choix 0.1.0

Inference algorithms for models based on Luce's choice axiom.

# 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.

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

• GMM using rank breaking

• Approximate bayesian inference with expectation propagation

## Installation

Simply type

pip install choix

The library is under active development, use at your own risk.

## References

• Lucas Maystre and Matthias Grossglauser, [Fast and Accurate Inference of Plackett-Luce Models][1], NIPS, 2015

• David R. Hunter. [MM algorithms for generalized Bradley-Terry models][2], The Annals of Statistics 32(1):384-406, 2004.

• François Caron and Arnaud Doucet. [Efficient Bayesian Inference for Generalized Bradley-Terry models][3]. Journal of Computational and Graphical Statistics, 21(1):174-196, 2012.

• Sahand Negahban, Sewoong Oh, and Devavrat Shah, [Iterative Ranking from Pair-wise Comparison][4], NIPS 2012

• Hossein Azari Soufiani, William Z. Chen, David C. Parkes, and Lirong Xia, [Generalized Method-of-Moments for Rank Aggregation][5], NIPS 2013

• Wei Chu and Zoubin Ghahramani, [Extensions of Gaussian processes for ranking: semi-supervised and active learning][6], NIPS 2005 Workshop on Learning to Rank.

[1]: https://infoscience.epfl.ch/record/213486/files/fastinference.pdf [2]: http://sites.stat.psu.edu/~dhunter/papers/bt.pdf [3]: https://hal.inria.fr/inria-00533638/document [4]: https://papers.nips.cc/paper/4701-iterative-ranking-from-pair-wise-comparisons.pdf [5]: https://papers.nips.cc/paper/4997-generalized-method-of-moments-for-rank-aggregation.pdf [6]: http://www.gatsby.ucl.ac.uk/~chuwei/paper/gprl.pdf