Counterfactual Fairness through Data Preprocessing
Authors: Haoyu Chen
Wenbin Lu
Rui Song
Pulak Ghosh
Venue:  (2021)
Keywords: Counterfactual fairness
data preprocessing
fairness test
discrimination detection
affirmative action

Abstract: Machine learning has become more important in real-life decision-making but people are concerned about the ethical problems it may bring when used improperly. Recent work brings the discussion of machine learning fairness into the causal framework and elaborates on the concept of Counterfactual Fairness. In this paper, we develop the Fair Learning through dAta Preprocessing (FLAP) algorithm to learn counterfactually fair decisions from biased training data and formalize the conditions where different data preprocessing procedures should be used to guarantee counterfactual fairness. We also show that Counterfactual Fairness is equivalent to the conditional independence of the decisions and the sensitive attributes given the processed non-sensitive attributes, which enables us to detect discrimination in the original decision using the processed data. The performance of our algorithm is illustrated using simulated data and real-world applications.

Under review as a conference paper at ICLR 2021
COUNTERFACTUAL FAIRNESS THROUGH DATA PREPROCESSING
Anonymous authors Paper under double-blind review
ABSTRACT
Machine learning has become more important in real-life decision-making but people are concerned about the ethical problems may bring when used im- properly. Recent work brings the discussion of machine learning fairness into the causal framework and elaborates on the concept of Counterfactual Fairness. In this paper, we develop the Fair Learning through dAta Preprocessing (FLAP) algorithm to learn counterfactually fair decisions from biased training data and formalize the conditions where different data preprocessing procedures should used to guarantee counterfactual fairness. We also show that Counterfactual Faimeess is equivalent to the conditional independence of the decisions and the sensitive attributes given the processed non-sensitive attributes, which enables us detect discrimination in the original decision using the processed data. The performance of our algorithm is illustrated using simulated data and real-world applications.
INTRODUCTION
The rapid popularization of machine learning methods and the growing availability of personal data have enabled decision-makers from various fields such as graduate admission (Waters Mi- ikkulliinen 2014). hiring (Ajunwa et al. 2016), credit scoring (Thomas 2009), and criminal jus- tice (Brennan et al., 2009) make data-driven decisions efficiently. However, the community and the authorities have also raised concern that these automatically learned decisions may inherit the historical bias and discrimination from the training data and would cause serious ethical problems
when used in practice (Nature Editorial 2016 (ngwin & Larson 2016 Dwoskin 2015 Executive Office the President et al. (016)).
Consider a training dataset D consisting of sensitive attributes S such gender and race, non- sensitive attributes and decisions Y. If the historical decisions Y are not fair across the sensitive groups, powerful machine learning algorithm will capture this pattern of bias and yield learned decisions Y that mimic the preference of the historical decision-maker, and it is often the case that the more discriminative an algorithm is, the more discriminatory it might be.
While researchers agree that methods should be developed to learn fair decisions, opinions vary on the quantitative definition of fairness. In general, researchers use either the observational or counterfactual approaches formalize the concept of fairness. The observational approaches often describe fairness with metrics of the observable data and predicted decisions (Hardt et al.) 2016 Chouldechoval (2077: Yeom & Tschantz) 2018). For example, Demographic Parity (DP) or Group Fairness (Zemel al., 2013] Khademi al., 2019 considers the learned decision Y to be fair if has the same distribution for different sensitive groups, i.e., P(Ý|S s) P(Ý s'). The Individual Fairness (IF) definition (Dwork et al., 2012) views fairness as treating similar individuals similarly, which means the distance between Y (st,, a.) and ((), 0,) should be small if individuals i and j are similar.
The other branch of fairness and/or discrimination definitions are built upon the causal framework Pearl (2009a), such as direct/indirect discrimination (Zhang et a 2017 Nabi & Shpitser 2018), path-specific effect (Wu al. 2019b), counterfactual error rate (Zhang & Bareinboim 201 Sa) and counterfactual fairness (Kusner et al. (017)) Wang et al., 2019 /w et 2019g.. These definitions often involve the notion of counterfactuals, which means what the attributes decision would be

---

Under review as a conference paper at ICLR 2021
if an individual were in a different sensitive group. With the help of the potential outcome concept, the measuring of faimesss is no longer restricted to the observable quantities (Kilbertus et al. 2017 Zhang & Bareinboim 2018b). For example, the Equal Opportunity (EO) definition Wang et al. (2019) has the same idea as IF but it can directly compare the actual and counterfactual decisions of the same individual instead of the actual decisions of two similar individuals. The Counterfactual Fairness (CF) definition (Kusner et al., (017)) or equivalently, the Affirmative Action (AA) defini- tion (Wang al., 2019) goes one step further than EO and derives the counterfactual decisions from the counterfactual non-sensitive attributes. We adopt CF as our definition of fairness and it is for- mally described
Section 2 We believe causal reasoning is the key fair decisions as DeDeoo (2144) pointed out that even the most successful algorithms would fail to make fair judgments due to the lack of causal reasoning ability.
For the observational definitions, fair decisions can be learned by solving optimization problems, either adding the fairness condition as a constraint (Dwork et al.] 2012) or directly optimize the fairness metric object (Zemel al. 2013). When using the counterfactual definitions, however, an approximation of the causal model or the counterfactuals is often needed since the counterfactuals unobservable. In the FairLearning algorithm proposed by Kusner al. (2017), the unobserved parts of the graphical causal model are sampled using the Markov chain Monte Carlo method. Then they use only the non-descendants of S learn the decision, which ensures CF but will have low prediction accuracy. In Wang et al. (2019). the counterfactual of A had $ been s' is imputed as the sum of the counterfactual group mean B(AIS 5') and the residuals from the original group A - E S = s). As we discuss later, this approach would only work when a strong assumption of the relationship between A and is satisfied.
1.1 CONTRIBUTIONS
We develop the Fair Learning through dAta Preprocessing (FLAP) algorithm to learn counterfactu- ally fair decisions from biased training data. While current literature is vague about the assumptions needed for their algorithms to achieve fairness, we formalize the weak and strong conditions where different data preprocessing procedures should be used to guarantee CF and prove the results under the causal framework of Pearl (209a)). We show that our algorithm can predict fairer decisions with similar accuracy when compared with other counterfactual fair learning algorithms using three simulated datasets and three real-world applications, including the loan approval data from a fintech company, the adult income data, and the COMPAS recidivism data.
On the other hand, the processed data also enable us to detect discrimination in the original decision. We prove that CF is equivalent the conditional independence of the decisions and the sensitive attributes given the processed nen-sensitive attributes under certain conditions. Therefore any well- established conditional independence tests can be used to test. CF with the processed data. To our knowledge, it is the first time that formal statistical test for CF is proposed. We illustrate the idea using the Conditional Distance Correlation test (Wang et al., 2015) in our simulation and test the fairness of the decisions in the loan approval data using parametric test.
2 CAUSAL MODEL AND COUNTERFACTUAL FAIRNESS
For the discussion below, we consider the sensitive attributes S E S to be categorical, which is reasonable restriction for the commonly discussed sensitive information such race and gender. The non-sensitive attributes A A C Rdd, and the decision Y is binary as admit or not in graduate admission, hire or not the hiring process, approve or not in loan assessment.
Us
S
U
S fs(Us),
A Sa(S,U
Y (r A,U))
Uy
Y
Uy
ÿ = Ux) < <p(S
Figure 1: Structural causal model.
2

