Fair Classification under Covariate Shift and Missing Protected Attribute
- an Investigation using Related Features

Automated decision making has become prevalent in our society today. Organizations such as companies, judiciaries, institutions, etc., rely on machine learning models, especially binary classifiers, to make important decisions about people, such as, loan crediting, admissions into university, etc. These decisions can get biased towards a specific group, such as, race or gender, if the classifier has been trained using a biased training-set. ¹¹1A bias in the binary-classification training-set can refer to, either an imbalance in the sample-sizes of the two groups (e.g., 1000 samples being available for males, whereas, only 100 being available for females), or an imbalance in the class-labels for the two groups (e.g., 90% of males being labeled as positive, whereas, only 10% of females being labeled as positive.) The field of fair-classification has developed many methods to tackle this problem, but mostly, they depend on the availability of the group-information, also known as the sensitive or the protected attribute.

But the availability of the protected attribute might not be realistic in a real-world setting, for example, due to a law prohibiting the collection of sensitive group information such as gender or race, thus, making achieving fairness challenging. To achieve fairness in such a case, when the true sensitive attribute is not available, Zhao et al. (2021) have suggested using a set of non-sensitive features that have been identified by domain experts as being highly correlated with the missing true attribute and provided beforehand. They call these as Related Features. We found that the use of related features to achieve fairness has been a quite unexplored direction in the fairness literature, and hence, explored their use to achieve fair classification under Covariate Shift.

Covariate-Shift is a very realistic issue faced by machine learning models, when after being trained on a particular data distribution, they have to be used on a new and different data distribution. We illustrate the issue by a hypothetical scenario of a company that had been using a model trained on the customer records of its own country for a past few years, but now, wants to expand its market to another country. As a result, it might face the difficulty of distribution-change and its existing model might prove unreliable. Moreover, due to limitations of data collection, the company may find it difficult to get labelled data for the new country that it could have used to train a new model. Thus, to build an accurate classifier will be a challenge. This is the standard problem of unsupervised covariate shift.

Further, the laws of the new country might require the company’s classifier to also be fair on the country’s population, but the knowledge of true protected attribute might not be available to the company due to limitations of data collection or legal restrictions. In such a case, the company might decide to seek help of domain experts, identify a set of non-sensitive but related attributes, and use them to achieve fairness instead.

In such a novel hybrid setting that involves both missing protected attribute and covariate shift, we investigated a simple possible approach based on Related Features to address the joint issue.

We have been given $N_{S}$ labelled samples from the source domain $(\mathbf{X}^{S},Y^{S})=\{(\mathbf{x}_{i}^{S},y_{i}^{S})\}_{i=1}^{N_{S}}$, and $N_{T}$ unlabelled samples $\mathbf{X}^{T}=\{\mathbf{x}_{i}^{T}\}_{i=1}^{N_{T}}$ from the target domain, where $\mathbf{x}_{i}\in\mathbb{R}^{d}$ and $y_{i}\in\{0,1\}$. Under covariate-shift assumption, the source-domain features $\mathbf{x}_{i}^{S}$ are assumed to be drawn from a source-distribution, $p_{S}(\mathbf{x})$, whereas, the target-domain features, $\mathbf{x}_{i}^{T}$, are assumed to be drawn from a different target-distribution $p_{T}(\mathbf{x})$. Conditional distribution $p(y|\mathbf{x})$ is assumed to be same in both the domains.

We wish to assign labels $Y^{T}=\{y_{i}^{T}\}_{i=1}^{N_{T}}$ to the samples in the target-domain using a classifier, $g_{\theta}:\mathbf{X}\rightarrow Y$ ²²2We will denote the classifier predictions after sigmoid with $h_{\theta}:\mathbf{X}\rightarrow[0,1]$, or $\tilde{y}$. , that is not only accurate, but also fair with respect to the missing protected attribute in the target-domain, $A^{T}=\{(a_{i}^{T})\}_{i=1}^{N_{T}}$.

Although the true protected attribute is absent, a set of $K$ features, $F^{T}=\{(x_{i1}^{T},x_{i2}^{T},...,x_{iK}^{T})_{i=1}^{N_{T}}\}$ have been identified by domain-experts as being highly correlated with the true attribute, and have to be used to enforce fairness in the classifier.

For all the approaches, the performance-vs-fairness tradeoffs are plotted in Figure 1. (For the approaches involving fairness coefficient, the results obtained for various values of fairness coefficient are plotted.) For detailed results, see the appendix.

Our goal with trying the Hybrid method, i.e. the one that uses related features for fairness along with covariate shift adaptation, was to see if it can outperform the baselines significantly either in terms of fairness, or performance, or both. We made the following observations:

Fairness

: In terms of best fairness, on the Adult dataset, it was a fair using related features approach Zhao et al. (2021) that achieved the lowest $\Delta_{DP}$ of around 0.05 (Notice the lowest red dot in Figure 1.), whereas, on the MEPS dataset, it was the covariate shift adapated approach that achieved the lowest. (Notice the green dot near the bottom in Figure 1.)

Performance

: In terms of best AUC, multiple approaches even other than the hybrid were able to achieve close to the best i.e. around 85% on Adult, and around 80% on MEPS.

Fairness-Performance tradeoff

: In terms of the best tradeoff, both on the Adult and the MEPS datasets, the Related features removed approach seemed to be the best, having, on Adult, an AUC of around 80% and $\Delta_{DP}$ of around 0.10; and on MEPS, an AUC of 80% and $\Delta_{DP}$ of 0.05. Although, for certain values of fairness coefficients, the Fair using related features and Hybrid approaches had similar tradeoffs, these did not seem significantly superior to the Related features removed approach.

Thus, the overall results indicate that the hybrid method, i.e. the use of related features along with covariate-shift adaptation, is not significantly more efficient than even simple baselines such as altogether removal of the related features.

In this study, we investigated the problem of fair classification under covariate shift and missing protected attribute using an approach involving importance weights for covariate shift adaptation and fairness using related features for handling the missing attribute, and found it to be not much significantly efficient than even simple baseline such as removal of related features.