One-Network Adversarial Fairness

FAD-MD leads to less distinguishable (less unfair) representations of data with different s than FAD.

“FAD-MD leads to less distinguishable (less unfair) representations of data with different s, than FAD.”

• AssumptionRests on an assumption: Most current frameworks of adversarial learning have the problem that the adversary bases its optimization on comparing data points instead of distributions or sets of points.

The heuristics proposed in Salimans et al. 2016 did not improve results in the one-network adversarial framework.

“We experimented with the heuristics proposed in (Salimans et al. 2016) but they did not improve results in our one-network adversarial framework.”

• cites Salimans et al. 2016Not checked yet

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With both datasets, classification accuracy has not considerably changed for β > 1.

“With both datasets, classification accuracy has not considerably changed for β > 1.”

They demonstrated strong empirical performance of their methods compared to previous leading approaches.

“We demonstrated strong empirical performance of our methods compared to previous leading approaches.”

Theorem 1: For distributions P0=P(x|s=0) and P1=P(x|s=1), with training data D of size n equally divided into D0 and D1, for a class H of binary classifiers and δ>0, with probability at least 1-δ, disc(P0,P1) ≤ disc(P0_hat,P1_hat) + sqrt(2 log(1/δ)/n) + 1/2(Rad_D0(Err(H))+Rad_D1(Err(H))).

“disc(P 0 , P 1 ) ≤disc( P0 , P1 ) + 2 log(1/δ) n + 1 2 (Rad D0 (Err(H))+Rad D1 (Err(H)))(16)”

• AssumptionThe authors state this as an assumption: The label y (as well as its estimate ŷ) and the sensitive attribute s values are binary.
• AssumptionThe authors state this as an assumption: Training data D with size n is equally divided into data points with s=0 and s=1.

Increasing the minibatch diversity in FAD-MD is effective, as shown by the MMD test.

“This also shows the effectiveness of increasing the minibatch diversity in FAD-MD.”

• AssumptionRests on an assumption: Most current frameworks of adversarial learning have the problem that the adversary bases its optimization on comparing data points instead of distributions or sets of points.

Classification accuracy values achieved by FAD and FAD-MD on both datasets are higher than previous state-of-the-art results.

“Classification accuracy values achieved by FAD and FAD-MD on both datasets are higher than previous state-of-the-art results.”

Increasing the minibatch diversity with FAD-MD improves the classification accuracy.

“In addition to its impact on fairness, increasing the minibatch diversity with FAD-MD improves the classification accuracy.”

• AssumptionRests on an assumption: Most current frameworks of adversarial learning have the problem that the adversary bases its optimization on comparing data points instead of distributions or sets of points.

Among fairness algorithms, FAD and FAD-MD achieve state-of-the-art classification accuracy on both datasets.

“Classification results on both datasets demonstrate that, among fairness algorithms, FAD and FAD-MD achieve state-of-the-art classification accuracy.”

Classification accuracy initially decreases when optimizing for fairness until it saturates with larger values of β.

“Classification accuracy initially decreases when optimizing for fairness until it rather saturates with larger values of β.”

Comparisons among the unfair and fair versions of FAD and FAD-MD and previous state-of-the-art algorithms show that optimizing for fairness with FAD and FAD-MD leads to minimal loss in accuracy.

“Comparisons among the unfair and fair versions of the proposed frameworks, FAD and FAD-MD, as well as previous stateof-the-art algorithms, show that the quest for fairness with FAD and FAD-MD leads to minimal loss in accuracy”

FAD-MD leads to a slightly higher classification accuracy than FAD.

“FAD-MD leads to a slightly higher classification accuracy than FAD.”

The impact on classification accuracy due to the optimization for fairness by FAD and FAD-MD is rather minimal.

“In addition, the impact on classification accuracy due to the optimization for fairness by the proposed algorithms, FAD and FAD-MD, is rather minimal.”

The FAD framework provides one way to quantify the tradeoff between fairness and accuracy.

“Our framework provides one way to quantify the tradeoff between fairness and accuracy, while also leading to strong empirical performance.”

The FAD model as stated is based on optimizing for disparate impact.

“The model, as such, is based on optimizing for disparate impact.”

The relaxed optimization problem expresses the labeling misclassification probability.

“Hence, we can relax this optimization problem and rewrite it as follows to express the labeling misclassification probability:”

In FAD, reversing the gradient from the sensitive attribute classifier makes the learned representation x maximally invariant to changes in the sensitive attribute s.

“During the backward pass (dotted lines), however, the gradient from the loss of the s classifier ∂L(φ (x ),s) ∂w φ is multiplied with a negative sign so that g adversarially aims at increasing the loss of φ , resulting in a representation x maximally invariant to the change in values of s.”

The FAD approach is prone to common problems of adversarial learning, including mode collapse.

“Although our approach avoids two 'dueling' networks, still it is prone to some of the common problems of adversarial learning, including 'mode collapse' (Goodfellow 2016;Goodfellow et al. 2014).”

• cites Goodfellow 2016Not checked yet

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• cites Goodfellow et al. 2014Not checked yet

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Multiplying φ(g(x)) with the ratio of Err(f(x_i), y_i) over n leads to the objective becoming an interpretation of disparate mistreatment.

“Multiplying φ (g(x)) with the ratio of Err(f (x i ), y i ) over n, which signifies the misclassification rate, leads to the objective becoming an interpretation of disparate mistreatment.”

To optimize for disparate mistreatment, the function φ(x)=φ(g(x)) should be multiplied by a term reflecting what is needed to be equal for subpopulations with different sensitive attribute values.

