The problem of fairness in AI can be tackled by minimising bias in the data (pre-processing), in the algorithms (in-processing), or in the results (post-processing). In the particular case of in-processing applied to supervised machine learning, state-of-the-art solutions rely on a few well-known fairness metrics - e.g., demographic parity, disparate impact, or equalised odds - optimised during training-which, however, mostly focus on binary attributes and their efects on binary classification problems. Accordingly, in this work we propose FaUCI as a general purpose framework for injecting fairness constraints into neural networks (or, any model trained via stochastic gradient descent), supporting attributes of many sorts-there including binary, discrete, or continuous features. To evaluate its efectiveness and eficiency, we test FaUCI against several sorts of features and fairness metrics. Furthermore, we compare FaUCI with state-of-the-art solutions for in-processing, demonstrating its superiority.
Nowadays, fairness has become a crucial issue in the development of AI systems, especially in the
context of ML [
One prerequisite for fairness enforcement in AI systems is measuring bias. In the literature, several metrics have been proposed to measure the degree of fairness of a predictive model.
Broadly speaking, these metrics score the extent to which a model treats diferent groups of individuals fairly and without prejudice. Technically speaking, they do so by relating sensitive attributes (e.g. gender, ethnicity, etc.) – and, in particular, their some protected values of their (e.g. female, black, etc.) – to some target variable of choice for the application at hand (e.g. loan approval, job hiring, etc.).
Once fairness metrics are defined, focus can be shifted to enforcing fairness in predictive models. Among the many techniques proposed in the literature, the so-called in-processing ones attempt to enforce fairness at the model level during training—as opposed to pre- or post-processing techniques, which operate before or after training, respectively.
Focussing on in-processing techniques, we acknowledge that state-of-the-art methods essentially rely on regularisation techniques to enforce fairness optimisation during training. In other words, these methods address ML models based on some loss-function minimization: the loss function is augmented with a fairness-related term – most commonly, derived from a fairness metric from the literature – to be minimised during training. While the approach is indeed efective, it is also limited by the fact that the fairness metrics used are mostly tailored to binary attributes and binary classification problems. This limitation may hinder the applicability of these methods to real-world datasets, where sensitive attributes may be of diferent sorts—e.g., categorical or continuous. Another practical issue characterising state-of-the-art methods is their reliance on several hyper-parameters, making them dificult to tune and use in practice.
To mitigate such issues, in this work, we propose FaUCI, a general-purpose method for enforcing Fairness Under Constraints Injection into any model trained via stochastic gradient descent (SGD). FaUCI advances the state-of-the-art of in-process fairness by letting users enforce the optimisation of diferent fairness metrics, over sensitive attributes of diferent sorts—namely, binary, categorical, and continuous. To let our method deal with non-binary sensitive attributes, we propose novel variants of the aforementioned fairness metrics, and we design FaUCI to support pluggability of these metrics. In other words, we let users choose the most adequate fairness metrics for their use case, while FaUCI takes care of the rest. Finally, to keep our method exploitable in practice, we design it to rely on a minimal set of hyper-parameters. In fact, apart from the fairness metric of choice, FaUCI users are only required to specify the batch size of the underlying training algorithm.
Despite its simplicity, it turns out that our method overcomes other similar state-of-the-art solutions in optimising fairness while retaining predictive accuracy. To verify this claim, we evaluate FaUCI on a real-world dataset and compare it with state-of-the-art methods. Experimental setup and results are presented in Section 4.
Accordingly, the paper is structured as follows: Section 2 provides background on fairness metrics and related works. Section 3 introduces variants of fairness metrics and our method, FaUCI, for enforcing fairness in ML models. The novelty of the approach is discussed. Section 4 presents results applying FaUCI to a real-world dataset, comparing with state-of-the-art methods. Section 5 concludes and discusses future work.
