FERMI-ODDS 0.0.1

Fair Empirical Risk Minimization via Exponential Renyi Mutual Information (ERMI)

Fair Empirical Risk Minimization Via Exponential Rényi Mutual Information

This repository is dedicated to implementation of Fair Empirical Risk Minimization (FERMI) algorithms proposed in . FERMI provides the first stochastic algorithm with theroretical convergence guarantees for promoting fairness in classification tasks. To balance the accuracy and fairness, fair risk minimization through exponential Rényi mutual information framework minimizes the following objective function:

where the first term represents the population risk (accuracy) and the second term is a regularizer promoting exponential Rényi mutual information (ERMI) between the sensitive attribute(s) and predictions. Note that ERMI is a stronger notion of fairness compared to existing notions of fairness such as mutual information [Kamishima et al., 2011, Rezaei et al., 2020, Steinberget al., 2020, Zhang et al., 2018, Cho et al., 2020a], Pearson correlation [Zafar et al., 2017], false positive/negative rates[Bechavod and Ligett, 2017], Hilbert Schmidt independence criterion (HSIC) [Pérez-Suay et al., 2017], and Rényicorrelation [Baharlouei et al., 2020, Grari et al., 2020, 2019], in the sense that it upper bounds all aforementioned notions. Thus, minimizing ERMI guarantees the fairness of model under those notions. In the following table we compare FERMI with several state-of-the-art approaches in the literature. Note that the abbrevations NB, Cont., Stoch., DP, EOD, MI and RC stand for Non-binary, Continuous, Stochastic, Dempographic Parity, Equalized Odds, Mutual Information, and Rényi Correlation respectively.

Reference	NB Target	NB Attribute	NB both exp.	Violation Notion	Unbiased Stoch. Alg	Convergence Guarantee
Sotchastic FERMI	:heavy_check_mark:	:heavy_check_mark:	:heavy_check_mark:	DP, EOD, MI, RC, ERMI	:heavy_check_mark:	O(ε-4) (Stoch)
Batch FERMI	:heavy_check_mark:	:heavy_check_mark:	:heavy_check_mark:	DP, EOD, MI, RC, ERMI	:x:	O(ε-4) (Batch)
Cho et al. [2020a]	:heavy_check_mark:	:heavy_check_mark:	:x:	DP, EOD, MI	:heavy_check_mark:	:x:
Cho et al. [2020b]	:heavy_check_mark:	:heavy_check_mark:	:heavy_check_mark:	DP, EOD	biased	:x:
Baharlouei et al. [2020]	:heavy_check_mark:	:heavy_check_mark:	:x:	DP, EOD, RC	:x:	O(ε-4) (Batch)
Rezaei et al. [2020]	:x:	:x:	:x:	DP, EOD	:x:	:x:
Jiang et al. [2020]	:x:	:heavy_check_mark:	:x:	DP	:x:	:x:
Donini et al. [2018]	:x:	:heavy_check_mark:	:x:	EOD	:x:	:x:
Zhang et al. [2018]	:heavy_check_mark:	:heavy_check_mark:	:x:	DP, EOD	biased	:x:

Dependencies

The following packages must be installed via Anaconda or pip before running the codes. Download and install Python 3.x version from Python 3.x Version: Then install the following packages via Conda or pip:

• Numpy
• Pandas
• Scikit learn
• Matplotlib
• PyTorch

Binary Classification with Binary Sensitive Attribute

To run the code for a binary classification problem with a binary sensitive attribute use the following command:

python BinaryClassification/Binary_FERMI.py

The above code updates the parameters of a logistic regression model via gradient descent algorithm. When the training dataset is large-scale, the implemented algorithm can be slow. Thus, we suggest to run the following code which updates the parameters using stochastic gradient descent. Note that, from a theoretical point of view the number of required iterations for FERMI (stochastic version) is not better than the deterministic algorithm, but the per-iteration cost is much smaller especially when smaller batches are chosen.

python BinaryClassification/Stochastic_FERMI.py

Stochastic FERMI for Large-scale Neural Networks on Datasets with Multiple Sensitive Attributes (Non-binary Labels and Sensitive Attributes)

The implementation of Algorithm 1 in paper, specialized to a 4-layer neural network on color mnist dataset can be found in NeuralNetworkMnist folder. You can run it on color mnist dataset via:

python NeuralNetworkMnist/code_cm.py