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 not in general applicable to 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 a synthetic, a medical diagnosis, and a gender classification (Gender Shades) 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/. A central challenge in practically all machine learning applications is the consideration of confounding biases. Confounders are extraneous variables that distort the relationship between the input (independent) and output (dependent) variables and hence lead to erroneous conclusions (Pourhoseingholi et al., 2012) . In a variety of applications ranging from disease prediction to face recognition, where machine learning models are built to predict labels from images, demographic variables (such as age, sex, race) of the study may confound the training process if the distribution of image labels is skewed with respect to them. In this situation, the predictor may learn the influence of the confounder and bias present in the data instead of actual discriminative cues. It is a cumbersome task to account for all biases when curating large-scale datasets (Yang et al., 2019) . An alternative approach is to account for the bias in the model. Traditionally, confounding variables are often controlled by statistical methods in either design or analytical stages (Aschengrau & Seage, 2013) . In the design stage, one can utilize randomization or matching of the confounding variables across different study groups. In the analytical stage, confounding can be controlled by standardization or stratification (Pourhoseingholi et al., 2012; Aschengrau & Seage, 2013) . Another common solution is to learn the influence of the confounding variables on the input (independent) variables by regression analysis. Then, the residuals derived from the optimal regression model are regarded as the confounder-free input to train the predictor (Wodtke, 2018) . The regression analysis works reasonably well under the assumption that the input variables represent deterministic features that are comparable across a population, e.g., morphometric measurements extracted from medical images or engineered features extracted from face images. The method fails, however, when this assumption does not hold such as for the pixel intensity values in images. Note, the raw intensities are only meaningful within a neighborhood but variant across images. Therefore, these regression approaches cannot be used in connection with deep learning methods that are di- † indicates equal contribution. Figure 1: Average face images across each shade category (first row), average saliency map of the trained baseline (second row), and BR-Net (third row) color-coded with the normalized saliency value for each pixel. BR-Net results in more stable patterns across all 6 shade categories. The last column shows the tSNE projection of the learned features by each method. Our method results in a better feature space invariant to the bias variable (shade) while the baseline shows a clear pattern affected by the bias. Average accuracy of per-shade gender classification over 5 runs of 5-fold crossvalidation is shown on each average map. The models are pre-trained on ImageNet and fine-tuned on GS-PPB. BR-Net is not only able to close the gap of accuracy for the darker shade but it also regularizes the model to improve per-category accuracy. rectly applied to images, such as convolutional neural networks (CNNs). Removing confounding factors for CNNs is an open question we aim to address here. We propose a feature learning scheme to produce features that are predictive of class labels while being unbiased to confounding variables. The idea is inspired by the domain-adversarial training approaches (Ganin et al., 2016) with controllable invariance (Xie et al., 2017) within the context of generative adversarial networks (GANs) (Goodfellow et al., 2014 ), but we argue that generic and widely used loss functions are not designed for controlling the invariance with respect to bias variables. Hence, we introduce an adversarial loss function that aims to quantify the statistical dependence between the learned features and bias variables with the correlation coefficient. This strategy improves over the commonly used cross-entropy or mean-squared error (MSE) loss that only aims to predict the exact value of the bias variables and thereby achieves stabler results within the context of adversarial training. Since our proposed model injects resilience towards the bias during training to produce confounder-invariant features, we refer to our approach as Bias-Resilient Neural Network (BR-Net). We evaluate BR-Net on three datasets to examine different aspects of the method and compare it with a wide range of baselines. First, we test on a synthetic dataset to outline how the learned features by our method are unbiased to controlled confounding variables. Then, we test it on a medical imaging application, i.e., predicting the human immunodeficiency virus (HIV) diagnosis directly from T1-weighted Magnetic Resonance Images (MRIs). As widely explored in the HIV literature, HIV disease accentuates brain aging (Cole et al., 2017) and if a predictor is learned not considering age as a confounder, the predictor may actually be learning the brain aging patterns rather than actual HIV markers. Lastly, we evaluate BR-Net for gender classification using the Gender Shades Pilot Parliaments Benchmark (GS-PPB) dataset (Buolamwini & Gebru, 2018) . We use different backbones pre-trained on ImageNet (Deng et al., 2009 ) and fine-tune them for predicting gender from face images. We show that prediction of the vanilla models is dependent on the race of the subject (alternatively we consider skin color quantified by the 'shade' variable) and show poor results for darker faces, while BR-Net can successfully close the gap. Our comparison with methods based on multi-task (Lu et al., 2017 ) prediction (i.e., predicting gender and shade as two tasks) and categorical GAN (Springenberg, 2015) (i.e., predicting shade as a categorical variable in the adver-sarial component) shows that BR-Net is not only able to learn features impartial to the bias of race (verified by feature embedding and saliency visualization), it also results in better performance in gender prediction (see Fig. 1 ). We proposed a method based on adversarial training strategies by encouraging vanished correlation to learn features for the prediction task while being unbiased to the confounding variables in the study. We evaluated our bias-resilient neural network (BR-Net) on a synthetic, a medical diagnosis, and a gender prediction dataset. In all experiments, BR-Net resulted in a feature embedding space that was agnostic to the bias in the data while all other methods failed to do so. Based on our experiments we can conclude that, besides the attempt to improve datasets and curate unbiased ones (Yang et al., 2019) , it is crucial to build models that properly account for the bias in data during training. Our bias-resilient model and some other recent works set on foot toward this direction. This is crucial as machine learning models are acceding to everyday lives, or are being developed for crucial medical applications. Failure to account for the underlying bias or confounding effects can lead to spurious associations and erroneous decisions. As a direction for the future work, other strategies such as deep canonical correlation analysis (Andrew et al., 2013) can be explored to form the adversarial component.
We propose a method based on the adversarial training strategy to learn discriminative features unbiased and invariant to the confounder(s) by incorporating a loss function that encourages a vanished correlation between the bias and learned features.
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