Fair Active Learning
Abstract
Bias in training data, as well as proxy attributes, are probably the main reasons for unfair machine learning outcomes. ML models are trained on historical data that are problematic due to the inherent societal bias. Besides, collecting labeled data in societal applications is challenging and costly. Subsequently, proxy attributes are often used as alternatives to labels. Yet, biased proxies cause model unfairness.
In this paper, we propose fair active learning (FAL) as a resolution. Considering a limited labeling budget, FAL carefully selects data points to be labeled in order to balance the model performance and fairness. Our comprehensive experiments on real datasets, confirm a significant fairness improvement while maintaining the model performance.
1 Introduction
Datadriven decision making plays a significant role in modern societies. Data science and advanced computational methods have enabled us to make wise decisions and to make societies more just, prosperous, inclusive, and safe. With this unique opportunity, however, comes a great deal of responsibilities as improper development of data science technologies can not only fail but make matters worse. Judges in US courts, for example, use criminal assessment algorithms that are based on the background information of individuals for setting bails or sentencing criminals. This is valuable as it can lead to safer societies but at the same time, if not properly developed, it has the potential to have a significant consequences on people’s lives. For instance, the recidivism scores provided for the judges are highly criticized as being discriminatory, since it turns out they assign higher risks to African American individuals Angwin et al. (2016).
Machine learning (ML) is in the center of datadriven decision making as it provides insightful unseen information about phenomena based on available observations. Besides many other applications, Machine learning has also been utilized to evaluate individuals and to make societal decisions. In this context, similar to other applications, ML models try to learn the system (individuals and society) based on some observations (historical data). Blindly applying machine learning without paying attention to societal impacts, however, can lead to serious issues such as biased decision making, resulting in racism or sexism. The following are two major reasons for this to happen:

Bias in training data: ML models use the background information of individuals that is usually biased due to the historical discriminations. For example, redlining is a systematic denial of services used in the past against (mainly) specific racial communities, leaving its footprint up to the day and the existing data records Jan (2018). Gender bias in Data Perez (2019), including health care Pley and Keeling (Sep. 2019) is yet another example of bias in training data.

Proxy attributes: labeled data is the cornerstone of supervised learning. Yet, in societal applications there is often limited labeled data. For example, the aforementioned recidivism scores are meant to show how likely an individual is to commit a crime in the future. Similarly, in the context of college admission the goal is to admit students who are likely to be the most successful in the future. Training data with such information is either not available or a very limited number of labeled data exists. As a consequence, other available attributes are typically used as proxies for the true labels. For instance, “getting arrested by cops” may be considered as a proxy for committing a crime, or GPA for future college success.
ML models rely on the data that can be highly biased. Bias in data can cause model unfairness which can give rise to discrimination in consequent decisions. For instance, a job platform can rank less qualified male candidates higher than more qualified female candidates Lahoti et al. (2019). As a result, a new paradigm of fairness in machine learning has emerged. Fairness has a different definitions and is measurable in various ways. To explain these arguments further, in the following we provide two running examples of applications that we shall use for clarity during the paper.
Example 1.
A company is interested in creating a model for predicting recidivism to help judges make wise decisions when setting bails; that is, they want to find out how likely a person is to commit a crime in the future.
Suppose the company has access to the background information of some criminal defendants
Example 2.
A loan consulting company is about to create models that will help financial agencies identify “valuable customers” who will pay off their loans on time. The company has collected a dataset of customers who have received a loan in the past few years. In addition to the demographic information, the dataset includes information such as education and income level of individuals. Unfortunately, at the time of approving loans, it is not known whether customers will pay their debt on time, and hence, the data are not labeled. Nevertheless, the company has hired experts who, given the information of an individual who has received a loan in the past, can verify their background and assess if payments were made on time. Of course, considering the costs associated with a background check, it is not viable to freely label all customers.
Both of the above examples use historical data for building their models that, as we observed in our experiments, are biased.
For instance, the income in Example 2 is known to include gender bias Jones (1983) or prior count in Example 1 is racially biased Angwin et al. (2016).
Also, in both examples the datasets are unlabeled.
