Certifying Fairness of Probabilistic Circuits

This repository contains the implementation of the exact and approximate search algorithms presented in our AAAI23 paper Certifying Fairness of Probabilistic Circuits. The code is written in Julia.

Requirements

• Julia 1.5.3
• Julia Packages
  • Juice.jl Packages: ProbabilisticCircuits, LogicCircuits
  • CSV
  • DataFrames
  • Random
  • DataStructures
  • Profile
  • Combinatorics
  • ArgParse
  • StatsBase

Julia can be obtained from https://julialang.org/downloads/oldreleases/. The required Julia packages can be installed by running import Pkg; Pkg.add("PackageName") in Julia.

Usage

All the required methods are provided in a modular format in pc_fairness.jl. This file also includes a main script that allows the user to quickly check PCs learnt on different datasets for discrimination and divergence patterns using our exact search algorithm.

The program takes 4 arguments:

• --scoretype / -s : "discrimination"/"divergence"
• --dataset / -x : "compas"/"adult"/"income"
• --threshold / -t : Float64 threshold to be considered a pattern.
• --delta / -d : Float64 delta for divergence score calculation.

Sample usage: julia pc_fairness.jl -s discrimination -x compas -t 0.1

The function signatures in pc_fairness.jl are self-descriptive and the user is encouraged to flexibly leverage these methods and modify the main script according to their needs. For instance, one could replace num_disc_patterns with get_maximal_patterns in the main script to obtain maximal patterns instead. We also provide sample scripts for evaluation of our sampling algorithm as example usage (see sampling_experiment.jl).

Some of the most useful top level functions are:

• learn_pc: Learn a PC from a given dataset.
• get_likelihood: Obtain log likelihood and average log likelihood per instance of PC.
• num_disc_patterns: Find number of discrimination patterns in PC.
• num_divergence_patterns: Find number of divergence patterns in PC.
• get_top_k: Find top k discrimination/divergence patterns in PC.
• get_top_one_random_memo_avg: Runs one iteration of the sampling algorithm and returns the highest score of pattern found. Other partial patterns visited in the run can be optinally cached.
• get_pareto_front: Find the set of pareto optimal patterns.
• get_maximal_patterns: Find the set of maximal patterns.
• get_minimal_patterns: Find the set of minimal patterns.

Other Notes

• All the datasets are included in the data directory. The user can add more datasets to the directory and learn a PC on the dataset using the learn_pc method. The user can leverage our library to check the learnt model for fairness.

• We provide pre-trained PCs for COMPAS datasets: compas_good.psdd and compas_good.vtree.