SlowGuess/NeurIPS_2023_OCR huggingface dataset:
The number of affected individuals in the test set for the COMPAS dataset is 745. We first split the affected individuals on the set of affected Caucasians  $D_{1}$  and the set of affected African Americans  $D_{0}$ . The number of subgroups formed by running fp-growth with support threshold  $1\%$  on  $D_{1}$  and on  $D_{0}$  and computing their intersection is 995. Our fairness metrics will evaluate and rank these subgroups based on the actions applied.
F.4 Comparison on SSL
The number of affected individuals in the test set for the SSL dataset is 11,343. We first split the affected individuals on the set of affected blacks  $D_{1}$  and the set of affected whites  $D_{0}$  based on the race attribute (appears with the name RACE CODE CD in the dataset). The number of subgroups
Table 18: Aggregated Rankings in Adult (protected attribute race)
(Equal Cost of Effectiveness (Macro), 0.3)	(Equal Cost of Effectiveness (Macro), 0.7)	(Equal Choice for Recourse, 0.3)	(Equal Choice for Recourse, 0.7)	Equal Effectiveness	(Equal Effectiveness within Budget, 1.15)	(Equal Effectiveness within Budget, 10.0)	(Equal Effectiveness within Budget, 21.0)	(Equal Cost of Effectiveness (Micro), 0.3)	(Equal Cost of Effectiveness (Micro), 0.7)	(Equal Conditional Mean Recourse)	(Fair Effectiveness-Cost Trade-Off, value)
(Equal Cost of Effectiveness(Macro), 0.3)	-	1.0	0.845	1.0	0.162	0.996	0.283	0.177	0.026	1.0	0.448	0.194
(Equal Cost of Effectiveness(Macro), 0.7)	0.7	-	0.9	0.829	0.147	0.973	0.315	0.169	0.698	0.05	0.421	0.12
(Equal Choice for Recourse, 0.3)	0.419	1.0	-	1.0	1.0	1.0	1.0	0.03	0.10	0.782	0.073	0.073
(Equal Choice for Recourse, 0.7)	1.0	0.095	0.909	-	0.644	1.0	0.003	0.328	1.0	0.1	0.041	0.011
Equal Effectiveness	0.023	1.0	0.909	1.0	-	1.0	0.01	0.0	0.023	1.0	0.0	0.0
(Equal Effectiveness within Budget, 1.15	1.0	0.048	1.0	0.857	0.069	-	0.047	0.07	1.0	0.05	1.0	0.102
(Equal Effectiveness within Budget, 10.0	0.395	0.048	0.818	0.571	0.001	1.0	-	0.001	0.395	0.05	0.611	0.002
(Equal Effectiveness within Budget, 21.0)	0.023	1.0	0.909	1.0	0.0	1.0	0.01	-	0.023	1.0	0.0	0.0
(Equal Cost of Effectiveness(Macro), 0.3)	0.023	1.0	0.845	1.0	0.162	0.998	0.284	0.177	1.0	0.449	0.195	0.195
(Equal Cost of Effectiveness(Macro), 0.7)	0.7	0.048	0.9	0.829	0.147	0.973	0.315	0.169	0.698	0.05	0.421	0.12
Equal(Conditional) Mean Recourse	0.979	1.0	1.0	1.0	0.628	1.0	0.778	0.633	0.979	1.0	-	0.721
(Fair Effectiveness-Cost Trade-Off Value)	0.023	1.0	0.818	1.0	0.001	1.0	0.012	0.001	0.023	1.0	0.003	-
Table 19: Ranking Analysis in COMPAS
# Most Unfair Subgroups	# Subgroups w. Bias against Caucasians (in Top 10% Unfair Subgroups)	# Subgroups w. Bias against African-Americans (in Top 10% Unfair Subgroups)
(Equal Cost of Effectiveness(Macro), 0.3)	51	0	11
(Equal Cost of Effectiveness(Macro), 0.7)	46	0	6
(Equal Choice for Recourse, 0.3)	13	12	8
(Equal Choice for Recourse, 0.7)	15	8	6
Equal Effectiveness	1	14	37
(Equal Effectiveness within Budget, 1.0)	4	16	30
(Equal Effectiveness within Budget, 10.0)	1	20	39
(Equal Cost of Effectiveness(Micro), 0.3)	51	0	11
(Equal Cost of Effectiveness(Micro), 0.7)	46	0	6
Equal(Convictional Mean Recourse)	37	19	24
(Fair Effectiveness-Cost Trade-Off, value)	5	18	62
Table 20: Aggregated Rankings in COMPAS
(Equal Cost of Effectiveness (Macro), 0.3)	(Equal Cost of Effectiveness (Macro), 0.7)	(Equal Choice for Recourse, 0.3)	(Equal Choice for Recourse, 0.7)	Equal Effectiveness	(Equal Effectiveness within Budget, 1.0)	(Equal Effectiveness within Budget, 10.0)	(Equal Cost of Effectiveness (Micro), 0.3)	(Equal Cost of Effectiveness (Micro), 0.7)	Equal/Conditional Mean Recourse)	(Fair Effectiveness-Cost Trade-Off, value)