A data scientist may decide to use a (problematic) proxy attribute as true label
Unfortunately, despite its importance, to the best of our knowledge none of the existing work in active learning takes into account the societal impacts of the models such as fairness and optimizes solely to maximize model performance. This is our goal in this paper. We aim to design an active learning framework that generates fair outcomes. As we shall further elaborate in § 2.3, we define the notion of fairness with respect to sensitive attributes such as race and gender. Focusing on the group fairness Dwork et al. (2012); Li and Cropanzano (2009), we consider a model fair if its outcome does not depend on the sensitive attributes. That is, we adopt demographic parity, one of the popular fairness measures Kusner et al. (2017); Dwork et al. (2012). Although we consider model independence as our measure of fairness, in § 4 we demonstrate how to extend our findings for other notions of fairness based on separation and sufficiency Barocas et al. (2019). In this paper, our focus is on classification models. In the rest of the paper, we simplify the word to “models”.
Summary of contributions. In this paper, we introduce fairness in active learning (FAL) for constructing fair models in the context of limited labeled data. We first provide the necessary theoretical background, definitions, and terms. Next, we propose our fair active learning (FAL) framework to balance model performance and fairness. The proposed framework is flexible to incorporate different measures for model performance and fairness. Finally, we conduct comprehensive experiments on real datasets to show that performing active learning while considering the fairness constraint can significantly improve the fairness of a classifier while not dramatically impacting its performance. As we shall present in § 5, our experiment results across different fairness metrics confirm improvements in fairness by around 50% without major reductions in model performance. In summary, our contributions are as following:

Carefully formalizing terms and background, we present different fairness measures based on model independence.

We introduce fairness in active learning, an iterative approach that incorporates the fairness measure in its sample selection unit and constructs a fair predictive model as a result.

We propose the expected fairness measure for unlabeled sample points based on the bestknown estimate of the function.

We conduct comprehensive experiments on realworld data, considering different fairness metrics based on model independence. Our results show an improvement of around 50% in fairness measures while not significantly impacting the model performance.

We discuss how to extend our framework for different fairness measures.
In the remainder of this paper, we start with a background on active learning and our fairness model in § 2. In § 3, we will present the FAL framework. In § 4, we will discuss how to extend our proposal for different fairness measures. We will provide our comprehensive experiments in§ 5, review the related work in § 6, and conclude the paper in § 7.
2 Background
2.1 Data Model
We assume the existence of a (training) dataset with instances, each consisting of features . For a data point , we use the notation for the vector of input features and to refer to the value of th feature, . We also assume each data point is associated with at least one sensitive attribute . As we shall further explain in § 2.3, sensitive attributes such as gender and race are nonordinal categorical attributes used in the fairness model. We use the notation to refer to the sensitive attribute(s) of . Without loss of generality and to simplify the explanations, unless explicitly stated, we assume is a single sensitive attribute. Still, we would like to emphasize that our techniques are not limited to the number of sensitive attributes. Each data point is also associated with a label attribute with possible values . We assume the labels of the data points are initially unknown. In § 2.2, we will explain how to obtain the label of a data point . At any moment during the training process, the subset of data points for which labels are known is referred to as labeled pool and the rest of them is called unlabeled pool. We note that every entry in is identified by the pair , while every entry in is the triple .
2.2 Learning Model
The goal is to learn a classifier function that maps the feature space to the labels. We use to refer to the predicted label for . Recall that data points are initially unlabeled. Poolbased active learning for classification, which was introduced in Lewis and Gale (1994), selects instances from an unlabeled data set to form a labeled set , sequentially for training. Active learning assumes the existence of an expert oracle that given a data point provides its labels. Labeling, however, is costly and usually there is a limited labeling budget . Using the sampling budget, one can randomly label data points and use them to train a classifier. The challenge, however, is to wisely exhaust the budget to build the most accurate model.
Different sampling strategies have been proposed in the context of active learning. Uncertainty sampling Lewis and Gale (1994) is probably the most common strategy in active learning for classification. It selects data points for labeling such that the model variance is maximally minimized. To do so, it chooses the point that the current model is least certain about its label. At every iteration of the process, let the classifier be the current model, using the labeled dataset . For every data point with the feature vector , let be the posterior probability that its unknown label will be based on .
