The End Of Knowledge - Vault 6/79 - CVPR - 2022 - Causal Conceptions of Fairness and their Consequences

graph LR classDef fairness fill:#d4f9d4, font-weight:bold, font-size:14px classDef utility fill:#f9d4d4, font-weight:bold, font-size:14px classDef counterfactual fill:#d4d4f9, font-weight:bold, font-size:14px classDef mathematical fill:#f9f9d4, font-weight:bold, font-size:14px A[Causal Conceptions of
Fairness and their
Consequences] --> B[Causal fairness:
fairness via
causal reasoning. 1] A --> C[Counterfactual equalized
odds:
equal rates in
counterfactual scenarios. 2] A --> D[Conditional principal
fairness:
independence given
outcomes, covariates. 3] A --> E[Path-specific fairness:
limits effects
along causal
paths. 4] A --> F[Counterfactual predictive
parity:
equal success rates
if accepted. 5] A --> G[Utility-maximizing policies:
maximize utility
within constraints. 6] B --> H[Pareto dominance:
preferred by
all decision
makers. 7] H --> I[Prevalence:
generalizes sets
to infinite
dimensions. 8] I --> J[U-fine distributions:
utilities with
a density. 9] J --> K[Threshold policies:
accept above
a utility
threshold. 10] H --> L[Multiple threshold
policies:
group-specific utility
thresholds. 11] C --> M[Budget-exhausting policies:
use full
available budget. 12] M --> N[Consistent utilities:
agree on sign,
ordering within
groups. 13] N --> O[Overlapping utilities:
positive decisions
in each
stratum. 14] O --> P[Splitting utilities:
all positive or
negative decisions. 15] D --> Q[Counterfactuals:
potential outcomes
in hypothetical
scenarios. 16] Q --> R[Path-specific counterfactuals:
intervening along
certain paths. 17] R --> S[Structural equations:
define causal
relationships
mathematically. 18] A --> T[Causal DAG:
graph of
causal
relationships. 19] T --> U[Total variation
norm:
metric for
comparing measures. 20] U --> V[Pushforward measure:
measure induced
by function
application. 21] V --> W[Radon-Nikodym derivative:
density of one
measure with
another. 22] A --> X[Absolute continuity:
zero measure
assignment
preservation. 23] X --> Y[Universal measurability:
measurable sets
under all
Borel measures. 24] Y --> Z[Shy sets:
measure zero
sets in
infinite dimensions. 25] Z --> AA[Probe:
subspace to
detect shy
sets. 26] A --> AB[Markov chains:
systems transitioning
between
states. 27] AB --> AC[Recurrent classes:
states where
systems get
trapped. 28] AC --> AD[Beta distribution:
probability distribution
on 0,1. 29] AD --> AE[Infra-marginality:
persistent group
differences despite
equality. 30] class B,C,D,E,F fairness class G,H,I,J,K,L utility class M,N,O,P,Q,R counterfactual class S,T,U,V,W,X,Y,Z,AA,AB,AC,AD,AE mathematical

Resume:

1.- Causal fairness: Algorithmic fairness definitions based on causal reasoning about the effects of protected attributes and decisions on outcomes.

2.- Counterfactual equalized odds: Requires equal true/false positive rates across groups in counterfactual scenarios where decisions are altered.

3.- Conditional principal fairness: Decisions should be independent of protected attributes given potential outcomes and reduced covariates.

4.- Path-specific fairness: Limits effects of protected attributes on decisions along certain causal paths while allowing effects along others.

5.- Counterfactual predictive parity: Among rejected applicants, proportion who would have succeeded if accepted should be equal across groups.

6.- Utility-maximizing policies: Decision policies that maximize a utility function while satisfying fairness constraints and budget limitations.

7.- Pareto dominance: A policy Pareto dominates another if it's preferred by all decision makers with a certain class of utility functions.

8.- Prevalence: Generalizes "full measure" sets to infinite-dimensional spaces, used to characterize generic properties of probability distributions.

9.- U-fine distributions: Probability distributions where utilities have a density, avoiding issues with atoms in the utility distribution.

10.- Threshold policies: Decision rules that accept individuals above a threshold value of utility.

11.- Multiple threshold policies: Decision rules with group-specific thresholds on utility.

12.- Budget-exhausting policies: Decision rules that use the full available budget (e.g. admit the maximum allowed number of students).

13.- Consistent utilities: A set of utility functions that agree on the sign and relative ordering of utilities within groups.

14.- Overlapping utilities: When a non-trivial threshold policy results in some positive decisions within each stratum of reduced covariates.

15.- Splitting utilities: When a threshold policy results in all positive or all negative decisions within each stratum of reduced covariates.

16.- Counterfactuals: Potential outcomes under hypothetical scenarios, like outcomes if decisions or protected attributes were different.

17.- Path-specific counterfactuals: Outcomes when intervening on protected attributes only along certain causal paths.

18.- Structural equations: Mathematical functions defining causal relationships between variables in a causal model.

19.- Causal DAG: Directed acyclic graph representing causal relationships between variables.

20.- Total variation norm: Metric for comparing probability measures, used to define convergence of measures.

21.- Pushforward measure: Measure induced on the output space by applying a function to a measure on the input space.

22.- Radon-Nikodym derivative: Density of one measure with respect to another, used to define densities of probability distributions.

23.- Absolute continuity: Property where one measure assigns zero to any set assigned zero by another measure.

24.- Universal measurability: Sets measurable under all finite Borel measures, used to define shy sets.

25.- Shy sets: Generalization of measure zero sets to infinite-dimensional spaces.

26.- Probe: Finite-dimensional subspace used to detect shy sets.

27.- Markov chains: Mathematical systems transitioning between states with probabilities depending only on the current state.

28.- Recurrent classes: Sets of states in a Markov chain that the system eventually gets trapped in.

29.- Beta distribution: Continuous probability distribution defined on the interval [0,1], used to model utilities in examples.

30.- Infra-marginality: Issue where group differences persist even after equalizing decision rates due to within-group heterogeneity.

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