---

Under review as a conference paper at ICLR 2021
To bring the discussion of fairness into the framework of causal inference, we begin by constructing the Structural Causal Model (SCM) for the data. As described in Inarr (2009)). an SCM M consists of set of exogenous variables U, a set of endogenous variables V. and F, set of functions that assign value to each endogenous variable given its parents in V and the exogenous variables U. In our case (Figure L. we consider V = {S, Y, Y), where {S, } are the observed data and Y is the prediction of Y we made based on S and A. The only exogenous variable affecting Y is Uniform(O,) 1) random variable Uy so that can conveniently express the value of Y with a structural equation. We assume that Us. UA, and Uy, which are the exogenous variables that affect S. A, and Y respectively, are independent of each other. The structural equations on the right side of Figure | are described with the functions in F, one for each component in V. Here we express fv as an indicator function so that Y is a Bernoulli random variable that takes value one with probability A). In general, p(s, a) could be any function that maps S x A to [0, 1], but we are more interested in such functions that will result in a fair decision, more details of which will be discussed in Section 3 It can be seen that the subset of exogenous variables {Us, UA. Uy} characterize everything we should know about a unit. Any two units with the same realization will have the same behavior and result irrespective of the other differences in their identities.
Here we give simplified loan approval model as a running example to help understand the SCM we considered.
Example 1. A bank asks each loan applicant for her/his race S and annual income A to decide to approve the application (Y = 1) or not (Y 0). There are two races in the population of the applicants, S = represents the advantageous group, and S = 0 for the disadvantageous one. Let Us Uniform(0, 1), we generate S = 1 [Ug < 0.7}. The annual income log-normally distributed for each race group and its scale and location parameters may depend on race:
A= cj explce + A.S + cg
where UA is standard normal random variable, c1 > O, and 02 are constants that affect the median and spread of the population income, X decides the difference in mean log income between the two race groups, and aa > 0 determines the standard deviation ratio of the log incomes. The decision by the bank can be simulated from a logistic model:
Y = 1(Uy < expit(3o + B.A + 3,5)}, where Uy Uniform 1) and expit(u)= (1+e-")-1
In this example, Bg characterizes the direct effect of the sensitive attribute on the decision: when B, > O, the applications from the advantageous group are more likely to be approved by the bank when holding the income fixed. On the other hand, Ån partly describes the indirect effect because when both X, and Be are positive, the advantageous group will have higher income than the other group on average and thus be favored by the bank even if B, = O. It is worth noting that, apart from the difference the mean, the difference in higher moments could also cause unfairness indirectly as alluded to in Fuster et al. (0118). In general, if there are any differences in the distribution of A across the categories in S, the decision based on A might be unfair. However, the indirect effect caused by the differences in the higher moments of A could be case dependent and thus harder to interpret. our case, da > will lead to a higher average income and hence higher approval probability on average for the advantageous group since the income distribution is right-skewed.
With the SCM hand, we are ready to define the causal quantity we are interested in. Since most sensitive attributes, such as gender and race, cannot be altered in experiments, the counterfactuals, namely, what the results Y would be had S been different from the observed facts. This quantity is expressed as YU( had S been s for a random unit with exogenous variables U sampled from the population. Define M, to be the modified SCM from M (Figure [ with the equation for S replaced with S = s. Then for any realization U u, the unit level counterfactuals (=(u) can be calculated from M,. Similarly, we can define Y,())) and Y, as the counterfactual predicted decision and its realization. The counterfactual fairness can then be defined on both the decision and the prediction based on the counterfactual result. Here we denote y as a placeholder for either or Y
will look into
Definition 1. Counterfactual Fairness. Given a new pair of attributes (s", aa),, a (predicted) deci- sion y is counterfactually fair for any s' E S,
)>(U) s", A a²) a
3

---

Under review as a conference paper at ICLR 2021
In other words, the conditional distribution of the counterfactual result should not depend the sensitive attributes. should be noted that there are two stages in evaluating the conditional coun- terfactuals. The first is updating the conditional distribution of U. Take the decision Y from Example 1. if s* = O, then Us|(S 8" = a²} is from Uniform(O.. 1) and UA|(S = 8", A = a } is constant (log(a"/ /ca) c2)/css c3. but ( 8 A = a²) is still Uniform(0, 1) random variable since Uy is independent of S and A from the SCM. The next stage is deriving the conditional dis- tribution of the counterfactuals from the structural equations of M, and the conditional distribution of U. Continuing with our example, (T))) = A = a would be equal in distribution to
fAL, UYS 0,A a"}
f1. (log(a" (oog((a//))=-0000000)))(>))) - (2))s))))ss, Uv)
=u{Uy < (3p Baci(a" /c1) ) exps>a (1 0a)c2) B.))
0, )²} - 1 [Uy < expit (30 (3p + )aa")). Thus the bank's decision Y would be and (s
counterfactually fair a2 = 1, A = and 3. = 0.
3 PREPROCESSING, LEARNING, AND TESTING
Define a preprocessing procedure (D a) S A - A' to be function that maps attributes (s, a) to the processed attributes a' given the training data D. Here we consider two such procedures. Denote Fr,
s) as the empirical p.m.f. of and E, (AIS s) as the empirical conditional mean of A given S learned from data D.
Definition (Orthogonalization), An orthogonalizationn procedure P' is preprocessing procedure such that
(o(s", = Σ (ss)
where à(s) = a- (AIS = 5*) En (AIS = 5) Vs
is easy see that Po a²) 0- -'
5* +E,
one-to-one function of for any
fixed s". Denote (z) = (A, S z = s) as the empirical marginal cumulative distribution
function (CDF) of the jth element of the non-sensitive attributes given the sensitive attribute S =
Define its inverse as
(x) inf (A, S x = =) 2}
(3.1)
Definition 3 (Marginal Distribution Mapping). A marginal distribution mapping Ph is a prepro- cessing procedure such that
PM a²) = (a(s)Pa(S=)) =S)))
where the jth element a(s) is [ā()]]s = P ([a*)s for = -,,... d
Let P. Po. and Par denote the population level preprocessing procedure corresponding to pD, Po and PP respectively. is obvious that Po(s", a²) = a" a"-E(AIS- = + is still a one-to-one function of a" for any fixed s", and the jth element of PM aa)) is
(aa(s,aa')) (F-
s),
where Fjs is the marginal CDF of the jth element of A given S and Fjel is defined similarly to (3.1) but replacing P,, with P. can be seen that if A, is a discrete variable, then strictly increasing for s"; and if Aj is continuous variable, then F (F).. (F) strictly increasing when Fjs- (z) is constant some interval of z. Therefore (s" is only one-to-one function of a" for any fixed s* when the marginal CDF of each continuous element in A
(x))
may not be
given S s* is strictly increasing.
4