By maximizing the uncertainty, active learning selects the points that are close to the decision boundary, where we are least certain about the class label. Uncertainty can be defined in different ways Settles (2009). In general, uncertainty sampling refers to maximum entropy Shannon (1948). Equation 1 denotes the Shannon entropy formulation for classifying with based on the probability obtained from the classifier for an unknown label variable .
(1) 
where is defined as follows:
(2) 
Algorithm 1 presents the standard active learning algorithm, using Equation 1. Iteratively, the algorithm selects a point from to be labeled next. It uses the classifier trained in the previous step to obtain class probabilities (initially, all the probabilities are equal), and to calculate the entropies. The algorithm passes the selected point to the labeling oracle, acquires its label, and adds the point to the set of labeled dataset . It uses to train the classifier , where shows the current iteration. This process continues until the labeling budget is exhausted.
difference  
ratio 
2.3 (Un)Fairness Model
Following many of the existing work, while founding our model on societal norms of fairness Barocas et al. (2017), we develop our fairness model on the notion of model independence or demographic disparities Barocas et al. (2019); Žliobaitė (2017); Narayanan (2018); Zafar et al. (2017), also referred by terms such as group fairness Dwork et al. (2012), statistical parity Dwork et al. (2012); Simoiu et al. (2017), and disparate impact Barocas and Selbst (2016); Feldman et al. (2015); Ayres (2005). Although our main focus in this paper is on fairness based on model independence, in § 4 we show how to extend our framework for other measures based on separation () and sufficiency () Barocas et al. (2019).
Apparently, disparities in the model does not necessarily imply that the designers intentionally want them to arise. The problem occurs as these models rely entirely on (biased) historical data for learning a system; therefore, the historical disparities in the data cause the (unintentional) bias in the model. We believe that machine learning practitioners are responsible to intervene in the modeling process (in different learning stages) to mitigate model disparities.
Given a classifier and a random point with a predicted label , demographic parity holds iff Barocas et al. (2017, 2019). Consider a binary classifier and think of as “acceptance” – in Example 2, the group that receive a loan. Demographic parity is the condition that requires the acceptance rate to be the same for all groups of i.e. female or male in this case. Under demographic parity, for a binary classifier and a binary sensitive attribute, the statistical independence of a sensitive attribute from the label causes the following:

: The probability of acceptance is equal for members of different demographic groups. For instance, in Example 1 members of different race groups have an equal chance for being classified as low risk.

: If the population ratio of a particular group is (i.e. , the ratio of this group in the accepted class is also . For instance, in Example 2, let be the female ratio in the applicants’ pool. Under demographic parity, female ratio in the set of admitted applications for a loan equals to .

: Mutual information is the measure of mutual dependence between two variables. Under demographic parity and are independent, hence their mutual information is zero. That is, the conditional entropy is equal to .

: The covariance between the target and sensitive features is zero. Under demographic parity and are independent. As a result, the covariance is equal to zero.
A disparity (or unfairness) measure can be defined using any of the above quantities. Table 1 summarizes some of the ways the disparity can be measured. As stated in the first row of the table, mutual information and covariance (or correlation) provide two natural measures. Another way of quantifying the disparity is by subtracting the probabilities (Row 2 of Table 1) or the ratios between probabilities (Row 3 of Table 1). Consistent with Row 2, we defined the ratiobased measures such that zero is the maximum fairness and the measure is in the range [0,1].
Finally, we would like to reiterate that we consider the societal norms, which are not always quite aligned with statistical measures. Due to the societal discrimination against some minority groups, social data is usually “biased” Olteanu et al. (2019). Hence, actions known as reverse discrimination (such as affirmative action) are taken to increase the presence of underrepresented groups in the outcomes. Such fairness guidance is usually provided by law. That can be viewed as a higher acceptance probability for certain protected groups of sensitive attributes. In this paper, we do not limit ourselves to any of the (demographic disparity) fairness measures and give the user the freedom to provide a customized measure. In other words, we are agnostic to the choice of fairness measure. It is worth mentioning that although we used a single binary sensitive attribute for the explanations and measures, a measure can be defined over multiple nonbinary sensitive attributes with overlapping protected groups. Generalizing our notion of fairness to any measure based on demographic disparity, in the rest of the paper, we use the notation to refer to the (userprovided) fairness measure. We simplify the notation to when is clear by context.
