Learning Representational Disparities

Daniel B. Neill; Pavan Ravishankar; Rushabh Shah

REVIEW 4 major objections 4 minor 42 references

Learning Representational Disparities

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper proves that, under simplifying assumptions, a neural network modeling the difference between observed and desired human decisions learns interpretable weights that fully eliminate downstream outcome disparity, with the optimal…

desk verdict Novel framing for modeling human decision biases with a downstream outcome objective, but the main theorem assumes away the biased-outcome cases the paper motivates and tests. read the letter →

arxiv 2505.17533 v1 pith:NQP4PCRT submitted 2025-05-23 cs.LG cs.AIcs.CY

Pavan Ravishankar , Rushabh Shah , Daniel B. Neill This is my paper · ORCID

classification cs.LGcs.AIcs.CY MSC 68T0568T07

keywords fairmachinelearningrepresentationaldisparityinterpretableweightsoutcomealgorithm-in-the-loopneuralnetworkL1regularizationhumandecision-making

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper aims to turn fairness in human-in-the-loop decision-making into a learnable, interpretable correction. It models the gap between an observed human decision process and a desired fairer process as a 'representational disparity'—a set of extra hidden neurons in a shallow neural network that only the desired decision-maker uses. Under simplifying assumptions, the authors prove that the globally optimal weights are interpretable and fully mitigate disparity in a downstream outcome: exactly one disparity node is active, with closed-form weights set by the observed log-odds gap. This matters because it converts an abstract fairness objective into concrete, actionable nudges to a human decision-maker. Experiments on semi-synthetic German Credit, Adult, and Heritage Health data show that this approach reduces outcome disparity and preserves decision accuracy better than a standard fair-representation baseline.

What carries the argument

The central object is the representational disparity node $R'$, an extra hidden neuron used only by the desired decision-maker, whose contribution to the decision logit is $\mathrm{RD}(s) = w\,\mathrm{ReLU}(w_{SR}\,s + \mathrm{bias})$. The loss is a weighted sum of outcome disparity $A$, an $\ell^1$ penalty $B$ on the disparity node's weights, cross-entropy for the observed decision $C$, and cross-entropy for the outcome $D$; the proof of interpretability rests on the identity that zero disparity forces $w[\mathrm{ReLU}(\mathrm{bias}) - \mathrm{ReLU}(w_{SR}+\mathrm{bias})] = \delta$, reducing the problem to a convex search over weight-sign regions with a closed-form optimum.

What would settle it

Generate a synthetic dataset satisfying assumptions (A1)-(A6) with a known nonzero $\delta$, initialize the disparity-node weights in the region Theorem 4.1 specifies, train with gradient descent, and verify that the final weights equal $w = -\operatorname{sign}(\delta)\sqrt{|\delta|}$, $w_{SR'} = \sqrt{|\delta|}$, $\mathrm{bias} = 0$ and that the measured outcome disparity is exactly zero; repeating the test with assumption (A3) violated, so that $\Pr(Y \mid S, H)$ depends directly on $S$, checks whether the claimed full mitigation actually holds in the biased-outcome regime the paper motivates.

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Extended reading notes

Core claim

On its own terms, the paper's central discovery is a characterization of the global minimum of the proposed multi-objective loss. Under assumptions (A1)-(A3) and (A6), the optimum is attained at a single active representational disparity node with weights $w_i = -\operatorname{sign}(\delta)\sqrt{|\delta|}$, $w_{SR'_i} = \sqrt{|\delta|}$, and bias zero, all other disparity-node weights zero, where $\delta$ is the logit difference between the protected and unprotected groups in the observed decision. The resulting correction satisfies $\mathrm{RD}(1) - \mathrm{RD}(0) = -\delta$, so the desired decision-maker exactly compensates the observed unfairness and the outcome disparity vanishes. When the disparity-loss weight is comparable to the interpretability-loss weight, several optimal strategies exist—shifting one group's probability toward the other, pushing both probabilities to an extreme—but the optimal weights remain interpretable.