(Equal Cost of Effectiveness(Macro), 0.3)	-	1.0	0.65	1.0	0.169	0.801	0.398	0.2	1.0	0.797	0.226
(Equal Cost of Effectiveness(Macro), 0.7)	0.96	-	0.925	0.625	0.127	0.518	0.236	0.96	0.2	0.52	0.149
(Equal Choice for Recourse, 0.3)	0.32	0.76	-	0.775	0.082	1.0	0.178	0.32	0.76	0.297	0.116
(Equal Choice for Recourse, 0.7)	0.9	0.46	0.8	-	0.424	0.484	0.057	0.9	0.46	0.259	0.045
Equal Effectiveness	0.2	1.0	0.75	1.0	-	1.0	0.003	0.2	1.0	0.003	0.002
(Equal Effectiveness within Budget, 1.0)	0.8	1.0	0.75	0.75	1.0	-	1.0	0.8	1.0	0.413	0.002
(Equal Effectiveness within Budget, 10.0)	0.2	1.0	0.75	1.0	0.003	1.0	-	0.2	1.0	0.003	0.002
(Equal Cost of Effectiveness(Micro), 0.3)	0.2	1.0	0.65	1.0	0.169	0.801	0.398	-	1.0	0.797	0.226
(Equal Cost of Effectiveness(Micro), 0.7)	0.96	0.2	0.925	0.625	0.127	0.518	0.236	0.96	-	0.52	0.149
Equal(Conditional) Mean Recourse	0.98	1.0	1.0	1.0	0.507	0.772	0.512	0.98	1.0	-	0.627
(Fair Effectiveness-Cost Trade-Off, value)	0.68	1.0	0.75	0.8	0.801	0.202	0.801	0.68	1.0	0.331	-
formed by running fp-growth with support threshold  $1\%$  on  $D_{1}$  and on  $D_{0}$  and computing their intersection is 6,551. Our fairness metrics will evaluate and rank these subgroups based on the actions applied.
Table 21: Ranking Analysis in SSL
# Most Unfair Subgroups	# Subgroups w. Bias against Whites (in Top 10% Unfair Subgroups)	# Subgroups w. Bias against Blacks (in Top 10% Unfair Subgroups)
(Equal Cost of Effectiveness(Macro), 0.3)	371	10	107
(Equal Cost of Effectiveness(Macro), 0.7)	627	26	124
(Equal Choice for Recourse, 0.3)	1	108	184
(Equal Choice for Recourse, 0.7)	16	78	229
Equal Effectiveness	1	15	389
(Equal Effectiveness within Budget, 1.0)	18	18	436
(Equal Effectiveness within Budget, 2.0)	2	19	532
(Equal Effectiveness within Budget, 10.0)	1	15	548
(Equal Cost of Effectiveness(Micro), 0.3)	458	5	135
(Equal Cost of Effectiveness(Micro), 0.7)	671	23	130
Equal(Conditional Mean Recourse)	100	41	434
(Fair Effectiveness-Cost Trade-Off, value)	80	76	544
Table 22: Aggregated Rankings in SSL
(Equal Cost of Effectiveness (Macro), 0.3)	(Equal Cost of Effectiveness (Macro), 0.7)	(Equal Choice for Recourse, 0.3)	(Equal Choice for Recourse, 0.7)	Equal Effectiveness	(Equal Effectiveness within Budget, 1.0)	(Equal Effectiveness within Budget, 2.0)	(Equal Effectiveness within Budget, 10.0)	(Equal Cost of Effectiveness (Micro), 0.3)	(Equal Cost of Effectiveness (Micro), 0.7)	Equal/Conditional Mean Recourse)	(Fair Effectiveness-Cost Trade-Off, value)
(Equal Cost of Effectiveness(Macro), 0.3)	-	0.883	0.854	0.988	0.216	0.401	0.285	0.238	0.3	0.843	0.678	0.338
(Equal Cost of Effectiveness(Macro), 0.7)	0.929	-	0.877	0.725	0.239	0.421	0.332	0.264	0.871	0.314	0.829	0.342
(Equal Choice for Recourse, 0.3)	0.143	1.0	-	1.0	0.328	0.704	0.464	0.368	0.143	1.0	0.727	0.601
(Equal Choice for Recourse, 0.7)	1.0	0.167	0.769	0.983	0.083	0.177	0.127	0.086	0.130	1.0	0.143	0.135
Equal Effectiveness	0.143	0.167	0.923	0.938	0.002	0.0	0.0	0.143	0.143	0.0	0.003
(Equal Effectiveness within Budget, 1.0)	0.857	0.833	0.854	0.881	0.89	-	0.923	0.876	0.857	0.857	0.327	0.0
(Equal Effectiveness within Budget, 2.0)	0.286	0.333	0.923	0.938	0.5	0.002	-	0.286	0.286	0.0	0.003
(Equal Effectiveness within Budget, 10.0)	0.143	0.167	0.923	0.938	0.0	0.002	0.0	0.143	0.143	0.0	0.003
(Equal Cost of Effectiveness(Micro), 0.3)	0.443	0.833	0.877	0.969	0.143	0.32	0.198	0.154	0.843	0.729	0.268
(Equal Cost of Effectiveness(Micro), 0.7)	0.9	0.383	0.892	0.788	0.203	0.406	0.299	0.225	0.886	-	0.816	0.327