3 Fair Active Learning
Smartly selecting samples to label, AL has the potential to mitigate algorithmic bias by incorporating the fairness measure into its sampling process. Still, not considering fairness while building models can result in model unfairness. As a naïve resolution, one could decide to drop sensitive attributes from the training data. This, however, is not enough as the bias in the features can cause model unfairness Salimi et al. (2019). For example, consider a linear regression model in the form of . Let the covariance between the model outcome and a sensitive attribute be the measure of fairness. Theorem 1 shows that only depends on and . In other words, the underlying covariance can cause model unfairness.
Theorem 1.
For a linear classifier in form of , .
Theorem 1 shows that dropping sensitive attributes is not enough for achieving fairness. An immediate question which might come to mind is that will any of the existing AL strategies generate fair models. The answer is: not necessarily. We show this in Theorem 2.
Theorem 2.
An active learning method with any sampling strategy that does not consider fairness may generate unfair models.
Following Theorem 2, AL strategies that do not consider fairness may generate unfair models. On the other hand, according to Theorem 1 and the existing literature Salimi et al. (2019); Buolamwini and Gebru (2018); Zou and Schiebinger (2018); Manrai et al. (2016), bias in labeled training data is the reason for model unfairness. In other words, the samples selected for labeling in an active learning framework can significantly impact the fairness of a trained model. Hence, a smart sampling strategy that mitigates bias in labeled data can resolve unfairness.
Yet, optimizing for fairness, the model may lose its purpose for accuracy while obtaining high performance is indeed the main objective in any ML framework, including active learning. For instance, in Example 1, consider a model that randomly (with equal probabilities) classifies individuals as highrisk. This model indeed satisfies demographic parity since the probability of the outcome is (random and therefore) independent of . However, such a model provides zero information about how risky an individual is.
To balance the fairness and accuracy tradeoff, we consider fairness as part of the AL sampling strategy in order to develop fair classifiers for applications with limited labeled data, similar to Example 1 and Example 2. The goal is to minimize the misclassification error as well as unfairness (c.f. § 2.3). Similar to standard AL, FAL is an iterative process that selects a sample from the unlabeled pool to be added to the labeled pool . Different from AL, however, FAL considers both fairness and misclassification error as the optimization objective for the sampling step. That is, to choose the next sample to be labeled, FAL selects the one that contributes the most to the reduction of the misclassification error as well as model unfairness. More Specifically, for a sample point , we consider the Shannon entropy measure for misclassification error, while considering demographic disparity for unfairness — is the classifier trained on at iteration , after labeling the point and is the entropy of the based on the current model . One way of formulating the optimization problem for sampling is as following:
(3) 
where denotes the restriction imposed by some regulations for fairness consideration. Similarly, one could consider misclassification error as a hard constraint while optimizing for fairness. Both of these models can be reformulated as unconstrained optimizations using Lagrange multipliers Rockafellar (1993). Another alternative is to add fairness to the optimization as a regularization term. The formulation can also be viewed as a multiobjective optimization for fairness and misclassification error. Equation 4 is consistent with all of these views and is therefore considered in our framework.
(4) 
where the coefficient is the userprovided parameter that determines the tradeoff between the model fairness and model performance. Values closer to put greater emphasize on model performance, while smaller values of put greater importance on fairness. Our experimental results verify fairness improves substantially through FAL optimization while maintaining the accuracy level. As we elaborate in § 5, entropy and fairness values are standardized to the same scale before combining them in Equation 4.
Having discussed the optimization function, next we will provide the details of our FAL framework.
3.1 Framework
At a high level, FAL is an iterative approach similar to standard active learning approaches. As shown in Figure 1, the central component of FAL is the sample selection unit (SSU) that chooses an unlabeled point from and asks the labeling oracle to provide its label. The labeled point are moved to , the set of labeled points. The set of labeled points are used to train : the classifier at iteration . In the next iteration, , SSU employs and selects the next point to be labeled. This process continues until the budget for labeling is exhausted.