In the literature, several metrics have been proposed to measure the degree of fairness of a predictive
model. These metrics can be classified into two main categories: group vs. individual fairness [
Once fairness metrics are defined, the focus can be shifted to enforcing fairness in predictive models.
There are three main approaches to this problem: pre-, in-, and post-processing. Pre-processing techniques
aim at removing bias from the training data [
In the remainder of this section, we provide a brief overview of the most common fairness metrics from the literature, as well as most recent in-processing algorithms relying upon them.
In AI, a fairness metric is a formula used to quantitatively measure the level of fairness or bias in the outcomes generated by AI algorithms. These metrics play a crucial role in evaluating whether the AI system treats various groups of individuals fairly and without prejudice. Fairness metrics encompass diverse formulae, each specifically designed to target particular aspects of fairness.
In this study, we focus on three well-known and extensively used metrics from the literature, which
guide our experiments. Additionally, in Section 3.1 we provide considerations and reformulations for
each metric aimed at ensuring a consistent comparison with other state-of-the-art techniques.
Demographic Parity (DP) DP – also known as “statistical parity” – is a metric that measures
whether the prediction of an ML model is independent w.r.t. a given protected attribute, i.e., values of
the sensitive feature do not afect the output of the model [
DP ℎ,() = ∑︁ ‖E[ℎ() | =] − E[ℎ()]‖
∈ where is a random variable ranging over the test data, is the random variable ranging over the admissible values of the sensitive attributes – in turn, denoted by –, E is the expected value function, and ‖ · ‖ denotes the absolute value operator. A model ℎ satisfies DP if its value is below an arbitrarily small bias threshold (a common value is 0.01).
DP can be useful in real applications like loan approval/denial. If a specific demographic group has
been disproportionately denied loans in the past, DP can be used to ensure that approval rates are
similar across diferent groups, helping to mitigate discrimination.
(1)
(2)
(3)
Disparate Impact (DI) DI measures how much a classifier disproportionally afects people given a
sensitive attribute [
E[ℎ() | =1]
E[ℎ() | =0]
However, this would make admissible values of DI unbound in value—which is undesirable for a scoring
function. Hence, to guarantee that DI values are always in [
DI ℎ,() = (di ℎ,()) Values of DI above 0.8 are commonly considered acceptable. In other words, values close to 0 imply high fairness violation, viceversa for values close to 1. For this reason, whenever requiring positive scores (i.e., scores where greater values are preferable), we may report the value 1 − DI (e.g., computing the loss function during the training of a neural network).
DI as well may be useful in real-life applications such as loans. It enables the identification of any
disproportionate denial rates that may have adversely afected specific demographic groups, historically.
Equalised Odds (EO) EO is a fairness metric scoring the extent to which a classifier equally predicts
a given class for all values of a sensitive attribute [
(,) where refers to the ground truth, the sum is aggregating all possible pairs (, ) s.t. ∈ and ∈ , and eo is a shortcut defined as follows: eoℎ,(, , ) = ‖E[ℎ() | =, =] − E[ℎ() | =]‖ (4) Similarly to DP, a classifier is considered fair w.r.t. a given sensitive attribute value and output value if its EO value is below an arbitrarily small bias threshold .
In real life contexts such as loan approvals, EO enables the identification of disparities in approval rates that may have disproportionately favored specific demographic groups.
Most recent state-of-the-art works for optimising fairness over neural classifiers 1 vary from one another
in terms of (i) the type of sensitive attributes they support (among binary, discrete, or continuous) and
for (ii) the fairness metrics they optimise [
The first method – FNNC [
The second work – Cho [
The third method – Wagner [
Finally, the fourth method – Jiang [
Other notable works for the fairness optimisation of ML models are the ones by Kamishima et al. [2012] and Berk et al. [2017]. The former proposes a regularisation method for probabilistic discriminative models, but it is tailored to the metrics the authors defined in that same work (i.e., prejudice index and underestimation index) that are not as common as other fairness metrics. The latter proposes a regularisation method for regression tasks.