---

Under review as a conference paper at ICLR 2021
3.1 FAIR LEARNING ALGORITHM
Besides preprocessing procedures, we also have different choices of learners. A Fairness- Throuuhh Unawareness (FTU) predictor (FTv(a) only uses the non-sensitive attributes to predict the conditional mean of Y. A Machine Learning predictor (M. a) uses both the sensitive and non-sensitive attributes to predict E A). An Averaged Machine Learning (AML) predictor (a) E. fMI (s, a)PP,S obtain the AML predictor, but it only needs the non-sensitive attributes as its input when mak- ing prediction since the sensitive attributes f E {f: A + [0, 1}} to learn the decisions from the processed data, and we would consider the FTU and AML learners in our numerical studies.
s)ds. Note that still need to train the ML predictor to
averaged out. Algorithm I could use any learnr
Algorithm 1: Fair Learning through dAta Preprocessing (FLAP)
Input: Training data D, preprocessing procedure pD, learner f. test attributes (s, a).
for (8:, a4 y/s in D do
a; (s,
end
Create the processed data D d(,,)
Learn predictor f from D' Calculate a' PP a)
Draw y from Bernoulli(f(d')
Output: y
Apart from the structural assumptions made Figure I extra conditions of the structural equation fs uA) must be satisfied for the preprocessing method to work.
Condition 1 (Strong non-sensitive). The partial derivative Jug Sa(s, does involve
Condition 2 (Weak non-sensitive). The sign of Bug fA, (s, UA) does not change with s for all uA and all j -1.....d .d
These two conditions describe the relationship between the sensitive and non non-sensitive attributes. Condition 2 is weaker than Condition] 1 For example, an additive model fs U.) Bo + 318 + $r4s satisfies both conditions, while an interaction model fA uA) = 30 + 318 + f24 + 8ysUA does not satisfy [ondition[] but will satisfy Condition if B3 + 333 is greater than (or less than, or equal to) zero for all s. In our running example, fA UA) )= = c1030 for s = 0,
> it meets Condition 2 but not Condition I We prove in the following theorem that these conditions, together with the SCM, are sufficient for Algorithm T too generate counterfactually fair decisions.
Theorem 1. Letr be the output from Algorithm i.e., 11Ug < (()))s,)))
If the procedure Py is adopted, Y is counterfuctually fair under Condition
2. If the procedure Ph is adopted, Ý is counterfactually fair under Condition
We prove Theorem D in Appendix A The intuition is that the FLAP algorithm learns the decision from processed data only, and the processed data contain sensitive information since the prepro- cessing procedure can remove A's dependence on under the non-sensitive condition.
3.2 TEST FOR COUNTERFACTUAL FAIRNESS
Data preprocessing not only allows us to learn a counterfactually fair decision but also enables us to test the decisions made in the original data are fair. When Condition [ holds, we can use the data processed by the orthogonalization procedure to test faimess. When the strong condition does not hold but Condition is satisfied, we need an extra condition to utilize the marginal distribution mapping procedure for fairesss testing.
5

---

Under review as a conference paper at ICLR 2021
Condition 3. The conditional marginal CDF Fjo(z) is strictly increasing for all such j that Ag is continuous and all s E S.
In other words, each non-sensitive attributes Aj should be either a discrete random variable continuous one with non-zero density on R. This condition ensures that Par (s" a²) is a one-to-one function discussed earlier. With these conditions, we can establish the equivalence between CF and the conditional independence of decision and sensitive information given the processed non- sensitive information.
Theorem 2. Consider the original decision Y:
1. Under Condition
Y is counterfactually fair if and only if (S
2. Under Conditions and 3 Y is counterfactually fair if and only Y a
Its proof in Appendix A Theorem 2 allows us to test CF using any well-established conditional obtain the empirical processed non-sensitive attributes PD (5,,00 a;) and test if Y L.SIIPP A). If the p-value of the test is small enough for to reject the conditional independence hypothesis, then the original decision is probably biased and algorithms such as FLAP should be used to learn fair decisions.
independence test. In practice, given decision dataset D (s,, as 34)
4 NUMERICAL STUDIES
In this section, we compare the decisions made by different algorithms in terms of fairness and ac- curacy using simulated and real data, and also investigate the empirical performance of the fairness test using simulated data with small sample sizes. We consider three cases for generating the simu- lation data. The first one is Example and the second one a multivariate extension where we introduce more sensitive group and include the education years of the loan applicants another non-sensitive attribute and Iet their annual income depend on it. The third example a replica of the admission example constructed by Wang al., (2019). The details of these examples and the parameters chosen in the simulation are presented in Appendix B
As discussed before, Condition 2 satisfied in Example [ but Condition 1 is not. Moreover, both Examples 2 and 3 do not satisfy either condition in general due to the cutoff in the value of their non-sensitive attributes, and hence neither of the proposed preprocessing methods in theory. However, the weaker Condition 2 will hold in Example 2 when the mean education years of the three sensitive groups are the same, which case the marginal distribution mapping method should work.
achieve CF
4.1 FAIRNESS EVALUATION
We compare our FLAP algorithm with
1. MI.: the machine learning method using both sensitive and non-sensitive attributes without preprocessing, which is a logistic regression of on S and A;
2. FTU: the Fairness- Tacesss-Thhouu--Uaaaaa
method which fits a logistic model of on non-
sensitive attributes A alone without preprocessing:
3. FL: the FairLearnngg algorithm proposed by Kusner et al. (001)):
4. AA: the Affirmative Action algorithm proposed by Wang et al. 2019).
All these methods can output predicted score p given the training data D and test attributes (s, a), denoted p(s, a; 'D and draw the random decision Y from Bernoullip(ss, a; D)). For MI method, p(s, D) fMLL (s, a)) for FTU method, that is frTO (a). We denote the predicted scores of the FairLearning and AA algorithms as (FL (s, a: D) and fAA(S, a; D). respectively. For our FLAP method, we use the marginal distribution mapping procedure and try both the AML and the FTU leamners described scores are fAML L (PD) (s) a)) and frrU (PR P (s, a)). respectively. We mainly use the Mean Absolute Error (MAE) of the predicted score on the test set to measure the prediction performance, and also include the area under the ROC curve and average precision of the prediction in Appendix B for
Section and name the methods as FLAP-1 and FLAP-2. Their predicted

