Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: The paper proposes a mechanism to perform fairness aware feature selection that achieve counterfactual fairness under certain assumptions. 



strengths_and_weaknesses: 
S1 Fairness aware feature selection is an important problem which is underexplored.
S2 Problem setting that complete causal graph may not be available is important.
S3 The paper is easy to follow.


Weaknesses
W1 The critical assumption is that the sensitive attribute does not have any ancestors. Another crucial assumption for the analysis is the absence of confounders. Please discuss the realistic implications of these assumptions and the challenges because of these.

W2 It is unclear how noise in MPDAG would affect the quality of this approach. Please discuss this in light of cases where it is learned from data.

W3 Experiments on real data do not show how their approach is able to ensure fairness of the trained classifier.

W4 Related Work: There is no discussion of these techniques as compared to this recent paper which does not assume knowledge of causal graph and performs feature selection.
[1] Causal Feature Selection for Algorithmic Fairness. S Galhotra, K Shanmugam, P Sattigeri, KR Varshney. SIGMOD 2022.

W5 Algorithm complexity seems quite high. Please discuss running time on real datasets.
questions: Please clarify the connection to related work and how sensitive this approach is with respect to noise in MPDAG.
limitations: The authors have clearly discussed their assumptions.
review_title: null

final_score: rating: 3: Reject: For instance, a paper with technical flaws, weak evaluation, inadequate reproducibility and incompletely addressed ethical considerations.
review_content: summary: This paper works within a structural causal modeling (SCM) framework for defining fairness of algorithms. Previous literature defining fairness this way assumes knowledge of the relevant SCM, which is a key limitation. The current paper relaxes this assumption to some specific contexts where the SCM is partially known, that is when a maximally partially directed acyclic graph (MPDAG) is available rather than a full directed acyclic graph (DAG). In the MPDAG framework a variable can be a definite descendent, definite non-descendent, or a possible descendent of other variables. This paper provides algorithms for determining which of these relationships holds for a given pair of variables and theorems to establish the correctness of the algorithms. The application to fairness involves considering which variables are definite or possible descendants of a sensitive attribute, and proposing corresponding definitions of fairness based on whether only definite non-descendants are used in the prediction (Fair) or possible descendants are also included (FairRelax) and only definite descendants are excluded. 

strengths_and_weaknesses: Strength: SCM approaches rely on very strong assumptions so it is useful to relax these.

Strength: The simulation results use fairly high dimensional DAGs compared to the common examples considered in counterfactual fairness.

Weakness: Many of the results and basically all of the illustrative figures are in appendices. I think the paper could be improved by reorganization that includes showing examples in the main text, like figures 2, 3, and 6 which are currently in the appendices. As it is now, a reader who is not already familiar with PDAG, CPDAG, MPDAG will not know how to visualize these unless they read the supplementary material, and will struggle to understand the definitions and lemmas. 

Weakness: It is possible the technical contribution of the current paper is a relatively small increment, extending Lemma 4.4 from previous work on CPDAGs. Since much of the details is in the appendix I did not review it all carefully enough to compare with the previous papers. This paper could be strengthened by clarifying which parts are new contributions.
questions: Q1: Counterfactual fairness is possible even with definite descendants provided counterfactual changes “cancel out” in the prediction. The current paper gives an incorrect definition on lines 51-53 which is based on a sufficient (but not necessary) condition for counterfactual fairness. 

Q2: Should the unfairness of Oracle and Fair methods in the simulations be exactly zero, even in samples? I would think it will be close to zero in each realization and very close to zero on average, with small standard errors- but not necessarily exactly zero.

Q3: Most of the methods proposed in this paper do not seem to be necessarily connected to fairness. Presumably it is of more general interest to determine the ancestral relationships in an MPDAG. Would it make more sense to reframe the paper as a general method within the SCM literature, and its application to fairness just one of the motivating examples? This may also strengthen the paper since, as I point out in Q1, the connection of the current methods to fairness is based on a sufficient condition which may not be necessary, and hence it may not be a strong enough connection for fairness to be a main focus of the paper.

Minor issue: In section 5.1, isn’t the inclusion of “(possibly small)” a bit of wishful thinking? The violation of fairness could also possibly be large. Without knowledge of a specific context to justify either possibility perhaps this speculation should be omitted.

Minor issue: citing preprints instead of published versions, e.g. of [21, 23, 56]

limitations: The weaknesses and questions above, as well as the limitations inherited by any SCM type of approach which include untestable assumptions. The current paper also acknowledges its assumptions of no confounding or selection bias, but it is reasonable to try to address that in future work rather than all at once.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: Given an MPDAG, the authors prove a method that can identify whether a variable is a definite descendant, definite non-descendant, or possible descendant of another variable. Building upon this result, the authors further study the problem of learning counterfactually fair models via selecting features.
strengths_and_weaknesses: Overall, I think this paper is relevant, new, and interesting. The paper is well-written and well-organized. The motivation is clearly described and the contribution is also clear. However, there is a technical lemma that seems flawed. Please refer to the detailed questions below.
questions: 1. The introduction of b-critical set (Definition 4.2) is not necessary. Since a chordless b-possibly causal path from S to T definitely has no chord, it degenerates to a partially directed path. Therefore, there is no essential difference between the definition of b-critical set and the definition of critical set defined by Fang and He (2020), except that the latter is defined with respect to CPDAGs.