Here we introduce variants of the previously mentioned fairness metrics, extending those definitions to support categorical and continuous data. Then, we present our method for fairness enforcement, and we discuss how it difers from the related works. Finally, we provide an in-depth analysis of the functioning and the computational cost of our method.
Here we propose weighted and generalised variants of the fairness metrics presented in Section 2.1, to support categorical and continuous attributes, respectively. Broadly speaking, such variants generalise fairness metrics beyond binary data. This may help in measuring fairness in real-world datasets. For instance, these may be useful to measure / mitigate bias by taking into account the frequencies of sensitive attributes’ values. In the loan approval example, one may e.g. prioritise fairness for most underrepresented ethnicity groups—provided that more than 2 groups exist.
=] and E[ℎ()] from Equation (1) are both in the range of [
A metric whose upper bound is not fixed is undesirable since it prevents comparisons among DP values on diferent datasets, or even on diferent samples of the same dataset—which may lack some values for sensitive features. To avoid this issue, we propose two variants of DP, namely weighted (WDP) and generalised demographic parity (GDP), supporting the discrete and continuous cases, respectively. We define WDP as the weighted mean of the absolute value of the diference between the two distributions:
WDP ℎ,() = ∑︁
‖E[ℎ() | =] − E[ℎ()]‖ · ∈ where is the weight of the -th value of the sensitive attribute . The sum of the weights must be equal to 1. In this way, we can compare WDP values across diferent datasets since the upper bound is always 1. The values of the weights can be chosen according to the distribution of the sensitive attribute in the dataset, or they can be set to the same value (i.e., every value of the sensitive attribute is equally important). Doing so prevents the metric from being biased towards the most frequent values of the sensitive attribute. For instance, if we use the frequency of the values of the sensitive attribute as weights, the metric will be biased towards the most frequent values of the sensitive attribute. This could be undesirable when the dataset is unbalanced.
The definition of the GDP has been already introduced in a recent work [
GDP ′ℎ,() =
(‖E[ℎ() | =] − E[ℎ()]‖ · P[=]) · where = min{} (resp. = max{}) is the minimum (resp. maximum) admissible value of and P[=] is the probability density function of . However, this definition of GDP could be blind to unbalanced distributions of the sensitive attribute due to the frequency weighting. So, we propose a variation of GDP where the weights can be chosen by the user: (5) (6) (7) (8) (9) ∫︁ ∫︁
Finally, we provide a continuous definition for disparate impact ( GDI), similarly to 6: ∈ WDI ℎ,() = ∑︁ (︂ E [ℎ() | =] )︂
E [ℎ() | ̸=] · GDI ℎ,() = ∫︁ (︂ E [ℎ() | =] )︂
E [ℎ() | ̸=] · · where , have the same meaning of eq. (6).
GDP ℎ,() =
(‖E[ℎ() | =] − E[ℎ()]‖ · ) · when = P[=], Equation (7) is equivalent to Equation (6). Similarly, in WDP, the integral of the weights must be equal to 1. (WDI) function as follows: Weighted and Generalised Disparate Impact The definition of DI can be straightforwardly extended to categorical sensitive attributes. It is worth noticing that DI for categorical sensitive features can be written with diferent aggregation functions. Here we use the weighted sum of all admissible values of (this is not the only admissible choice: e.g., the minimum function is a valid alternative). In this way, we average over all admissible values of the sensitive attributes, similarly to Equation (5). Notably, when computing the conditional probability w.r.t. some admissible value of the sensitive feature , there are now two relevant cases: = and ̸= . Accordingly, we define the weighted DI Weighted and Generalised Equalised Odds Despite Equation (3) already handling both binary and categorical data for the protected feature, the metric sufers the lack of limits in the resulting value. To overcome this issue, and to be uniform with the other metrics as well, we define the weighted version of EO (WEO) as follows:
× WEO ℎ,() = ∑︁ eoℎ,(, , ) · (,) (10) There, eo is defined as in eq. (3).