---

Under review as a conference paper at ICLR 2021
completeness. All these metrics show similar results about the prediction performance. The metric for measuring the counterfactual fairness (CF-metric) is defined as
Nteat
max r.IES
Io(r, R (r, 81, 8;, (1,
Neest
where /z/ (8, a")) is defined as a(s) Definition 3 Note that the CF-metric should be zero when decisions CF under Condition In real world applications where the condition cannot be verified, a CF decision is not guaranteed to have zero CF-metric, although we expect the CF- metric to be lower for fairer decisions in general. This definition is different from the AA-metric proposed by Wang et al. (2019) in two folds. First, it allows us to consider more than two sensitive groups by taking the maximum the pairwise difference of predicted scores, but reduces to the AA-metric for two sensitive groups. Second, we use the marginal distribution mapping method to compute the counterfactual non-sensitive attributes a (s, s", aa) had the unit been in different sensitive group s. This ensures that all the derived counterfactual attributes are within the range of observed attribute values. comparison. Wang al. (2019) use the orthogonalization method to compute the counterfactual attributes and thus female student having test score 0.98 would have a counterfactual score of 1.48 had she been male if the male mean test score 0.5 higher than female. This out-of-range counterfactual score is unreasonable and problematic when being used as the input of the score prediction function p.
For Example 1 we hold other parameters fixed while increase de from 1 to 2.8 to how the difference in the variation of the non-sensitive attribute between sensitive groups affects fairness. As expected, the AA algorithm which essentially uses the orthogonalization method cannot achieve CF since Condition is not met. However, both FLAP algorithms' CF-metrics are zero when using the marginal distribution mapping preprocessing (Figure 2ap
0.32
0.60
FTU
FTU
3
0.30
PLAn-2
0.12
0.29
0:31
58-
0.3
2.0
2.5
2.0
04
0.2
(a) Example D with incrcasing Ca-
(b) Example 3 with different mean by gender.
Figure 2: Comparison of CF-metric and MAE of decision making algorithms
Wang et al. (2019) showed that the AA algorithm can achieve zero AA-metric in Example 3 but does not satisfy either of the non-sensitive conditions for achieving CF. As shown in Figure 2b all algorithms we consider cannot achieve CF, but the FLAP algorithms still have the lowest CF-metric. The results of Example 2 are shown in Appendix B and there is significant difference between the MAE of the AA and FLAP algorithms in all examples. In general, we expect fairer predictions to have higher MAES since they correct the discriminatory bias of the original decisions.
4.2 FAIRNESS TEST
The Conditional Distance Correlation (CDC) test (Wang et al. 2015) is well-established non- parametric test for conditional independence. We use here illustrate the performance of the fairness test with the three simulated examples. For each example, we use different combinations of parameters obtain simulated datasets with different faireess levels, which are measured by the CF- metric. A CDC test with significance level of 0.05 is then conducted to test Yf LYYLSPP LS)PP(S A) for each dataset. The simulation-test process is repeated 1000 times for each combination of parameters to estimate the power of the test, namely the probability of rejecting the null hypothesis that the decisions are counterfactually fair. The results are summarized in Figure 3
When the decisions generated fair, which shown the points with CF-metrics equal to zero, the type eиror rate is around 0.05 for all examples. The power the test grows as we make the decisions unfair, or increase the sample size.

---

Under review as a conference paper at ICLR 2021
300
(a) Example
(b) Example
(c) Example
Figure 3: Power for testing CF using conditional independent test plot against the CF-metric
REAL DATA ANALYSIS
We apply methods loan application dataset from a fintech company, the adult income dataset from UCI Machine Learning Repository[ and the COMPAS recidivism data from ProP- ublica" (Angwin & Larson 2016). Here we present our analysis of the loan application data, and the results from the other two publicly available datasets are shown in Appendix C since the conclusions similar.
In the loan application case, the fintech lender aims to provide short-term credit to young salaried professionals by using their mobile and social footprints to determine their creditworthiness even when a credit history may not be available. To get a loan, a customer has to download the lending app, submit all the requisite details and documentation, and give permission to the lender to gather additional information from her/his smartphone, such as the number of apps, number of calls, and SMSs, and number of contacts and social connections. We obtained data from the lending firm for all loans granted from February 2016 to November 2018. The decisions Y are whether or not the lender approves the loan applications. The attributes are applicants' gender, age, salary, and other information collected from their smartphones. Both gender and age are regarded as sensitive information here and we find that the decisions are made in favor of the senior and female applicants. Since can only deal with categorical sensitive attributes, groups by the lower quartile of the age distribution and create a categorical variable S E {0, 1, 2, to denote the group of the applicants: female younger than 28; male younger than 28; female older than 28; and male older than 28. The effective sample size after removing missing values is 203,656.
divide the applicants into two age
Mon-parametric conditional independence tests will not be efficient for this real case due the large sample size. Therefore we test the conditional independence of Y and S given PR (S, A) by fitting a simple logistic model for Y with S and (S, A) as the explanatory variables and testing if the coefficient of S is significantly different from zero. The p-value of the F-test is almost zero and indicates that the decisions are unfair for applicants in different groups. When other attributes are fixed to their means, the predicted approval probabilities of the four groups from the logistic model are 0.924 (young female). 0,899 (young male). 0.948 (senior female), and 0.946 (senior male), also indicating that the decisions are most in favor of the senior and female applicants.
We then separate the data into a training set of 193,656 samples and a test set of 10,000 samples. The training dataset used to learn the decisions with different algorithms and the test dataset is used to evaluate the CF-metric and MAE. The results are summarized in Table [ Our FLAP al- gorithms have lower CF-metrics compared with other algorithms and their MAES are only greater than the MI method. Among the FLAP algorithms, the two using the marginal distribution map- ping preprocessing procedure have better CF-metric and similar MAE. The FLAP algorithm using the FTU learner (FLAP-2) performs slightly better than the one using the AML learner (FLAP-1). Note that in real-world applications, fairer decisions may not have higher MAES as expected in the simulation studies because we do not have access to all the variables possessed by the original decision-maker. When the original decisions depend on additional information, the FLAP and other
https://githube http:/hhww..cocoooooeoeoeoo htte:://ggtthb..coom/moooooo1o//
wwtp://lliicaaccccaaaaaaaaa www.cc/mma...oocccccccccc ysis
8

