Paper:
Presence of bias and confounding effects is inarguably one of the most critical challenges in machine learning applications that has alluded to pivotal debates in the recent years. Such challenges range from spurious associations of confounding variables in medical studies to the bias of race in gender or face recognition systems. One solution is to enhance datasets and organize them such that they do not reflect biases, which is a cumbersome and intensive task. The alternative is to make use of available data and build models considering these biases. Traditional statistical methods apply straightforward techniques such as residualization or stratification to precomputed features to account for confounding variables. However, these techniques are generally not suitable for end-to-end deep learning methods. In this paper, we propose a method based on the adversarial training strategy to learn discriminative features unbiased and invariant to the confounder(s). This is enabled by incorporating a new adversarial loss function that encourages a vanished correlation between the bias and learned features. We apply our method to synthetic data, medical images, and a gender classification (Gender Shades Pilot Parliaments Benchmark) dataset. Our results show that the learned features by our method not only result in superior prediction performance but also are uncorrelated with the bias or confounder variables. The code is available at http://blinded_for_review/.

Review:
The authors propose a method based on GAN  to classify data while automatically removing confounding effects during training, in order to obtain a classifier whose features are not biased by any confounding effect. The proposed idea is based on the extension of classical classification architectures to account for bias prediction. In practice, the parameters of the feature extraction component are updated to solve both bias prediction and the desired classification problem in adversarial fashion. Pearson’s correlation was chosen as a metric for bias.
The paper is interesting and addresses an important problem for the application of machine learning methods in several real context. The feeling is however that the paper should have better explored the implication of the proposed model of bias, and better investigated the relationship with simpler approaches relying on similar hypothesis.
Here are my main comments for this work:
- Why Pearson’s correlation should be a reliable metric to quantify bias? This metric is insensitive to affine scaling of the data, which is a quite common form of bias (for example in medical images).
- The authors should have investigated the relationship between the proposed method and bias removal through canonical correlation analysis (CCA), and perhaps its non-linear variants. At the end this is what their network is doing, although in an end-to-end fashion. Using the CCA projections in the latent space for classification would be the closest approach to the state of the art for bias removal in statistical analysis (residual analysis). 
- The experimental setting illustrated in 4.1 is not clear. In which sense \sigma_A is a common factor for the two groups? Why the theoretical maximum classification accuracy is 90%? Figure 2 is not clear either and doesn’t help understanding the structure of the generated data (e.g. axis labels missing, colorbars units not specified). 
- It is not clear why authors quantify the correlation in the latent space with tSNE projections. tSNE is highly sensitive to the choice of parameters and it would be important to ensure that it was a “fair competition” between all the methods, when showing the results of the dimensionality reduction. This is another modelling step relying on specific assumptions which decreases interpretability of the findings. The authors also proposed to assess the decorrelation of the estimated features throughout the different methods by measuring the squared distance correlation. Naturally, their method is the one which exhibits the best performances using this metric. However, this way of assessing the decorrelation of the features with the biases is unfair to the other methods, as in their case they specifically built their model to avoid statistical correlation between features and biases.  
- Experiment 4.2 has some controversial aspects, as the bias correction is performed on the control population only, while the model is trained on the entire population. I understand the fact that confounding can be estimated only on healthy conditions, however in this case the network is going to be biased by the control group by construction. The effect of such a choice in the end-to-end optimisation scheme is really not clear.
- We also observe that the results of the baseline CNN are very close to the BR-Net. The main difference lies in the fact that the CNN tends to have an unbalanced classification between true negatives and true positives. However, what would happen if we corrected for age before applying the CNN ?
- In the case where the performances of the CNN would be improved, this last question would raise another one. Indeed, if I already know the confounding effects I want to correct for, why wouldn’t I correct them beforehand in order to avoid to train a complex GAN, which leads to more instability during training. This aspect points to the limit of having an online bias-correction (at least for the medical data case).