2. It seems to me that Lemma B.2 is flawed. Lemma B.2 states that if $R\subseteq sib(X, G)$ has a subset that induces a complete subgraph, then there is a DAG $D$ in $[G]$ such that $pa(X, D)=pa(X, G)\cup R$. If Lemma B.2 is correct, then for any $R\subseteq sib(X, G)$ that induces a complete subgraph, there is a DAG $D$ in $[G]$ such that $pa(X, D)=pa(X, G)\cup R$. However, this is impossible. For example, consider a complete graph with 4 variables: $X, S_1, S_2, C$. Every edge except $C\to S_1$ is undirected. Let $R=\\{S_1, S_2\\}$. $R$ induces a complete subgraph, but orienting $R\to X$ and $X \to C$ will lead to a directed cycle.

3. A minor point. Some cited papers have been published. Please revise the bib to make sure that their latest versions are cited. 

limitations: The limitations of the paper have been addressed.
review_title: null

Meta-review: metareview: This paper has divergent views in the sense two reviewers have given positive assessments (6 and 7) while the other reviewer has given a negative assessment (score of 3). This paper also had very 'heavy' discussions between the reviewer with negative opinion and the authors.

First of all I would like to thank the reviewer involved in patiently discussing with the authors dedicating valuable personal time. 
Let me start with the aspects all reviewers *more or less agree* on :

a) The main technical piece is an efficient algorithm and provable guarantees for identifying definite non-descendants and definite descendants from an MPDAG - maximum partially directed acyclic graph - the equivalence class of Causal DAGs one obtains after incorporating any arbitrary side information. Previous such results were known for CPDAGs and they don't carry over to MPDAGs. Therefore it is a non trivial result (specifically Lemma 4.4 ). So all reviewers agree that finding definite non descendants in Equivalence classes that also include side information is a very solid contribution. 


b) The aspect in which reviewers had divergent opinion is this:  the paper's claim to be able to train counterfactual fair classifiers leveraging the result from [Kusner et. al 2017] that any function of non-descendants is counterfactually fair.

One of the reviewer's strong contention is that in most fairness datasets, most variables that are highly predictive of outcomes will also be downstream of sensitive attributes like race etc.. and therefore relying only on non-descendants is not exactly a realistic application. Authors cited their empirical structure learning results that show very few descendants and comments from Kusner et. al 2017 paper to bolster their case. Reviewer responded by citing alternate statements from the same paper etc.. 

*My opinion* is that in a specific context when fairness with respect to a specific sensitive attribute is desired, there are also often other features that has no causal relationship with the sensitive attribute but has a *correlation* (Examples include age and race, race and gender etc.. ).  To cite a recent reference please see Example 15 in https://arxiv.org/pdf/2207.11385.pdf (this reference is recent and I am *not* expecting authors or anyone else to have known this - it is just to demonstrate the point). The example shows *testable* correlations between sensitive attributes and non-descendants in COMPAS and Adult datasets. 

This shows that a) neither causal sufficiency  nor b) the non-existence of non-descendants are realistic . In fact, spuriously related non-descendants give rise to spurious bias which may not be an object of correction for fairness (broadly speaking). This shows that causal sufficiency is a strong assumption (as authors have assumed) and also non-descendants do exist.

c) Another point to be noted is that Kusner et. al. 2017 do consider confounded models unlike the authors. Once you view exogenous, endogenous (observed) variables and sensitive attribute as one full deterministic system, their point is ALL exogenous + non descendant endogenous variables are "non-descendants" topologically and therefore could be used. They did not imply non-descendants endogenous 'only' as the authors contend in their discussions.  In fact, the algorithm section in Kusner et. al. 2017 - advocates for sampling Exogenous from some side information (level 2 and 3 information) and forming a predictor as a function of exogenous *and* non descendant endogenous variables. 
Therefore, reviewer has a valid point on the discussed aspect as well. Authors may want to pay attention to this.


*In summary*: Authors' contention that Kusner et al 2017 paper advocates for non-descendant endogenous as their main sufficient criterion appears to be not exactly correct. However, non-descendants and their confounding with sensitive attribute is a more realistic model. However, authors core technical structure learning contribution is also noteworthy.

 If this line of work is to be pursued where one could find non descendants even under limited confounding (between sensitive attributes and non- descendants - a mild violation of causal sufficiency) - it would be a step towards obtaining counterfactually fair classifiers (although even such a classifier would have to sacrifice a lot on accuracy depending on how many descendants one observes).  However, even positive reviewers have opined that main strength of the paper is a solid structure learning result that identifies non-descendants in a fully observational setting.

*Recommendation*: In the spirit of not blocking valid ideas that are fundamental and also the fact that one cannot always make the weakest set of assumptions to make progress, I tend to favor acceptance. A *very strong* suggestion to authors - I would place structure learning as the centerpiece and motivate it by a need to learn non-descendants (in the general sense) motivated by Kusner et al 2017. Authors also need to highlight Fair relax - a relaxation that they have proposed that uses possible descendants and definite non descendants to predict - it seems to be closer than other approaches to counterfactually fair one and therefore removing the singular focus on (as the discussions would have one believe) only observed definite non-descendants.



confidence: Less certain
Decision: Accept