README

This repository contains code relative to the WSDM'22 paper Introducing the Expohedron for efficient Pareto-optimal fairness-utility amortizations in repeated rankings by Kletti et al.

1. Installation

It is sufficient to clone the repository. The requirements are listed in the file requirements.txt. If conda is used, they can be installed in a virtual environment expohedron as

conda create --name expohedron
conda activate expohedron
conda install --file requirements.txt

2. Get started

A complete working example is available in the file examples/example.py.

In the following we give examples of some common operations.

2.1. Create and expohedron

from expohedron import *

# set parameters
relevance_values = np.array([0.8, 0.8, 0.7, 0.3])
n = len(relevance_values)
dcg = 1 / np.log2(np.arange(2, n+2))

# create expohedron
expohedron = PBMexpohedron(dcg, relevance_values)
print(expohedron)

2.2. Compute the Pareto curve

from pareto import *

# set parameters
relevance_values = np.array([0.8, 0.8, 0.7, 0.3])
n = len(relevance_values)
dcg = 1 / np.log2(np.arange(2, n+2))

pareto_curve = pareto_curve_pbm_individual(dcg, # position based model (PBM)
                                           relevance_values,  # relevance values
                                           fairness="meritocratic", # set "demographic" for demographic fairness
                                           verbose=1)  # set `verbose=0` for muteness

2.3. Carathéodory decomposition

from pareto import *

# set parameters
relevance_values = np.array([0.8, 0.8, 0.7, 0.3])
n = len(relevance_values)
dcg = 1 / np.log2(np.arange(2, n+2))

# compute target exposure
target = fairness_endpoint_individual_meritocratic_intersection(dcg, relevance_values)
# Decompose the target exposure as a convex sum of vertices
convex_coefficients, vertices = caratheodory_decomposition_pbm_gls(dcg, target)

3. License

The license is available in the file LICENSE

4. References

To cite this repository, please use

@inproceedings{kletti_introducing_2022,
	address = {New York, NY, USA},
	series = {{WSDM} '22},
	title = {Introducing the {Expohedron} for {Efficient} {Pareto}-optimal {Fairness}-{Utility} {Amortizations} in {Repeated} {Rankings}},
	isbn = {978-1-4503-9132-0},
	url = {https://doi.org/10.1145/3488560.3498490},
	doi = {10.1145/3488560.3498490},
	urldate = {2022-02-21},
	booktitle = {Proceedings of the {Fifteenth} {ACM} {International} {Conference} on {Web} {Search} and {Data} {Mining}},
	publisher = {Association for Computing Machinery},
	author = {Kletti, Till and Renders, Jean-Michel and Loiseau, Patrick},
	month = feb,
	year = {2022},
	keywords = {ranking, fairness, balanced words, gls, amortization, expohedron, muli-objective optimization, pareto-optimal},
	pages = {498--507},
}

5. Contact us

Should you have any questions, problems or remarks, do not hesitate to raise an issue or to write to us at [email protected].