Equal(Conditional) Mean Recourse	0.6	0.733	0.946	0.969	0.244	0.464	0.395	0.378	0.514	0.729	-	0.396
(Fair Effectiveness-Cost Trade-Off, value)	0.971	0.967	0.838	0.869	0.967	0.774	0.977	0.96	0.971	0.971	0.837	-
F.5 Comparison on Ad Campaign
The number of affected individuals in the test set for the Ad campaign dataset is 273,773. We first split the affected individuals on the set of affected males  $D_{1}$  and the set of affected females  $D_{0}$  based on the gender attribute. The number of subgroups formed by running fp-growth with support threshold  $1\%$  on  $D_{1}$  and on  $D_{0}$  and computing their intersection is 1,432. Our fairness metrics will evaluate and rank these subgroups based on the actions applied.
Table 23: Ranking Analysis in Ad Campaign
# Most Unfair Subgroups	# Subgroups w. Bias against Males (in Top 10% Unfair Subgroups)	# Subgroups w. Bias against Females (in Top 10% Unfair Subgroups)
(Equal Cost of Effectiveness(Macro), 0.3)	427	0	44
(Equal Cost of Effectiveness(Macro), 0.7)	264	0	26
(Equal Choice for Recourse, 0.3)	2	10	66
(Equal Choice for Recourse, 0.7)	384	0	39
Equal Effectiveness	15	0	123
(Equal Effectiveness within Budget, 1.0)	1	0	42
(Equal Effectiveness within Budget, 5.0)	10	0	114
(Equal Cost of Effectiveness(Micro), 0.3)	427	0	44
(Equal Cost of Effectiveness(Micro), 0.7)	264	0	26
Equal(Conditional Mean Recourse)	108	9	74
(Fair Effectiveness-Cost Trade-Off, value)	15	0	128
Table 24: Aggregated Rankings in Ad Campaign
Equal Cost of Effectiveness (Macro), 0.3)	Equal Cost of Effectiveness (Macro), 0.7)	Equal Choice for Recourse, 0.3)	Equal Choice for Recourse, 0.7)	Equal Effectiveness	Equal Effectiveness within Budget, 1.0)	Equal Effectiveness within Budget, 5.0)	(Equal Cost of Effectiveness (Micro), 0.3)	(Equal Cost of Effectiveness (Micro), 0.7)	Equal (Conditional Mean Recourse)	(Fair Effectiveness-Cost Trade-Off, value)
(Equal Cost of Effectiveness(Macro), 0.3)	-	0.7	0.483	0.6	0.167	1.0	0.276	0.25	0.7	0.487	0.154
(Equal Cost of Effectiveness(Macro), 0.7)	0.25	-	0.35	0.333	0.082	1.0	0.21	0.25	0.5	0.506	0.079
(Equal Choice for Recourse, 0.3)	0.25	1.0	-	1.0	0.73	1.0	1.0	0.25	1.0	0.037	0.338
(Equal Choice for Recourse, 0.7)	0.5	0.65	0.333	-	0.296	0.851	0.385	0.5	0.65	0.566	0.273
Equal Effectiveness	0.25	0.5	0.333	0.333	-	1.0	0.205	0.25	0.5	0.002	0.001
(Equal Effectiveness within Budget, 1.0)	1.0	1.0	1.0	1.0	0.714	-	0.671	1.0	1.0	0.305	0.395
(Equal Effectiveness within Budget, 5.0)	0.25	0.5	0.333	0.333	0.001	1.0	-	0.25	0.5	0.002	0.001
(Equal Cost of Effectiveness(Micro), 0.3)	0.25	0.7	0.483	0.6	0.167	1.0	0.276	-	0.7	0.487	0.154
(Equal Cost of Effectiveness(Micro), 0.7)	0.25	0.5	0.35	0.333	0.082	1.0	0.21	0.25	-	0.506	0.079
Equal (Conditional) Mean Recourse	0.525	0.75	0.65	0.7	0.25	1.0	0.408	0.525	0.75	-	0.267
(Fair Effectiveness-Cost Trade-Off, value)	0.25	0.5	0.333	0.333	0.001	1.0	0.205	0.25	0.5	0.002	-
G Discussion of Limitations & Responsible Usage Guidelines
Determining costs for specific counterfactuals poses numerous challenges and constraints. The associated cost functions are intricate, dataset-specific, and frequently require the expertise of a domain specialist. These cost functions can depend on individual characteristics or human interpretation of the perceived difficulty of specific changes, potentially giving rise to concerns like breaches of user privacy (as the expert may require access to all individual user characteristics [25]) or potential manipulation of cost functions by malicious specialists to conceal existing biases.