“In order to optimize for disparate mistreatment, a modification to ( 9) is needed.The function φ (x ) = φ (g(x)) should be multiplied by a term reflecting what is needed to be equal for subpopulations with different sensitive attribute values such that disparate mistreatment is achieved.”

Using a one-class SVM to form minibatches is a step toward establishing adversarial learners with better coverage of all regions of the data space.

“We claim that using the efficient one-class SVM to form minibatches is a step in the direction of establishing adversarial learners with a better coverage of all the regions of the data space.”

Simply discarding the sensitive attribute s and using only x as input to classifier f suffers because x may contain significant information about s.

“A naive approach is to simply discard s and let classifier f have input x -this has some proponents in terms of process (Grgic-Hlaca et al. 2018a;2018b) but suffers since x might include significant information about s.”

• cites Grgic-Hlaca et al. 2018aNot checked yet

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• cites Grgic-Hlaca et al. 2018bNot checked yet

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The larger the value of the fairness hyperparameter β, the higher the impact of this term on the optimization of the objective.

“Also, the larger the value of the fairness hyperparameter β, the higher the impact of this term on the optimization of our objective.”

The whole optimization in their framework is implemented within one neural network, compared to up to four neural networks in Madras et al. (2018).

“The whole optimization in our framework is implemented within one neural network, compared to up to four neural networks in (Madras et al. 2018).”

• cites Madras et al. 2018Not checked yet

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They extend beyond Edwards and Storkey (2016) by linking fairness, distances between distributions, and the adversary's ability to predict the sensitive attribute to the original labeling classification accuracy.

“In addition to having a different approach, we extend beyond that by linking all these notions to the original labeling classification accuracy as well.”

• cites Edwards and Storkey 2016Not checked yet

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The distance between P0 and P1 is inversely proportional to the performance of the classifier.

“where the distance (H-divergence, which is equivalent in this case to the discrepancy distance) between P0 and P1 is inversely proportional to the performance of the classifier.”

Their approach applies to existing architectures.

“Our approach applies to existing architectures; hence, it will be interesting to study how a pre-trained network adapts to the new dual objective.”

The label classifier f(g(x)) aims at minimizing the second term on the right of (21).

“The label classifier f (g(x)) aims at minimizing the second term on the right of ( 21).”

They introduced a fair adversarial framework applicable to differentiable discriminative models.

“We introduced a fair adversarial framework applicable to differentiable discriminative models.”

For a 0-1 classification error and a hypothesis class consisting of the loss on each hypothesis Err(h), the discrepancy distance disc(P0_hat,P1_hat) is equivalent to H-divergence.

“As noted in (Mansour, Mohri, and Rostamizadeh 2009), for a 0-1 classification error and for our hypothesis class consisting of the loss on each hypothesis, Err(h), the discrepancy distance disc( P0 , P1 ) is equivalent to the following notion of distance, referred to as H-divergence (Ben-David et al. 2007;2010;Devroye, Gyorfi, and Lugosi 1996;Kifer, Ben-David, and Gehrke 2004):”

• cites Mansour, Mohri, and Rostamizadeh 2009Not checked yet

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• cites Ben-David et al. 2007Not checked yet

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• cites Ben-David et al. 2010Not checked yet

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The proposed platform can be applied to an existing neural network architecture with rather slender modifications, without reconstructing everything from scratch.

“Our proposed platform can be applied to an existing neural network architecture with rather slender modifications.We do not have to reconstruct everything from scratch to obtain a potentially fair model.”

The third term on the right of (21) tends to zero as the sample size n goes to infinity.

“The third term on the right of (21) tends to zero as the sample size n goes to infinity.”

The term 4/n I(x∈D0)+4/n I(x∈D1) is what is estimated in the proposed formulation (9) by -β max φ (L(φ(g(x_i)), s_i)).

“The term 4 n I(x ∈ D 0 )+ 4 n I(x ∈ D 1 ) is what is estimated in our proposed formulation in (9) in the main document by -β max φ (L(φ (g(x i )), s i )).”

They make slight adjustments to an existing differentiable classifier by adding a new hidden layer and a new classifier above it, to concurrently optimize for fairness and accuracy.

“Instead of having to establish the architecture from scratch, we make slight adjustments to an existing differentiable classifier by adding a new hidden layer and a new classifier above it, to concurrently optimize for fairness and accuracy.”

Implementing the whole optimization within one neural network avoids some well-documented problems of adversarial learning that appear when two or more neural networks are involved.

“This leads to avoiding some of the well documented problems of adversarial learning that appear when two or more neural networks are involved in the optimization (Goodfellow 2016;Goodfellow et al. 2014).”

• cites Goodfellow 2016;Goodfellow et al. 2014Not checked yet

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It is straightforward to see that f(g(x_i)) naturally aims at minimizing the second term in the bound in (21), (Rad_D0(Err(H)) + Rad_D1(Err(H))).

“It is therefore straightforward to see that f (g(x i )) naturally aims at minimizing the second term in the bound in ( 21 ), (Rad D0 (Err(H)) + Rad D1 (Err(H))).”

H-divergence can be approximated by performing a classification task of data D into points belonging to D0 or D1.

“As proved in (Ben-David et al. 2007;2010) (Lemma 2 in (Ben-David et al. 2010)), the H-divergence in such case can be approximated by performing a classification task of the data D into points belonging to D 0 or to D 1 :”

• cites Ben-David et al. 2007Not checked yet

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• cites Ben-David et al. 2010Not checked yet

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