PDF《Avoiding Discrimination through》

s causal interpretation of Simpson'

s paradox [11, Section 6], we propose causality as a way of coping with this unidenti?ability result. An interesting non-observational fairness de?nition is the notion of individual fairness [3] that as- sumes the existence of a similarity measure on individuals, and requires that any two similar individ- uals should receive a similar distribution over outcomes. More recent work lends additional support to such a de?nition [12]. From the perspective of causality, the idea of a similarity measure is akin to the method of matching in counterfactual reasoning [13, 14]. That is, evaluating approximate counterfactuals by comparing individuals with similar values of covariates excluding the protected attribute. Recently, [15] put forward one possible causal de?nition, namely the notion of counterfactual fair- ness. It requires modeling counterfactuals on a per individual level, which is a delicate task. Even determining the effect of race at the group level is dif?cult;

see the discussion in [16]. The goal of our paper is to assay a more general causal framework for reasoning about discrimination in machine learning without committing to a single fairness criterion, and without committing to evaluating in- dividual causal effects. In particular, we draw an explicit distinction between the protected attribute (for which interventions are often impossible in practice) and its proxies (which sometimes can be intervened upon).

2 Moreover, causality has already been employed for the discovery of discrimination in existing data sets by [14, 17]. Causal graphical conditions to identify meaningful partitions have been proposed for the discovery and prevention of certain types of discrimination by preprocessing the data [18]. These conditions rely on the evaluation of path speci?c effects, which can be traced back all the way to [11, Section 4.5.3]. The authors of [19] recently picked up this notion and generalized Pearl'

s approach by a constraint based prevention of discriminatory path speci?c effects arising from counterfactual reasoning. Our research was done independently of these works. 1.3 Causal graphs and notation Causal graphs are a convenient way of organizing assumptions about the data generating process. We will generally consider causal graphs involving a protected attribute A, a set of proxy variables P, features X, a predictor R and sometimes an observed outcome Y. For background on causal graphs see [11]. In the present paper a causal graph is a directed, acyclic graph whose nodes represent random variables. A directed path is a sequence of distinct nodes V1,Vk, for k ≥ 2, such that Vi → Vi+1 for all i ∈ {1,k ? 1}. We say a directed path is blocked by a set of nodes Z, where V1, Vk / ∈ Z, if Vi ∈ Z for some i ∈ {2,k ? 1}.1 A structural equation model is a set of equations Vi = fi(pa(Vi), Ni), for i ∈ {1,n}, where pa(Vi) are the parents of Vi, i.e. its direct causes, and the Ni are independent noise vari- ables. We interpret these equation........