---

Under review as a conference paper at ICLR 2021
fair learning methods may yield predictions closer to further away from the original decisions, and thus leading to lower or higher MAEs.
Table 1: Comparison of the CF-metric and MAE of decision making algorithms the fintech data. FLAP-1(O) and FLAP-2(O) use the orthogonalization and FLAP-1(M) and FLAP-2(M) use the marginal distribution mapping preprocessing procedure.
ML
FTU
FL
AA
FLAP-1(O)
FLAP-2(0)
FLAP-I(M)
FLAP-2(M)
CI-metric
0.0392
0.0130
0.0011
0.0011
0.0011
0.0011
0,0008
0.0007
MAE
0.1249
0.1261
0.1258
0.1266
0.1258
0.1258
0.1258
0.1258
DISCUSSION
We propose two data preprocessing procedures and the FLAP algorithm to make counterfactually fair decisions. The algorithm is general enough that any learning methods from logistic regression to neural networks can be used, and counterfactual fairness is guaranteed regardless of the learning methods. The orthogonalization procedure is faster and ensures counterfactually fair decisions when the strong non-sensitive condition is met. The marginal distribution mapping procedure more complex but guarantees fairness under the weaker non-sensitive condition.
We also prove the equivalence between counterfactual fairness and the conditional independence of decisions and sensitive attributes given the processed non-sensitive attributes under the non-sensitive assumptions. We illustrate that the CDC test is reliable for testing counterfactual fairness when the sample size small. When the size gets bigger, however, we need more efficient testing method for the fairness test.
well understood but still worth noting that causal inference comes with strong assumptions, such as the SCM and the non-sensitive conditions in our case. Moreover, these assumptions are often unverifiable in general, although we may test some of them when only considering a restricted class of models. As the saying goes, "all models are wrong, but some are useful". The FL.AP method may require unverifiable assumptions in practice, we make general enough and easy to follow in the hope that this would encourage decision-maker to address the fairness issue with its help.
REFERENCES
Ifcoma Ajunwa, Carlos Scheidegger, and Suresh Venkatasuurammanian. Hiring by algorithm: pre- dicting and preventing disparate impact. Presented at the Yale Law School Information Society Project conference Unlocking the Black Box: The Promise and Limits of Algorithmic Account- ability in the Professions, 2016.
Julia Angwin and Jeff Larson. Bias in criminal risk scores is mathematically inevitable, researchers say. Propublica, 2016.
Tim Brennan, William Dieterich, and Beate Ehret. Evaluating the predictive validity of the compas risk and needs assessment system. Criminal Justice and Behavior, 36(1):21-40, 2009.
Alexandra Chouldechova. Fair prediction with disparate impact: A study of bias in recidivism prediction instruments. Big data, 5(2):153-163, 2017.
Simon DeDeo. Wrong side of the tracks: Big data and protected categories. arXiv preprint 1rX4v:1412.4643, 2014.
Cynthia Dwork, Moritz Hardt, Toniann Pitassi, Omer Reingold, and Richard Zemel. Fairness through awareness. In Proceedings of the 3rd innovations in theoretical computer science confer- ence, pp. 214-226, 2012.
Elizabeth Dwoskin. How social bias creeps into web technology. The Wall Street Journal, 21, 2015.

---

Under review as a conference paper at ICLR 2021
Executive Office of the President, Cecilia Munoz, Domestic Policy Council Director, Megan (US Chief Technolocy Officer Smith (Office of Science, Technology Policy)), DJ (Deputy Chief Tech- nology Officer for Data Policy, Chief Data Scientist Patil (Office of Science, and Technology Pol- iey)). Big data: A report on algorithmic systems, opportunity, and civil rights. Executive Office of the President, 2016.
Andreas Fuster, Paul Goldsmith-Pinkhaan Tarun Ramadorai, and Ansgar Walther. Pre- dictably unequal? the effects of machine learning on credit markets. 2018. Available at SSRN: https://sst /ss..//ss...../ com/ httm/abssractt 2139/ssrn. 3072033
or http: http://dx.doi.oro// org.11100..
Moritz Hardt, Eric Price. and Nati Srebro. Equality of opportunity in supervised learning, In
Advances in neural information processing systems, pp. 3315-3323, 2016.
Aria Khademi, Sanghack Lee, David Foley, and Vasant Honavar. Fairesss in algorithmic decision making: An excursion through the lens of causality. In The World Wide Web Conference, pp. 2907-2914, 2019.
Niki Kilbertus, Mateo Rojas Carulla, Giambattista Parascandolo, Moritz Hardt, Dominik Janzing, and Bernhard Schölkopf. Avoiding discrimination through causal reasoning. In Advances in Neural Information Processing Systems, pp. 656-666, 2017.
Matt J Kusner, Joshua Loftus, Chris Russell, and Ricardo Silva. Counterfactual fairness, In Advances in Neural Information Processing Systems, pp. 4066-4076, 2017.
Razieh Nabi and Ilya Shpitser. Fair inference on outcomes. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 2018, pp. 1931, 2018.
Nature Editorial. More accountability for big-data algorithms. Nature, 537(7621))449, 2016.
Judea Pearl. Causal inference in statisties: An overview. Statistics surveys, 3:96-146, 2009a.
Judea Pearl. Causality. Cambridge university press, 2009b.
Lyn Thomas. Consumer credit models: pricing, profit and portfolios. OUP Oxford, 2009.
Xueqin Wang, Wenliang Pan, Wenhao Hu, Yuan Tian, and Heping Zhang. Conditional distance correlation. Journal of the American Statistical Association,
2015.
Yixin Wang, Dhanya Sridhar, and David M Blei. Equal opportunity and affirmative action via counterfactual predictions. arXiv preprint arXiv:1905.10870 2019.
Austin Waters and Risto Müikkulainen. Grade: Machine learning support for graduate admissions.
Al Magazine, 35(1):64 64, 2014.
Yongkai Wu, Lu Zhang, and Xintao Wu. Counterfactual faimess: Unidentification, bound and algorithm. In Proceedings of the Twenty-Eighth International Joint Conference on Artificial In- telligence, pp. 1438-1444, 2019a.
Yongkai Wu, Lu Zhang, Xintao Wu, and Hanghang Tong. Pe-fairness: A unified framework for measuring causality-based fairness. In Advances in Neural Information Processing Systems, pp- 3404-3414, 2019b.
Samuel Yeom and Michael Carl Tschantz. Discriminative but not discriminatory: A comparison of fairness definitions under different worldviews. arXiv preprint /808.080 2018
Rich Zemel, Yu Wu, Kevin Swersky, Toni Pitassi, and Cynthia Dwork. Learning fair representations. In International Conference on Machine Learning pp. 325-333, 2013.
Junzhe Zhang and Elias Bareinboim. Equality of opportunity in classification: A causal approach. In Advances in Neural Information Processing Systems, pp. 367 3671-3681, 2018a.
Junzhe Zhang and Elias Bareinboim. Fairness in decision-making In Proceedings of the AAAI Conference on Artificial Intelligence, 2018b.
causal explanation formula.
Lu Zhang, Yongkai Wu, and Xintao Wu. A causal framework for discovering and removing di- rect and indirect discrimination. In Proceedings of the 26th International Joint Conference on Artificial Intelligence, pp. 3935- 2017.
10