Recognizing the difficulties of finding the dataset-dependent cost functions, we implement various "natural" cost functions tailored to different feature types (e.g.,  $L_{1}$  norm, exponential distances, etc.). These serve only as suggestions to the expert using our framework, are susceptible to change, and can be customized for specific datasets. While the creation of precise cost models is an interesting research area, it is not our primary focus. Instead, our primary goal is to identify a specific type of bias (difficulty to achieve recourse) towards specific subpopulations. Therefore, we have introduced fairness metrics that are independent of cost considerations, recognizing the aforementioned inherent difficulties in defining costs. We recognize that a single metric, whether cost-dependent or not, cannot identify all forms of bias that may be present within a model's predictions. We do not aim to replace the existing statistical measures for bias detection, rather than complement them and capture possible gaps, as described in the introduction of our paper and Section 5.
Our framework evaluates subgroups based on a range of fairness metrics, identifying 'candidate' subgroups that may experience unfair treatment under scrutiny. While the number of such 'candidate' subgroups can be substantial across different metrics, this abundance can serve as a safeguard against malicious users, as cost-oblivious rules are immune to user influence. We emphasize our efforts to produce comprehensive summaries that are easily understandable for the end-users and help them make informative decisions regarding the existence of the groups that are unfairly treated.
The ultimate decision regarding which of the 'candidate' subgroups are considered unfairly treated rests with the expert. Our comprehensive summaries highlight the top-scoring 'candidate' subgroups across multiple metrics, with the ultimate goal of helping the end users and deterring malicious users from deliberately ignoring the framework's suggestions. Explanations accompany FACTS' suggestions, requiring users to justify their rejection and serving as a barrier against deliberate malicious actions. While our summaries are interpretable and customizable, we plan to enhance our framework with visualizations in future work to further assist end-users. A user study would also be helpful to assess FACTS' interpretability to the end-user.
It is important to note that FACTS, like other resource generation algorithms, may be susceptible to errors, as demonstrated in prior research [31]. The outcomes produced by FACTS can vary based on the chosen configuration, including hyperparameters and metric selection. These variations can either obscure biases present within a classifier or indicate their absence. It is crucial to emphasize that since FACTS is an explainable framework for bias assessment within subgroups, its primary purpose is to serve as a guidance tool for auditors to identify subgroups requiring in-depth analysis of fairness criteria violations. Responsible usage of our framework necessitates transparency regarding the chosen configuration. Therefore, we recommend running FACTS with different hyperparameters and utilizing as many metrics as possible.
Another potential limitation relates to GDPR and similar regulations, which may restrict access to protected attributes (confidential information, etc.) even in bias detection applications. It's important to clarify that our framework maintains privacy and avoids personal information leakage. Only summaries of results are presented to the end-users, limited to subgroups that impose the minimum size requirement. These features could be further enhanced by adding restrictions to the size requirements if legislation or standardized requirements existed. In essence, our approach addresses complex challenges in bias detection, while upholding fairness, respecting privacy requirements, and ensuring interpretability for end-users.
An acknowledged constraint of our framework pertains to how we generate actions, as explained in Section 3. Both actions and subgroups are derived using a frequent itemset mining algorithm. We have consciously opted against altering our approach to action generation, to minimize computational complexity and enhance action effectiveness. Importantly, the same actions are applied to all groups sharing a common predicate during the computation of fairness metrics.