Targeted Learning for Inference on Data Fairness

Joseph H. Rudoler; Alexander Asemota; Giles Hooker

cs.LGFeb 6, 2025

Targeted Learning for Inference on Data Fairness

Authors: Joseph H. Rudoler, Alexander Asemota, Giles Hooker

Organizations: University of California Berkeley, USA · University of Pennsylvania, USA

Abstract

As algorithmic decision making has become increasingly ubiquitous even in high-stakes settings, significant effort has been invested in defining, detecting, and eliminating unfair model-driven outcomes. Prior work has largely focused on estimating the fairness properties of a given predictive model, and quantifying uncertainty based on variability in a fixed model's performance across evaluation datasets. Alternatively, we can also ask about uncertainty that the model inherits from its training data; here we evaluate data fairness - fairness in the data generating process used for training. We perform inference on data fairness using targeted learning, a flexible framework for nonparametric inference, and derive estimators for demographic parity, equal opportunity, and conditional mutual information. Simulations show that our data fairness estimators improve confidence-interval coverage and reduce false detections of population unfairness relative to fixed-model inference. We also demonstrate their application to real data.

Figures & tables

Figure 1. Coverage (top) and rejection rate (bottom) under independent retraining. Columns show the null and two population disparities. Color indicates evaluation size; line style distinguishes TL and model fairness. Reference lines mark nominal coverage $0.95$ and null rejection rate $0.05$ . Under the alternatives, rejection is power. Each point uses 1000 independent training datasets and 50 evaluations per fit; bars and bands show $\pm 1.96$ Monte Carlo standard errors accounting for shared fits.

Figure 2. Coverage (left) and signed bias relative to population data fairness (right) as training size increases. Bias is

100\{R^{-1}\sum_{r=1}^{R}\hat{\Psi}_{r}-\Psi\}

in percentage points. Each point uses

R=1000

replicates and 2000 evaluation observations. Color identifies tree-ensemble capacity; solid circles denote TL and dashed squares denote model fairness. Bars show approximate pointwise Monte Carlo uncertainty (

\pm 1.96

MCSE), not the fairness intervals evaluated within replicates. Reference lines mark

0.95

coverage and zero bias.

Figure 3. CMI estimates and empirical Wald rejection rates as the conditioning set changes. The true CMI is zero when all confounders

Z

are included; outcome-only predictors and noise features are always retained. Left: mean TMLE estimate, with shading between the mean endpoints of the nominal

95\%

two-sided confidence intervals

\hat{I}\pm 1.96\,\widehat{\mathrm{se}}

. Right: empirical rejection rate of the one-sided rule

\hat{I}-1.645\,\widehat{\mathrm{se}}>0

, with the dashed line at the nominal

0.05

level. Each point uses 200 simulations.

Metric	Dataset	Data fairness	Model fairness
Prob. Parity	Adult	0.180 (0.170, 0.191)	0.178 (0.170, 0.185)
	Law	0.192 (0.172, 0.212)	0.194 (0.179, 0.208)
Prob. Eq. Opp.	Adult	0.072 (0.039, 0.105)	0.101 (0.074, 0.129)
	Law	0.135 (0.120, 0.150)	0.127 (0.113, 0.141)
Parity (thresholded)	Adult	0.176 (0.166, 0.186)	0.176 (0.166, 0.186)
	Law	0.228 (0.204, 0.252)	0.228 (0.204, 0.252)

Table 1. Data- and model-fairness estimates with nominal

95\%

confidence intervals in parentheses. Parity and equal-opportunity comparisons share the fitted outcome model and evaluation split. CMI uses TMLE (Section 2.5 ) and is reported only for data fairness.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

		$n_{\rm train}=500$		$n_{\rm train}=10{,}000$
Outcome $\hat{D}$	Group $\hat{\pi}$	Coverage	Bias (pp)	Coverage	Bias (pp)
Oracle	Oracle	0.952 (0.007)	0.01 (0.04)	0.951 (0.007)	0.03 (0.04)
Oracle	Linear	0.949 (0.007)	0.01 (0.04)	0.951 (0.007)	0.03 (0.04)
Linear	Oracle	0.953 (0.007)	0.03 (0.04)	0.955 (0.007)	0.04 (0.04)
Quadratic	Quadratic	0.917 (0.009)	-0.01 (0.04)	0.950 (0.007)	0.03 (0.04)
Quadratic	Linear	0.903 (0.009)	0.02 (0.05)	0.950 (0.007)	0.03 (0.04)

Appendix

Table 2. TL coverage and signed bias for

R=1000

replicates per configuration, at the smallest and largest training sizes in the nuisance-specification experiment. Intervals have nominal 95% coverage. Parentheses contain Monte Carlo standard errors; bias is in percentage points (pp).