---

Under review as a conference paper at ICLR 2021
A PROOF OF MAIN RESULTS
A.1 PROOF OF THEOREM 1
Proof. We prove the theorem for general class of learners {ff A + [0, 1]} that only take the non-sensitive attribute a as the imput. Clearly, both fETU or fAML belong to this class. We follow the Abduction ceneeiionnActti--Prerriii
steps in Theorem 7.1.7 Pearl 2009b) to evaluate the conditional expectation of Y. (U) given the evidence
A= a².
(U) 8", = a²) -=)=)==== ((PP()) (All'' fald, ()) = 8 a')du,
where (uls" aa)) denotes the conditional density of UA given S = = and A a". If (D(('' fA u)) does not depend on so will
8" A a²) and we will have d²) E(Y,- (U)IS s A a*) Note that DD SA('s, u)) = E. (. = 8) for both the preprocessing procedures we are considering. Therefore, suffices to show that (s)) does depend on s'.
E(Y (U)|S =
First, consider the Orthogomalization procedure pg where
a(s) fa(s', u) E., (AIS 5 (AIS =5)
fa(l',u) E(AIS = 5') + EAIS = s) -En, (AIS = s').
Note that ( 5') (a(s'(UA) and the first order Taylor expansion of it gives
E(ASS = 5¹) E fa(s',u) u) +
fa(s,
(UA - u)
Du
NWW
= Ja(', u) + Du (s( u)
E(UA u)
for some u' between and UA. By Condition
I
0
a(s) Ou
(s, u)
EEu UA) + E, (AIS 8) + or()
and thus it does not depend on s'.
Second, consider the Marginal Distribution Mapping procedure Ph- Let fA, (s, u) = fA u) where Ej is d-dimensional vector with the jth element being one and all other elements being zeros. The jthh element of ā(s) is [ā(s]]; = Fj. (F (fA, u))) for j = i. d. Again, the first order Taylor expansion of fa, (s', UA) gives
Fr (Ja u)) (A, S (s' =
=P(JA,(S,UA) S fA,(5',u) +P,, (Pn-P)(A) $ fa,(5, = =P -P(1,,00.
0 [1, u8)
(A- < faz(6 [n)(6, or((n)
sm6',umu
for some w' between u and UA- Under Condition
a [, (s)
Pr = sign
(U un <0) + or(n)
Tu
aama
does not depend on and hence (s)) is function of and alone.
A.2 PROOF OF THEOREM 2
Proof. The steps of proving the two statements of Theorem 2 are similar. To remove redundancy,
we use the notation whenever the argument is true for both the preprocessing procedures Po and PM-
11

---

Under review as a conference paper at ICLR 2021
First, we show that Y is counterfactually fair if Y A)) The posterior mean of the counter- factual (U)) given S = s" and A = =a can be evaluated in two steps: first find the conditional distribution of U = AU Us. Uy), }. and then calculate the conditional expectation of the counter- factuals from the SCM. Since the effect of Us is blocked by setting S = s' and Uy is independent of S and A, only the distribution of UA will be affected by the given information and effect the counterfactuals Yg (U).
B(Y) = s
=ad-- ''A==''
B[fr falss's u). Uy
(A.1)
Under the SCM, [[ /a(s' uu), Uv) is the same as the expectation of the observed decision Y given the attributes S = 8 A [s('', u). Therefore (A.1) equal to
BYYIS= = 8 A= fa(s', ( s" == a d')du
(A.2)
= I / |E(YIP(S. = fald (1l =5, 1==aa)pp a')du
P(ss (U) s", a" d')du
(A.3)
(A.4)
/ B(YIP(S P(s", (4)) = , =5, "= = a² )du
(A.5)
(A.6)
A.3 replaces the condition A = fA(s', u) with P(S, = P(s', Ja(s', u)) because (o A) one-to-one function of A given S and (S, A) is also a one-to-one function of A given S under Condition 3 Equation (A.4) is due to the conditional independence of Y and S, and ) uses the result that fa u)) P(s ff'""((", (u)) which can be shown fol- lowing the proof of Theorem M Repeat the steps T.. to (A.5) and we shall get the same result for B(,, (U))S s" A a Note that both (U) and Y, (U) are binary random variables, therefore the equivalence in expectation implies that
Equation
(U)ISS s", A= aa) (U-))
A=
The above result holds for any s', s* E S, so the definition of counterfactual fairness is satisfied.
Next we show that (LS if Y is counterfactually fair. The counterfactual faimess of Y implies
Es ff(s', (A(S',AA), Uy)S s" =Effy(s" fA(s" = ==,A=="")
(A.7)
=
Let a' = =Pss" a²), then sS _ (UA, (s' A)= d'}
(A.8)
since P(s", a²) is one-to-one function of a" for each s².
Using the Bayesian formula, the posterior density U is
PUlls.p(uIS = 5" , P(ss, (is",A) A) d')
(A.9)
PU, (W) = 5*) PPPSSU (a'1S = 8² UA = u)
(A.10)
P(S PU, (0 (u) (a' SS = 8* UU u)du''
where Pu.ls.p(uls" a') denotes the conditional density of U given = s" and P(s", = dd, pUA (u) denotes the prior density of UA and PPIS.U (a')s = 8", Un , = u) denotes the conditional s* and U = u. As density function, (A. is proportional to
density of PPss, A) given its kernel pu, (u))pp|s,,,(a' (a' =0===0;00 UA = u). which equals pu, (u)ppIs.u, (a'1S s', = u) because P(S, A) does not depend on S when UA is given as shown in the proof of Theorem ] Repeating the steps and we can show that the posterior density of UA given S S= s', P(s', A) a is also proportional to PU (u)Pr) (.U,,,ssUUU (a'|S = s', UA = u). Together with the assumption in the SCM that Uy is independent of S, P(S,A), A), we have
(UA, s P(s' A) a'} - (S P(8", A) =d).
(A.11)
12

