Learning Disentangled Representations for Fairness with Limited Demographics

• My main concern with the proposed method is around “limited fairness information,” which is the key condition or problem this paper aims to address. The author spent a lot of effort in the introduction discussing how existing works address this issue. However, in this paper, the description of this part is limited a few words (lines 295 to 307) and is highly empirical ('we empirically justify that only a few samples are needed to search the sensitive-related dimensions in the latent space'). Overall, whether it’s the use of nonlinear ICA, the calculation of MMD scores, or the focus on removing sensitive information in representation learning, the author does not emphasize how this method is related to or specifically addresses the problem of limited sensitive information. The relationship between these aspects could be made more explicit.

• The captions of each figure and table could be extended with a few words to provide a brief explanation (very minor, just a suggestion).

• As stated in the limitations section, the method requires a relatively large-scale dataset to learn a high-quality latent representation, so the experimental results on the tabular data (which is relatively small compared to the two image datasets) are not as strong as those on the image datasets. It would be interesting to include more explanation, such as convergence analysis, regarding the method, for example, discussing the convergence bound related to sample size.

• “Each dataset is divided into Group-labeled and Group-unlabeled sets, in line with the limited demographics fairness research......” It would be better to move the information from appendix b into the main manuscript to provide an overview of the ratio between group-labeled and group-unlabeled sets.

• Lack of an experiment on how the ratio of group-labeled to group-unlabeled samples affects the results....

• Limited discussion/theoretical support of "sensitive-information-free": as claimed by the authors, the proposed method only uses a very small fraction of sensitive information, which will make it preferable over other methods. While in the paper, it seems the only evidence (in terms of the fraction of training samples $v$) is from the Figure 3, which is merely from one dataset. A major question is: how is the overall performance linked with the fraction $v$ of sensitive information used to identify latent representations? More discussion (or theoretical insights) should be provided.

• Experiments: the experiments show the effects of $\lambda$, which controls the number of latent variables to be removed. However, no experiment shows the effects of $v$, which is the fraction of samples containing sensitive information. To investigate the performance of the proposed method with limited sensitive information given, the authors may need more empirical evidence showing the proposed method will provide better results than others while controlling $v$. For example: comparing the proposed method to all baselines across a range of $v$ values (e.g. 1%, 5%, 10%, 25%) on multiple datasets.

• Scalability/Efficiency: in the algorithm, it needs computing MMD for each $z_i | a, u$, how does it scale well with multiple $a, u$ (and potentially $y$ when considering equalized odds or equal opportunity)? The authors may need to discuss the scalability (or computational efficiency) and compare it with other benchmarks. For example: time and memory complexity analysis of the algorithm as a function of number of attributes, auxiliary variables, and dataset size; empirical runtime comparisons to baselines as dataset size and number of attributes increase.

• Organization: the organization of the "Method" part seems a bit disorganized. The authors should consider putting the algorithm in the main text or at least showing the overall algorithm first as a high-level overview and then breaking down each component in detail in subsections.

The paper is not well defined regarding its theoretical objective. The authors repeatedly claim they can mitigate several fairness criteria simultaneously, without acknowledging their inherent incompatibilities. Specifically the claim "we can simultaneously improve all three fairness metrics" (p.9) overlooks that Demographic Parity (DP) and Equal Opportunity (EO) are often incompatible with each other [1]. While empirical improvements are shown for CelebA and UTK datasets (Figure 5), this success cannot be generalized, particularly for datasets with strong Y-A dependencies

The paper presents inconsistent formulations of the disentanglement function, varying between the equation, algorithm, and implementation (see my questions 2 to 5)

[1] Kleinberg, Jon, Sendhil Mullainathan, and Manish Raghavan. "Inherent trade-offs in the fair determination of risk scores." ITCS 2017

1. A primary challenge is whether this method scales well to multiple criteria. Because the latent space is tied to the sensitive attribute target (e.g. age), it seems the model need be retrained under varying fairness criteria, rather than a post-processing method that doesn't require base model retraining, but only the instance reweights. This furthermore means that this is strictly an in-processing method that isn't amenable to varying base models. This might be very limiting in applications.

2. Nonlinear ICA seems challenging in terms of interpretability (specifically in the tabular domain, not image). While ICA and PCA can be interpretable within a few clean components, in practice this is an art. Gradient Boosting models seem more amenable to extracting rules or feature attribution wrt fairness.