Following the same generalisation approach used for DP, we extend EO defining the generalised equalised odds (GEO) for a binary classification task:
GEO ℎ,() =
∫︁
(eoℎ,(, , 0) + eoℎ,(, , 1)) · ·
(11)
3.2. FaUCI
Our method targets all ML models that are trained with stochastic gradient descent (SGD)—and, in
particular, neural networks (NN). Similarly to other fairness algorithms, the main idea consists of
introducing a specific cost factor in the loss function of the model. The cost factor depends on the
specific fairness metric to be minimised. More precisely, the fairness metrics are the ones presented
in Section 2.1—WDP and GDP, WDI and GDI, WEO and GEO for categorical and continuous versions
of DP, DI, and EO, respectively. Unlike other methods, FaUCI (i) requires that the fairness metric to
optimise is bounded in the range [
In particular, FaUCI prescribes the adaption of a loss function matching the following pattern: ℒℎ,(, ) = (ℎ(), ) + ℎ,(, ) (12) where is the function scoring the error of the model, ℎ, is an additive regularisation component aimed at scoring fairness w.r.t. – and, potentially, also –, and ∈ R>0 is a hyperparameter that weights the regularisation term. The particular choice of depends on the learning task at hand. So, for instance, classification tasks may rely on accuracy or cross-entropy. Similarly, may be chosen among the fairness metrics presented in Section 2.1.
In practice, one key aspect of applying eq. (12) is w.r.t. to which input data () the fairness metric (ℎ,) is computed. Ideally, the bigger the dataset, the better. However, as a loss function aimed at steering the SGD process, ℒℎ, must be computed several times along the many epochs of a model’s training. The amount of data upon which the loss function is computed is called batch size, and it is commonly a hyperparameter of any implementation of SGD. So, the batch size is controlling the goodness of the fairness estimation provided by ℎ,, for the current epoch. This implies FaUCI is essentially subject to an implicit trade-of: the greater the batch size, the more accurate the fairness metric will be, at the price of a slower learning process.
About novelty. FaUCI difers from other related works in many aspects. First, it supports sensitive attributes of any kind – i.e., binary, categorical, and continuous –, and it is agnostic w.r.t. the fairness metric of choice—e.g., DP, DI and EO. The resulting loss function (ℒℎ,) can be exploited in binary classification problems.
Second, FaUCI relies on a straightforward estimation of the probabilities that appear in the fairness metrics during training. Given a batch of size , it is reasonable to consider the probabilities computed on the batch similar to the ones computed on the entire dataset if is suficiently large. This approximation does not hold if is not high enough, i.e., if the distributions in the batch difer from the distributions in the whole dataset with statistical significance. Other approaches, e.g. the ones based on kernel density estimation (KDE) such as Cho, require the fine-tuning of additional hyper-parameters to estimate the probabilities—and therefore to compute fairness metrics. By avoiding KDE, FaUCI does not require ifne-tuning additional hyperparameters, other than in Equation (12).
Third, because in Section 3.1 we introduced the weighted versions of the fairness metrics, FaUCI does not sufer from unbalanced distributions of the sensitive attribute. Indeed, despite being a relatively small change, the weighted versions of the fairness metrics are paramount to avoid biases towards the most frequent values of the sensitive attribute. Unbalanced datasets are common in real-world applications, and the weighted fairness metrics are a key feature to ensure fairness in such scenarios. Using the non-weighted versions of the fairness metrics could lead to misleading values that suggest absence of bias when it is not the case.
Finally, FaUCI is general enough to be easily extendible with fairness metrics of other sorts. Moreover, one intriguing possibility is to use FaUCI to achieve intersectional fairness [16]. We will discuss this in Section 3.4.