The sample selection unit is in charge of selecting the next point to be labeled. SSU uses Equation 4 to balance the tradeoff between fairness and misclassification error for the next sample selection. A problem, however, is that at the time of evaluating the candidate points, we still do not know their labels as those belong to . In contrary, to evaluate the impact of each of the points on the model fairness, we need to know what the model parameters will be after adding the point to . This requires knowing all labels beforehand which contradicts with the fact the is unlabeled.
To resolve this issue, using a decision theoretic approach Settles (2009), we consider the Expected Unfairness Reduction: selecting the point that is expected to impart the largest reduction to the current model unfairness, after acquiring its label. That is to say, we use Equation 5 to pick a sample. In this way we are approximating the expected future fairness of a model using over all possible labels under the current model. In other words, SSU should select the sample point , which if labeled and added to would result in a new model with reduced unfairness.
Let be the unfairness of the current model.
Consider a point .
Let be the new unfairness measure after adding to if the true label is .
Of course, SSU does not know the label in advance. Hence, it must
instead calculate the unfairness as an expectation over the possible labels
(5) 
Equation 6 denotes the expected unfairness computation used by SSU (as shown in Figure 2):
(6) 
where is the model trained using .
Following Figure 2, for every point in the unlabeled pool, SSU considers different values of as possible labels for . For every possible label , it updates the model parameters to the intermediate model using .
We note that the set of labeled points has a different distribution from the underlying data distribution. That is because the labeled points are carefully selected from and hence are not unbiased samples from the underlying data distribution. As a result, even though the model is trained using these data points, cannot be used for evaluating the fairness of the model. On the other hand, the points in the unlabeled pool are expected to be drawn according to the underlying distribution. Therefore, to create a dataset for evaluating the fairness of a model, we select a random subset of and move it to a verification set . The verification set is created once and is used in different FAL iterations.
Following the standard AL, at every iteration, for every possible outcome for a point , SSU uses the current model for calculating .
Having the fairness measures and the probabilities for each possible outcome, the expected unfairness is computed by aggregating for different values of (Equation 6). After computing the expected unfairness for each data point in , SSU identifies the one that optimizes Equation 5 and passes it to the labeling oracle. Algorithm 2 shows the pseudocode of FAL. It uses the function of Algorithm 3 for computing the expected unfairness.
4 Extension to Other Fairness Models
So far in this paper, we considered independence () for fairness. Here we discuss how to extended our findings to other measures based on separation and sufficiency Barocas et al. (2019), such as predictive parity, error rate balance, and accuracy equity Narayanan (2018).
FAL follows balancing fairness and misclassification error, using Equation 5. Certainly, the entropy term does not depend on the choice of fairness measure. Also, the abstract fairness term is not limited to a specific definition. However, despite being abstract, computing the expected unfairness (based on separation or sufficiency) is challenging.
Looking at Figure 2, recall that we use the verification set for estimating the fairness of a model. As an unbiased sample set from , follows the underlying data distribution and, hence, can be used for the demographic disparity. However, this set cannot be used for estimating fairness according to separation or sufficiency since its instances are not labeled. On the other hand, the pool of labeled data is not representative of the underlying data distribution.
In order to extend our results for other fairness measures, it is enough to label . Once is labeled, it is easy to see that our framework performs asis for any such fairness measure. We understand that since the labeling budget is limited, labeling may reduce the number of instances we can use for training the model. One resolution is to limit to a small set and accept the potential error in estimations. How small can be to still provide accurateenough estimations, besides other resolutions, are interesting questions that we will consider for future work.
5 Experiments
The experiments were performed on a Linux machine with a Core I9 CPU and 128GB memory. The algorithms were implemented using Python 3.7.
5.1 Datasets
COMPAS
5.2 Algorithms Evaluated
We evaluate the performance of the following approaches on the benchmark datasets in § 5. We apply the standard logistic regression as the classifier in all of the cases.