---

Under review as a conference paper at ICLR 2021
The intuition here is that if the processed non-sensitive data equal, then they provide the same information about UA regardless of the sensitive information in the original data. Substituting the conditions {S s" A = a²} in (A.7) with the equivalent conditions in (A.8) and (A.11) gives
= f (s', fa(s', UA), = s', a'] a'].
(A.12)
= = [f ff((s* , =
Under the SCM and structural equations defined in Figure (A.12) implies
E[ = s', P(S, A) = d') = E 8 P(S, A) = a'}- Since A.13 holds for any 8',8" 5= S, it yields that
(A.13)
S, (S, A) E(
and hence Y Y1S)P(S,A) for binary Y.
B DETAILS OF SIMULATION EXAMPLES
Example 2. The bank now collects the race S, education year E and annual income A information from loan applicants. There are three possible race groups S = = and = 1(Ug > 0.76} + 1 1 > 0.92}. meaning that random applicant could be from the majority race group (0) with probability 0.76, or from the minority group or 2 with probability 0.16 or 0.08. Let Ug be standard normal random variable and μa λd + 1 1) + 1 2) X22 the education
year is
max (0, μo + 0.AuEUB). Let μA log(Aao + +1s = 1}} + 1 222) the annual income is A= cxp + 0.4ugUe + O.1UAA)
The decision of the bank is modeled as
Y 1(Ux- < expit(Bu + 1(S 1381 + 1(S 2332+ B BeE)).
Here Xeo det and Asz decide the mean education year of the three race groups. Xao dat and Au2 decide the median annual income. The annual income and the education year are positively correlated through Ug. 31 and B2 characterize the direct effect of the race information while the X's indicate the indirect effect together with Be and Ba. In this example, neither of Conditions holds if Se and Ar and/or λez are not zero due to the maximum operator in fE- Even if
and
2
Ae1
Ae2 = 0, only the weaker Condition 2 will hold due to the same reason for Example
Example 3 is replica of the admission example constructed by Wang et al. (2019).
Example 3. The admission committee of university collects the gender S and test score T infor- mation from applicants. The gender is simulated from 5 1UUs < 0.5), where S = for male and 5 for female. Let UT ~ Uniform(0, 1) and we generate the test score as
T min (0, (0. AS 1}.
The decision of the committee is
Y= 1(U < expit(80 3T + (,5)].
worth noting that both Examples 2 and do not satisfy either of Conditions I and 2 due to the cutoff in the value of their non-sensitive attributes education years and test score. Take Example 3 there will be a positive probability (A to be exact) of seeing male students with test score if 0. Check that
①
1,
As 0 uT
fr(s, uT)
Our
0, 1- As < wr < 1
and we can see that its sign does change with s for any fixed ur. Therefore, neither of the proposed preprocessing methods can achieve CF in theory.
In Figures 2a and 4c we choose C₁ = 0.01, C2 = 4, c3 = 0.2 and fix 30 = -1,
11, 8, = 2, 3, = 1, Xa 0.5 while increase a, from 2.8 to see how the difference in the variation of non-sensitive
13

---

Under review as a conference paper at ICLR 2021
0.25
0.90
0.20
0.3
ITU
0.33
0.4
FL
BoC
AA
FEAP-1
TEAP-
0.1
(0.900
(0.0
0 iiffrrncc due Ao.
Difference due Me..Ae
Difference due to (e.
Difference due A4.
(a) Ex. with different mean income by race.
0.35
0.90
Neero prddtoo
0.30
AOC.MIC
0.80
032
0.00
0.87
10.0)
(0-10
(b) Ex.
with different mean education years by race.
6.92
0.75
0.02
2.50
Aueeap prectton
0.72
0.88
TTU
0.53
2.54
KAP
KLPPL
0.65
0.92
0.53
3.70
2.0
3.5
Sfffrence
(c) with increasing da-
(d) Ex. with different by gender.
Figure 4: Comparison of CF-metric and prediction performance of decision making algorithms
14

---

Under review as a conference paper at ICLR 2021
attribute between sensitive groups affects faimess. In Figures 2b and 4d set Po -1, B1 2, 3, = and increase À from O to 0.8 to see how the mean difference of test scores affects fairness.
In Figure 4a
and 4b choose 30 -1, 31 = 82 0, 3u 1, 3e = 2. A 1.07, A 0.58.
In Figure 4a, wC change (Ar1 A22) while fix Ae1 = and X22 = 0 to see how the mean difference of income affect fairness. The results telling the same story Figure 2a since only the weaker non-sensitive condition met, the AA-algorithm cannot achieve CF but the FLAP algorithms with marginal distribution mapping procedure can.
we change (Aet, Ar2) while fix An = 0 and X22 = 0 to see how the mean difference of education affect fairness. The results similar those of Figure 2b where all algorithms consider cannot achieve CF but the FLAP algorithms still have the lowest CF-metric.
In Figure 4b,
C DETAILS OF REAL DATA ANALYSIS
We use the adult income data to predict whether an individual's income is higher than $50K with information including sex, race, age, workelass, education, occupation, marital-status, capital gain and loss. Sex and race are regarded as sensitive attributes. The training set has 32,561 samples and the test set has 16281 samples. The comparison of the FLAP and other methods are shown in Table 2
The COMPAS (Correctional Offender Management Profiling for Alternative Sanctions) recidivism data contains the demographic data such as sex, age, race, and record data such as priors count, juvenile felonies count, and juvenile misdemeanors count of over 10,000 criminal defendants in Broward County, Florida. The task is to predict whether they will re-offend in two years. According to ProPublica, "Black defendants were often predicted to be at higher risk of recidivism than they actually were." Here treat sex and race sensitive attributes and try to predict recidivism in counterfactually fair manner. We only use the data for Caucasian, Hispanic, and AfricnnAAmrice individuals due to the small sample sizes of other races. The remaining data are divided into training set of 5,090 samples and test set of 1697 samples. The results are shown in Table
Table 2: Comparison of the CF-metric and MAE of decision making algorithms on the adult income data. FLAP-I(O) and FLAP-2(O) use the orthogonaliization and FLAP-I(M) and FLAP-2(M) use the marginal distribution mapping preprocessing procedure.
MI.
FTU
AA FLAPP-(O)
FLAP--2(0)
FLAP-I(M)
FLAP-2(M)
CF-metric
0.2779
0.2338
0.0228
0.0268
0.0280
0.0228
0.0020
0.0022
MAF
0.2388
0.2396
0.2406
0.2356
0.2452
0,2406
0.2430
0.2401
Table 3: Comparison of the CF-metric and MAE of decision making algorithms on the COMPAS data. FLAP-1(O) and FLAP-2(O) use the orthogonalization and FLAP-1(M) and FLAP-2(M) use the marginal distribution mapping preprocessing procedure.
ML
FTU
FL.
AA
FLAP-1(O)
FLAP-2(0)
FLAP-I(M)
FLAP-2(M)
CF-metric
0.2274
0.1406
0.0054
0.0060
0.0058
0.0054
0.0026
0.0027
MAE
0.4256
0.4274
0.4402
0.4391
0.4395
0.4401
0.4393
0.4393
Similar to the results we have shown for the loan application data, the FLAP methods using the marginal distribution mapping preprocessing procedure have lower CF-metric and are thus consid- ered fairer than other fair leamning algorithms, and their MAES are comparable to other methods.
15