Panel of Figure 4 — Figure 4. CMI estimation error for TMLE and KNN (left, 10 replicates per estimator and configuration) and nominal two-sided TMLE interval coverage (right, 100 replicates per configuration). Reference lines mark zero error.

$\kappa$	$I(Y;G\mid X)$
0	0.0000
0.5	0.0054
1	0.0420
1.5	0.1189
2	0.2080
2.5	0.2770

Appendix

Table 3. Monte Carlo conditional CMI truth

I(Y;G\mid X)

by coupling weight; the value at

\kappa=0

is exactly zero.

Figure 5. Paired one-step and TMLE results at the largest sample size in each experiment. Top: bias and two-sided coverage as coupling varies (

n=10{,}000

R=100

). Bottom: mean CMI and one-sided rejection rates as confounders are added (

n=5000

R=200

). Dashed lines mark zero, nominal coverage, or the nominal rejection cutoff.

Experiment	$n$	Method	Bias	Coverage	Rejection
Conditioning	5000	One-step	-0.0186 (0.00039)	0.03 (0.01)	0.00 (0.00)
Conditioning	5000	TMLE	0.000568 (4.4e-05)	0.97 (0.01)	0.09 (0.02)
Coupling	10000	One-step	-0.00971 (0.0002)	0.00 (0.00)	0.00 (0.00)
Coupling	10000	TMLE	0.000128 (1.5e-05)	1.00 (0.00)	0.00 (0.00)

Appendix

Table 4. Empirical bias, two-sided coverage, and one-sided rejection at conditional independence, using the largest sample size in each design. Parentheses contain Monte Carlo standard errors.

Dataset	Observations	Features in $X$
Adult-Income	49,531 total 29,718 training 19,813 evaluation	hours-per-week, age, capital-gain, capital-loss, workclass, education, marital-status, relationship, race, native-country, occupation
Law School	20,798 total 12,478 training 8320 evaluation	decile1b , decile3 , lsat , ugpa , zfygpa , zgpa , fulltime , fam_inc , male , tier

Appendix

Table 5. Dataset sizes and features used in Section 4 . The outcome

Y

and group

G

are excluded from

X

in both datasets.

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Fair Finetuning Mitigates Distribution Inference Attacks

Rakshit Naidu

Georgia Institute of Technology

Data Leakage Algorithmic Fairness Privacy-Preserving ML

Open paper AskPDF arXiv

Machine learning models trained on sensitive data can inadvertently leak population-level information about their training distributions -- a threat known as distribution inference attack (DIA). An adversary with black-box access can infer sensitive demographic properties, such as subgroup proportions, without observing any training data directly. While defenses such as differential privacy and property unlearning have been proposed, the link between fairness constraints and distributional leakage remains unexplored. We propose Fair Fine-tuning (FFt): a trained model is fine-tuned on samples from the complementary distribution under an Equalized Odds (EO) constraint. We provide a complete theoretical characterization, proving the tight bound

\text{Adv}(\mathcal{A},M_f) \le Δ_{\text{EO}} \cdot W

, where

W

quantifies how distinguishable the two training distributions are by their sensitive-attribute composition. We also establish a necessary condition for FFt to reduce adversarial advantage and prove tightness of the bound. We evaluate across six datasets spanning tabular (ACS Income, COMPAS, German Credit), image (UTKFaces), and NLP (Bias in Bios) modalities. Rehearsal-based FFt consistently reduces the adversarial accuracy gap below the detection threshold

τ!=!0.1

across all settings; on ACS Income, the gap falls from

\sim!15%

to under

4%

. Our work provides the first formal bound connecting a model's measured EO disparity directly to its adversarial advantage in the DIA game, opening a new avenue for unified fairness-and-privacy defenses.

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