Fair Active Learning (FAL). Algorithm 2, as described in § 3 is our proposal in this paper. As an implementation note, we are paying attention to the fact that the two components of the optimization objective function, entropy, and expected unfairness reduction are on different scales. Consequently, we need to standardize the measures to the same magnitude in order to be able to combine them. For the points in , let , , , and be the minimum entropy, maximum entropy, minimum expected unfairness reduction, and maximum expected unfairness reduction, respectively. To ensure that the measures are in the same scale and the tradeoff between two components is consistent, we standardize entropy and expected unfairness reduction as in Equations 7 and 8, correspondingly.
(7) 
(8) 
Consequently, Equation 5 can be rewritten as:
(9) 
Active Learning (AL). In AL, Algorithm 1, we choose the sample selection based on minimizing the missclassification error through uncertainty sampling. To do so, we calculate the entropy of each unlabeled instances in and choose the point with maximum entropy to label next.
Random Labeling (RL). As mentioned briefly in § 1, a baseline approach for the limited labeling context is to randomly label a subset of points in . In RL, we ask the labeling oracle to provide the label of random samples and use them to train the classifier.
5.3 Performance Evaluation
We evaluate the performance of FAL, AL, and RL, with different demographic disparity functions defined in Table 1. We labeled the Fairness measures as , which is consistent with the corresponding cell that each measure is located in Table 1. For instance, refers to Mutual Information located in cell [1,1] (first row and first column) of Table 1. We study the tradeoff between the accuracy and fairness, by changing the coefficient in Equation 5 while considering different Fairness metrics in Table 1. For each scenario, we ran the experiments on 10 different random splits of data and considered the accuracy, Precision/Recall, and the corresponding demographic function used in the optimization step, as evaluation measures.
For COMPAS dataset, we perform the experiments using 10 random splits of the dataset into training ( of the examples), verification ( of the examples), and testing ( of the examples). We study the values of for , plus AL and RL. We consider the mean and variance over the 10 random splits. We specify the maximum labeling budget to 400, where the performance leveled off in our preliminary results. In each FAL and AL scenario, we start with six labeled points and sequentially select points to label, until the 400 budget is exhausted.
Summary of results:
Figures 6–10 provide the results of the evaluation for each method. Each pair of plots corresponds to a measure of fairness in Table 1. Due to the space limitation, we show the results for four of the measures listed in Table 1
Figures 6 and 6 corresponds to employing Mutual Information, , in optimization step. We note that adding the fairness measure to the optimization for candidate selection does not significantly impact the overall accuracy of the model across different values, Figure 6. Compared to AL also, the accuracy does not drop dramatically. As we observe, the demographic disparity of the model though, dropped by almost on average compared to AL and RL. Figure 6 indicates that AL and RL have fairly lower precision and recall. Precision and recall are better evaluation measure for unbalanced data classification, thereby, FAL outperforms AL and RL in predicting the right class.
Moving to second fairness measure, Figures 6 and 6 shows the results using , the covariance metric, as fairness metric in optimization. We note that the accuracy of the model across different scenarios has a negligible difference. The covariance metric of FAL on average is lower than AL and RL.
6 Related work
Algorithmic Fariness. Algorithmic fairness has been extensively studied in recent years. Barocas et al. (2017); Žliobaitė (2017); Romei and Ruggieri (2014); Mehrabi et al. (2019) provide surveys on discrimination and fairness in algorithmic decision making and machine learning.
Existing works have formulated fairness in classification as a constrained optimization Zafar et al. (2017, 2015); Menon and Williamson (2018); CorbettDavies et al. (2017); Celis et al. (2019); Hardt et al. (2016); Huang and Vishnoi (2019). A body of work focus on modifying the classifier, inprocess, to build a fair classifiers Fish et al. (2016); Goh et al. (2016); Dwork et al. (2012); Komiyama et al. (2018); CorbettDavies et al. (2017). Some others remove disparate impact through preprocessing the training data Luong et al. (2011); Zemel et al. (2013); Kamiran and Calders (2010, 2012); Feldman et al. (2015); Krasanakis et al. (2018); Sun et al. (2019); Asudeh et al. (2019b); Salimi et al. (2019), while the last group postprocess model outcomes to develop fairness Kim et al. (2018); Hardt et al. (2016); Pleiss et al. (2017); HébertJohnson et al. (2017). Fairness has also been studied in special ML context such as reinforcement learning Jabbari et al. (2017), adversarial networks Wadsworth et al. (2018); Xu et al. (2018), and feature acquisition NoriegaCampero et al. (2019). Fairness in datadriven decision making has also been studied in related topics, such as ranking Asudeh et al. (2019a); Guan et al. (2019); Yang et al. (2018); Zehlike et al. (2017) and recommendation systems Burke (2017); Tsintzou et al. (2018); Yao and Huang (2017).