Reviews:
[{"review_id": "yBU6grqgBfw", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The authors propose a preprocessing method that eases fair learning called FLAP.\nThey focus on counterfactual fairness introduced by Kusner et al. 2017. Under certain conditions, the preprocessing allow to biased the data such that traditional learning becomes fair.\nThis is a very interesting idea that is novel to me.\n\nThe paper is well written, and the related work is coherent with the work done. However, I think a few new paper are missing, for example Counterfactual Fairness: Unidentification, Bound and Algorithm from Wu et al 2019 that bounded the reachable counterfactual fairness. It would have been interesting to see how the results related to these bounds.\n\nI think that the statement:  “We prove that CF is equivalent to the conditional independence of the decision and the sensitive attributes given the processed non-sensitive attributes” is a bit misleading. As far as I understand, this is only true given that either condition 1 is satisfied or conditions 2 and 3 are satisfied. There exists statistical test for conditional independence but checking for condition 1, 2, 3 seems more complicated.\n\nOn the real data, I would like to see a discussion on the meaning of CF-metric and FLAP method given that the condition 1, 2,3 are not verified.\n\nI think that theses clarifications are needed for a clear accept.\n\n----- edit after the authors' answers -----\nI'm not convinced by the authors' answer on the meaning of the CF-metric when condition 2 is not verified, which is the case on real data. \"... but we would expect fairer decisions to have smaller CF-metric in practice\" doesn't seem enough to claim that FLAP is better because its CF-metric is lower. In addition we don't have confidence interval to assess if FLAP is really better on MAE.\n\nFinally the review of reviewer1 made me realize that CF-metric and FLAP are based on the same function. I partly agree with the authors' answer, i.e., we need a counterfactual function to construct a good metric and then it is optimal to use it as well in the algorithm. However it is not fair to use that metric to claim that the algorithm is fairer. \n\nTherefore I lower my rating to 5. ", "extra_scores": {}, "extra_text": {}}, {"review_id": "lL19bF7BdrL", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This paper proposed a method to preprocess the dataset, so a machine learning classifier learned on the pre-processed data would be counterfactually fair.\n\nStrong points:\n+ The studied fairness problem is very important, and the causality-base fairness is a very challenging question\n+ The proposed method is very intuitive and easy to follow\n\nPoints for Improvements:\n- On the experiments part, I was wondering why the paper didn't compare to the original Counterfactual fairness paper's algorithms by Kusner et al. 2017. They have proposed three levels of algorithms to study the counterfactual fairness.\n- On the experiment evaluation part, I was wondering why the paper chose MAE as the performance metrics, because we are talking about classification problems here. Are the ground truth scores just 1, and 0, and we are comparing our prediction probability to these 1 and 0's?\n- Sorry if I missed the point, but I would appreciate the authors kind clarification: the dataset is preprocessed using a function we proposed, and the counterfactual metric (CF-metric) is also evaluated using this exact preprocessing function, while all other methods have no access to this function. Would this appear to be unfair to other baselines? What if say the EO, AA algorithm was also trained on the pre-processed dataset?\n- The paper assumes a causal model as in Fig. 1. Does this model always hold in practice? If it is not, what should we do?\n- Minor: Page 4 Section 3, Line 1, $\\mathcal{S} \\times \\mathcal{A} \\rightarrow \\mathcal{A}'$, missing a '\n- Minor: Above Page 3 Definition 1., U is used as unit and also previously as noise variable. Would probably be less confusing to choose another character. ", "extra_scores": {}, "extra_text": {}}, {"review_id": "QRquqbP3bQ", "reviewer": "AnonReviewer4", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The paper addresses the problem of preprocessing the data in a way that the predictions of a learning task will be counterfactually fair. The counterfactual fairness definition is borrowed from that of (Kusner et al., 2017). The authors propose ortogonaliza tion and marginal distribution mapping so as to achieve counterfactual fairness. They test their proposed approach on synthetic and real data.\n\nThe math of Definition 1, Counterfactual Fairness of (Kusner et al., 2017) is wrongly stated. Counterfactual fairness is defined over the predicted $\\hat{Y}$. I suppose (although am not sure) that it’s a typo because it’s correct in the proof of the theorem in the appendix.\n\nThe MAE of FLAP-1 and FLAP-2 are higher than other methods in Figure 2, although are lower in the loan application experiment. The authors can elaborate on why this is the case and provide some discussion. This is also the trend in examples 2 and 3 in Figure 4. The authors discuss the DF-metric which has shown promising results in these figures. More discussion on the MAE would be appreciated.\n\nI would encourage the authors to run more experiments with more real-world datasets (possibly ones that are publicly available) so that the readers can get a more comprehensive comparison of the methods. \n\nIt is not clear what the difference is between the FTU predictor and the AML predictor? The text says, in Section 3.1., that “A Fairness-Through Unawareness (FTU) predictor $f_{FTU}(a)$ only uses the non-sensitive attributes” and that “An Averaged Machine Learning (AML) predictor [the mathematical expression] only needs non-sensitive attributes a as its input”. These descriptions are confusing. \n", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: The paper introduces an approach to counterfactual fairness based on data pre-processing, and compare it to other two counterfactual fairness approaches on the Adult and COMPAS datasets.

The reviewers are in agreement that, in its current state, the paper should not be accepted for publication at the venue. Their main concerns are around the metric used to measure fairness, and these were not resolved during the discussion. The reviewers would have also appreciated more experiments on real-world datasets to get a more comprehensive comparison of the methods. Finally,  discussion and comparison with other methods to achieve counterfactual fairness from the literature were limited. 
Decision: Reject