During the training of a NN the training set is organised into batches. For each epoch of the training, all batches are used exactly one time to perform one step of inference (propagation) and one step of gradient descent (backpropagation). Between the two steps, the loss function is computed. Here we report the algorithms for computing the fairness cost factor for WDP, WDI and WEO metrics (continuous variants are omitted as algorithms are identical). For the sake of simplicity, we choose as weights the frequencies of the values of the sensitive attribute (note that this choice does not change the overall computational cost).
Algorithm 1 Weighted demographic parity (returns ) Require: ℎ Require: Require: ℎ 1: ← 0 2: ← E[ℎ(ℎ)] 3: for all in do 4: _ ← E[ℎ(ℎ) | =] 5: _ ← P[=] 6: ← + (‖ − _‖ * _) the predictive model
sensitive attribute a batch of the dataset
Algorithm 1 describes the steps needed for computing the WDP metric within a single batch. The computational cost for computing the estimated probability in line 2 is (), where is the batch size. Similarly, () is the cost for computing the values at lines 4 and 5, while line 6 has a constant cost (we treat the operation of computing the output value of the model as having a constant cost). These steps are repeated for every admissible value of . Accordingly, the resulting computational cost of the algorithm is () + 2( ) + ( ) = ( ), where is the number of diferent values of . Algorithm 2 Weighted disparity impact (returns ) Require: ℎ, , ℎ like in Algorithm 1 1: ← 0 2: for all in do 3: _ ← E[ℎ(ℎ) | =] 4: __ ← E[ℎ(ℎ) | ̸=] 5: _ ← P[=] 6: ← + (min{ ___ , ___ } * _)
Algorithm 2 elicits the steps for computing WDI. Values at lines 3, 4 and 5 have computational cost (), whereas line 6 has a constant cost and each of them is repeated times. Overall, the resulting cost of the algorithm is 3( ) + ( ) = ( ).
Algorithm 3 Weighted equalised odds (returns ) Require: ℎ, , ℎ like in Algorithm 1, 1: ← 0 2: __ ← E[ℎ(ℎ) | =] 3: for all in do 4: ___ ← E[ℎ(ℎ) | =, =] 5: _ ← P[=] 6: _ ← ‖ ___ − __‖ 7: ← + ((_0 + _1) * _) : ground truth ∀ ∈ {0, 1} ∀ ∈ {0, 1} ∀ ∈ {0, 1}
Finally, Algorithm 3 shows the steps for WEO metric. As Equation (10) is designed for binary classification tasks, there is no need to iterate over an undefined number of admissible classes; rather, only two classes need to be considered. This simplifies the formulation of the algorithm and lowers the resulting computational cost. Values computed at lines 2 and 3 cost (). Inside the loop, the computational cost of the values from lines 5-7 is also (), for values from lines 8-10 is (1). So, the resulting cost of the algorithm is 2() + 3( ) + 3( ) = ( ).
All three algorithms have a computational cost that is linear both in the batch size () and in the number of possible values of ( ). Their continuous variants have similar steps. The main diference is that instead of working with equalities and inequalities w.r.t. the values of , we work with integrals. The implementation used for the experiments is histogram-based, i.e., several non-overlapping intervals of the same width. Then, the resulting computational cost depends on the number of intervals instead of the number of possible values of .
We extend FaUCI to support the optimisation of fairness in an intersectional setting, i.e., when the intersections of groups of protected attributes are considered (a.k.a., subgroups). FaUCI can support the optimisation of fairness metrics involving multiple protected attributes in two ways.
The first one consists in creating, before computing the loss cost, a dummy protected attribute by combining the original ones that the user wants to consider (i.e., computation of the subgroups). In this scenario, FaUCI can be used as-is (see Equation (12)) to optimise the fairness of the intersection of the original protected attributes. It is worth noticing that using the combination of multiple attributes could easily become intractable due to the computational cost of the underlying fairness metric (see Section 3.3). For this reason, we propose an alternative approach.
The second method consists in combining multiple loss factors, each one penalising the violation of the fairness of a single protected attribute.
