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

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
• Case study: analyzing the GIFGIF dataset
• Using ChoiceRank to understand traffic on a network
• Approximate Bayesian inference using EP

You can also find more information on the official documentation. In particular, the API reference contains a good summary of the library's features.

• 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.