.cc/paper/4997-generalized-method-of-moments-for-rank-aggregation.pdf

.. _Efficient Bayesian Inference for Generalized Bradley-Terry models: https://hal.inria.fr/inria-00533638/document

.. _Extensions of Gaussian processes for ranking\: semi-supervised and active learning: http://www.gatsby.ucl.ac.uk/~chuwei/paper/gprl.pdf

.. _MM algorithms for generalized Bradley-Terry models: http://sites.stat.psu.edu/~dhunter/papers/bt.pdf

.. _Inverting a Steady-State: http://theory.stanford.edu/~sergei/papers/wsdm15-cset.pdf

.. _Fast and Accurate Inference of Plackett-Luce Models: https://infoscience.epfl.ch/record/213486/files/fastinference.pdf

.. _ChoiceRank\: Identifying Preferences from Node Traffic in Networks: https://infoscience.epfl.ch/record/229164/files/choicerank.pdf

.. _Iterative Ranking from Pair-wise Comparison: https://papers.nips.cc/paper/4701-iterative-ranking-from-pair-wise-comparisons.pdf

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