ℒℎ,¯(, ) = (ℎ(), ) + 1ℎ,1 () + · · · + ℎ, () where ¯ is a set of protected attributes 1, . . . , . In this way, multiple fairness metrics can be simultaneously optimised for the same sensitive feature by keeping the computational cost of the fairness metric tractable (i.e., the cost of computing the fairness metric is linear in the number of protected attributes and not exponential). This approach is a trade-of between the computational cost and the complexity of the fairness metric. Further details and empirical results about FaUCI in the context of intersectional fairness will be presented in another work.
We validate FaUCI on a well-known and widely-used real-world dataset for fairness algorithms: the
UCI Adult dataset [17]. The dataset is already divided into two sets – training and test – with 32, 561
and 16, 281 records respectively. There are 14 independent features of diferent types (i.e., boolean,
categorical and continuous) and one dependent variable. Each record represents one individual and the
task consists of classifying whether the individual earns more than 50, 000 USD per year or less/equal
to that amount. Adult is a standard de facto in the fairness community, mostly because it inherits the
biases of the real world. Despite its limitations [18], it is still a valid benchmark for our purposes.
4.1. Setup
We endeavor to maintain a consistent setup with other works [
The model that we train is a feed-forward fully connected NN with 2 hidden layers of 100 and 50 neurons respectively. The number of epochs is up to 5, 000 and the batch size is set to 500. We include two early stop conditions: the first one happens when both accuracy and the fairness metric reach a predefined target, while the second is triggered if there is no improvement for a specified amount of epochs (patience). In detail, we set the target accuracy to 0.9, and the thresholds for the fairness metrics to 0.01, 0.99, 0.01 for DP, DI, and EO respectively (we remind that the final value of DI metrics is expressed as 1 − to be compliant to the definition from the literature). The patience for the second condition is 100. These two conditions are evaluated at the end of each epoch on the validation fold. We additionally include in the experiments the evaluation of the NN without any fairness constraint, denoted as the “vanilla model”, serving as our baseline.
We conduct experiments with our method using WDP, GDP, WDI, GDI, WEO and GEO fairness metrics on three diferent sensitive attributes: sex (binary), ethnicity (categorical) and age (continuous). We decide to assign for the W* metrics the same weight to each value of the protected attribute, i.e., = 1 for all ∈ where is the number of unique values of . This choice is motivated by the fact that we want to give the same importance to each group of since the attributes we want to protect are unbalanced (i.e., sex and ethnicity). Instead, for the G* metrics we use the density of the continuous attribute (i.e., age) as weight since it is far less unbalanced than the other two attributes. We want to underline that the user can choose arbitrary weights as long as they fulfill the properties in Section 3.1.
We are also able to fully reproduce and reuse the code of two state-of-the-art methods—Cho, Jiang. Unfortunately, we are unable to replicate the same procedure for the other two approaches—FNNC, Wagner. However, due to the similarity of their original setups with ours, we still report their results for discussion purposes.
FaUCI shares with Cho and Jiang one hyper-parameter – lambda ( ) – that weights the contribution of the fairness metric. All experiments are conducted by varying the value of . The other hyperparameters of Cho and Jiang are the same used in their papers. The source code of the experiments is available at https://anonymous.4open.science/r/FaUCI-aequitas-2024.