Active Learning. Different active learning scenarios (Membership Query Synthesis, StreamBased Selective Sampling, poolBased Active Learning) and sampling strategies (Uncertainty Sampling, QueryByCommittee, Expected Model Change, Variance Reduction, etc.) are surveyed in Settles (2009). Active Learning has been widely used in different applications for training a wide range of classifires, where the labeling process for these datasets is laborintensive and costly. The examples are image and speech recognition Hoi et al. (2006); Joshi et al. (2009); Minakawa et al. (2013); Yu et al. (2010); Riccardi and HakkaniTur (2005), information retrieval Tian and Lease (2011), text analysisTong and Koller (2001); Cormack and Grossman (2016); Hu et al. (2016); Davy and Luz (2007), recommender systems Sun et al. (2013); Resnick and Varian (1997); Houlsby et al. (2014).
7 Conclusion
In this paper, we introduced fairness in active learning. Our framework computes the expected unfairness reduction for each unlabeled sample point and selects the one that maximizes a linear combination of misclassification error and expected unfairness reduction. We carried out experiments with different fairness measures across different weights. The results confirmed that our proposed FAL frameworks work properly in terms of building a fair model without majorly affecting its performance. The comparison with the standard active learning shows an improvement in the fairness quality of the constructed classifier by about .
APPENDIX
Appendix A Proofs
Theorem 1: For a linear classifier in form of , .
Proof.
(10) 
∎
Theorem 2: An active learning method with any sampling strategy that does not consider fairness may generate unfair models.
Proof.
We provide the proof by construction. In the following, we construct a case where between a pair of points, the one that worsens the fairness is preferred to be labeled. Consider a toy 2D setting where are the features used for training a linear classifier . Let color be the binary sensitive attribute with values blue and red. Assume the underlying distribution for the red points is uniform in range for and (the two features are independent for the red points). Now consider an active learning method (AL) that has labeled a set of points , so far. AL can use any arbitrary sampling strategy that is specified by a function , which should get maximized, i.e., the points with higher scores are preferred. Suppose using the labeled points , the current weights of the classifier are and and the decision boundary is at . That is, as shown in Figure 11 with the black solid line, for a point , iff .
Now consider the two points and specified in the figure. Note that AL chooses between and purely based on and . That is, it prefers for choosing between these two points. Suppose is the point that maximizes and, hence, is preferred to be labeled next (the following argument can be easily adjusted if is preferred). Suppose and . Therefore, after labeling and adding it to , the decision boundary gets updated to (the dashed line in Figure 11). Suppose the dotted line would be the decision boundary if had been selected.
First, assuming that all lines , , and divide the space by half, while considering the uniform distribution of red points in the space, for all three decision boundaries colorred.
Next, let the underlying distribution of blue points
Appendix B Additional Experiment Results
Figures 15–15 provide the results of the evaluation for and , as presented in Table 1. We note a very small change in the accuracy score across different values of . Figures 15 and 15 demonstrate that, in both cases, FAL significantly improves the . The results indicate that compared to FAL, AL and RL have lower precison and recall.
Footnotes
 In the US, such information is provided by sheriff offices of the counties. For instance, for the COMPAS dataset, ProPublica used information obtained from the Sheriff Office of the Broward County. https://bit.ly/36CTc2F
 In the rest of the paper we refer to true label as label.
 In addition to the measures in Table 1, one could use correlation , or as in Agarwal et al. (2018) for measuring disparity.
 Proofs are provided in the Appendix.
 Note that since is equal for all points, the second term in Equation 5 maximizes the expected unfairness reduction.
 ProPublica, https://bit.ly/35pzGFj
 We refer to the appendix for more results.
 Note that since AL does not consider demographic distributions for choosing the points, we have the freedom to pick the demographic distributions as we wish.
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