Load-bearing premise

The proof's guarantee holds only when the downstream outcome depends on the protected group solely through the human decision (so correcting the decision can fully remove the disparity), not when the outcome itself is directly biased by group membership.

Editorial extensions

If this is right

Fair algorithms can produce actionable nudges: the optimal correction is a single recognizable weight pair, so a practitioner can tell a decision-maker exactly which input to weigh differently.
Learning fair representations that ignore the downstream outcome are insufficient; accounting for bias in $\Pr(Y \mid H)$ is what lets the correction eliminate disparity rather than merely making $H$ independent of $S$.
The closed-form optimum implies the correction's magnitude scales with the square root of the observed log-odds gap, giving a precise calibration target for interventions.
When disparity and interpretability losses are comparable, the method offers a menu of equally optimal corrections (shift one group, push both to extremes), letting policymakers choose by side constraints.
In practice, convergence to the optimal weights is not guaranteed, but multiple random initializations reach it consistently, so the method is usable with an ensemble or selection strategy.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the $\sqrt{|\delta|}$ scaling holds beyond the paper's toy setting, behavioral nudges derived from this model should follow a square-root law: the logit correction needed grows more slowly than the bias itself.
A natural extension the paper leaves implicit is a two-stage correction for settings where outcome bias is too large to be offset by changing $H$ alone; the theory would need to let $H$ depend on $X$ or the bias structure to borrow power from attributes.
The product $w\,w_{SR'}$ emerging from the theorem gives a ready-made audit statistic: measure the learned disparity-node product on real decisions to quantify how much a human's hidden representation shifts by group.
Testing the method on intersectional groups (multiple sensitive attributes) would likely require the disparity node to become a small sub-network rather than a single unit, since one signed scalar can only correct one logit gap.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper has a genuinely new way to frame fair-ML interventions for human decision-makers: learn an interpretable 'representational disparity' between observed and desired decisions, with a downstream outcome objective. That framing is worth taking seriously. The theory, however, supports less than the abstract claims: the key assumption A3 (Y conditionally independent of S given H) rules out exactly the biased-outcome scenarios the paper motivates and tests.

What is new and good: the representational disparity architecture is a real departure from prior fair representation learning, which typically ignores downstream outcomes. The paper correctly identifies that if Pr(Y | H, S) itself is biased, then simply making H independent of S is insufficient; one may need to overcompensate. The empirical comparison to LFR is clean: LRD achieves much lower outcome disparity in the semi-synthetic Cases I-IV while maintaining or improving accuracy. The consistency measure (lower variance in the correction) is a nice touch. The theoretical result that under A3 the optimal correction is a single constant logit shift is clean and interpretable, and the 100-fit synthetic validation shows the optimization works when the assumptions hold.

Three soft spots. Most important, A3 is load-bearing. The theorem proves that fully mitigating disparity is achieved by making H independent of S, but if Y depends on S given H (the Cases I-IV setup), that same solution leaves a residual disparity proportional to the outcome bias b. So the headline 'fully mitigate' guarantee does not apply to the settings the paper argues are novel. The empirical success there is real, but it is not backed by the theorem. Second, the proof of Theorem 4.1 contains a false statement: it claims w=0 makes the total loss infinite; in fact with w=0 the disparity loss is finite (Aw = |α||σ(logit(O(1))) − σ(logit(O(0)))|). That weakens the convergence argument, though the conclusion may be salvageable by a different argument. Third, the synthetic validation of Theorem 4.2 is circular in the sense that the data is generated to satisfy the theorem's assumptions, so recovering the optimal weights is a consistency check, not independent confirmation. Also the real-data results lack error bars, and the comparison is only to LFR.

Who this is for: people working on fairness in human-in-the-loop decision-making, algorithmic nudges, and outcome-based fairness. It deserves a serious referee but not publication in current form. The authors should either restrict the theoretical claims to the A3 setting and present the biased-outcome results as empirically motivated, or extend the theory to cover the biased-outcome case. With those revisions, it could be a solid paper.