Figure 1 shows the accuracy-demographic parity trade-of between FaUCI, Cho and Jiang methods (also FNNC and Wagner when using “sex” as sensitive attribute). Figure 1a reports the experiments using “sex” as a binary protected feature. FaUCI and Jiang have similar behaviour, while Cho is worse. FNNC and Wagner results are included, noting that only one accuracy-fairness metric result is reported by the authors, hence represented by a single dot in the plot. The accuracies are 84% and 87.7% respectively. FaUCI reaches an accuracy of 85.27% with ≤ 0.01. While the result for FNNC could be coherent with the experiment setup, the one for Wagner is more uncertain. The authors reported that the accuracy of the model using their method is 87.7%, which is far more than the vanilla model 0.02 Demographic Parity
0.04 0.06 0.08 (a) Sensitive attribute: sex (b) Sensitive attribute: ethnicity
Cho FaUCI Jiang
Vanil a 0.00 W0e.0i2ghted Demographic Parity
0.04 0.06 0.08 0.10 (86.7%) that is trained without any fairness constraint. Figure 1b shows the experiments with “ethnicity” as categorical sensitive feature. We observe that FaUCI outperforms the other methods. Jiang has similar performances until DP is above 0.04, while Cho is always worse. We motivate this behaviour because the categorical sensitive feature “ethnicity” has 5 diferent groups, and they are unbalanced. Also “sex” is slightly unbalanced, but it has just 2 groups. Finally, Figure 1c reports the experiments for the continuous protected features “age”. In this scenario, our method and Jiang’s method have similar performance but ours is generally better. Cho’s method performs always worse than the others. Overall, our approach performs better than the others when optimising both accuracy and demographic parity for all kinds of sensitive attributes.
Figure 1 shows the trade-of between accuracy and disparate impact with FaUCI method. Here a comparison with other approaches can be done only with FNNC and Wagner when using a binary sensitive attribute and with the vanilla NN. Figure 1d describes the results with “sex” as protected Cho FaUCI Vanil a FNNC 0.02 0.03Equ0a.0l4ized0O.05dds0.06 0.07 (g) Sensitive attribute: sex 0.04 0.06 0.08 0.10 0.12 0.14 0.16
Weighted Equalized Odds (h) Sensitive attribute: ethnicity
Generalised Equalized Odds 0.07 0.03 0.04 0.05 0.06 (i) Sensitive attribute: age feature. The vanilla NN has an accuracy of 86.7% with = 0.34. FaUCI can reach ≥ 0.8 – which is a commonly agreed threshold in the literature for DI – preserving an accuracy of 85.6%. Authors of FNNC say that their method with ≥ 0.8 reaches 82.2%, under the same DI condition Wagner method can reach 87.7% of accuracy. We emphasize that the results of FNNC and Wagner presented here are reported by the original authors, and we are unable to independently reproduce them. For this reason, and because Wagner’s method reaches a higher accuracy than the vanilla NN (87.7% and 86.7% respectively), there is a possibility that the comparison is not straightforward. Figure 1e shows the performance of FaUCI when using the categorical sensitive attribute “ethnicity”. The vanilla NN has a DI of 0.47 and its accuracy is 86.8%. Our method can preserve the accuracy of the vanilla model with a satisfactory DI ≥ 0.8. Finally, in Figure 1f there are the results of the experiments with “age” as continuous protected feature. The vanilla NN reaches an accuracy of 86.4% with = 0.47. FaUCI cannot achieve the desired value of 0.8 for DI. However, it improves the metric until = 0.58 with an accuracy of 85.5%. Overall, experiments show that FaUCI can significantly improve DI metric while preserving high accuracy.
In this work we present FaUCI, a general purpose method to enforce fairness constraints in NN. The main features of this approach are the ability to work with diferent fairness metrics, the possibility to use it on any data type of sensitive attribute, the resilience to unbalanced datasets, and the ability to work with multiple sensitive attributes. We introduce a new formulation of some fairness metrics used by FaUCI enabling the utilization of these metrics with continuous sensitive attributes and enhancing resilience to unbalanced datasets. We validate our method on a real-world dataset and compare it with other state-of-the-art methods. Results show that FaUCI is able to improve the fairness metrics while preserving a high accuracy-metric trade-of. Future works will be devoted to investigating the potential application of FaUCI to enhance fairness in cases involving multiple sensitive attributes within the context of intersectionality. Another interesting direction is to compare FaUCI, and in general in-processing techniques, with post-processing methods.
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