Paper:
Machine learning algorithms have been increasingly deployed in critical automated decision-making systems that directly affect human lives. When these algorithms are solely trained to minimize the training/test error, they could suffer from systematic discrimination against individuals based on their sensitive attributes, such as gender or race. Recently, there has been a surge in machine learning society to develop algorithms for fair machine learning. In particular, several adversarial learning procedures have been proposed to impose fairness. Unfortunately, these algorithms either can only impose fairness up to linear dependence between the variables, or they lack computational convergence guarantees. In this paper, we use Rényi correlation as a measure of fairness of machine learning models and develop a general training framework to impose fairness. In particular, we propose a min-max formulation which balances the accuracy and fairness when solved to optimality. For the case of discrete sensitive attributes, we suggest an iterative algorithm with theoretical convergence guarantee for solving the proposed min-max problem. Our algorithm and analysis are then specialized to fair classification and fair clustering problems. To demonstrate the performance of the proposed Rényi fair inference framework in practice, we compare it with wellknown existing methods on several benchmark datasets. Experiments indicate that the proposed method has favorable empirical performance against state-of-the-art approaches.

Review:
This paper proposes a method to use renyi correlation to improve fairness of ML models by reducing the dependence of outputs wrt sensitive inputs such as gender. Previous models either use a linear dependence measure or use more complex optimization objectives; this paper improves upon them. They first build a min-max objective where the goodness-of-fit and fairness are jointly optimized. This non-convex objective is difficult to optimize and the authors propose a reformulation of the renyi correlation for discrete random variable case where it reduces to finding second largest eigenvalue. Based on this, they reformulate the objective which can be optimized more efficiently. They show the performance of their model for supervised and unsupervised learning problems on 4 different dataset by comparing to standard correlations such as Pearson.
Overall the paper is clearly written and I liked the idea of using renyi correlation which also has a nice theoretical formulation allowing to be optimized more efficiently. But, the experimental results are a bit weak since the only model they experiment with is logistic regression. Given that their main motivation is to capture non-linear dependencies, I think some results with neural networks is necessary. Since their main focus is on discrete case, the authors can show if training a word embedding model with renyi regularization helps improve fairness of word embeddings.
I have several question regarding the paper:
The datasets that authors use have a predefined feature space. Can you show if the sensitive feature is really important for high accuracy? Can we get the same performance without the sensitive features?
Since the model is trained with gradient descent, how would a more simple baseline where the gradient of the sensitive feature is penalized work?
How would this algorithm generalize to larger problems such as language models since Q_{theta} is regenerated at every iteration?