Referee Report

4 major / 4 minor

Summary. The paper proposes LRD, a neural-network method that models the difference between an observed human decision-maker and a desired fairer decision-maker as sparse hidden-layer nodes called representational disparity nodes. The method is trained with a multi-objective loss combining outcome disparity, L1 interpretability regularization, fidelity to the observed decision, and fidelity to the downstream outcome. Under simplifying assumptions (A1)-(A6), the paper proves closed-form characterizations of the global minimizer, claiming that the learned weights are interpretable and fully mitigate outcome disparity. The method is validated on synthetic data and on semi-synthetic versions of German Credit, Adult, and Heritage Health, with comparisons to Learning Fair Representations (LFR).

Significance. If the theoretical claims held for the settings the paper emphasizes, this would be a useful contribution: it makes the downstream outcome explicit in fair-representation learning, produces sparse interpretable corrections, and gives closed-form optimal weights under simplifying assumptions. The paper also provides an honest discussion that convergence to the global optimum is not guaranteed in the general case, and it reports sensitivity experiments with respect to the trade-off parameter a. However, the central theoretical guarantee is shown only under assumptions that exclude the biased-outcome cases used to motivate and evaluate the method, and the proof of Theorem 4.1 contains a false statement. The significance therefore depends on whether the claims can be re-scoped or the theory extended.

major comments (4)

[Section 4, Assumption (A3); Section 1; Section 5, Table 4] Assumption (A3) excludes the outcome-bias settings that the paper motivates and evaluates. Section 1 explicitly considers an outcome model Pr(Y | H, S, X) that is biased by S, and the semi-synthetic Cases I–IV (Section 5, Table 4 and Appendix B.2) set b = Pr(Y=1|S=1,H=h) − Pr(Y=1|S=0,H=h) ≠ 0, so A3 is violated by construction for those cases. If Y depends on S directly, then even the Theorem 4.2 solution Dw(x,1)=Dw(x,0) leaves a residual disparity: for the paper's constant-b construction, the residual disparity is exactly b. Thus the proof of 'fully mitigate' does not cover the settings where the paper claims an advantage over LFR. The comment in Section 4 that A3 'is feasible as the outcome need not depend on S to mitigate disparity' conflates feasibility with applicability.
[Appendix A, proof of Theorem 4.1] The proof claims that 'w = 0 results in the total loss blowing up to ∞'. This is false: for w = 0, RD(s) = 0, so Aw = |α||O(1) − O(0)| and Bw = |w_SR′| + |bias_R′| are both finite. This false claim is used to argue that non-zero initial weights cannot cross into another feasible region and hence that gradient descent reaches the claimed global minimizer. Additionally, the proof minimizes over the open region bias_R′ > 0 and concludes bias_R′ → 0; the value 2√|δ| is an infimum over that region, not an attained minimum, so the stated optimum with bias_R′ = 0 is not established by the argument as written.
[Theorem 4.2 statement and Appendix A proof] Theorem 4.2 in the main text claims to follow from assumptions (A1)–(A3) and (A6), but the proof in Appendix A additionally assumes 'the outcome Y does not depend on the sensitive attribute S, i.e., Pr(Y = 1 | X = x, S = s, H = h) = Y(x, h)'. This is conditional independence of Y and S given X and H, which is stronger than A3 (Y ⊥ S | H) when non-sensitive attributes X are present; Assumption (A2), S ⊥ X, does not imply Y ⊥ S | X, H. The theorem as stated is therefore not proved, and this discrepancy matters because the paper's central examples include X and allow Y to depend on S.
[Section 4, Theorems 4.2 and 4.3; Appendix B.1.2, Table 3] Section 4 explicitly states that Theorems 4.2 and 4.3 do not prove convergence to the global minimum, and Appendix B.1.2 (Table 3) shows that, even in the simplified A4–A5 setting, training can converge to a local optimum or to the 'no change' solution depending on initialization. The abstract and contribution 3 nevertheless claim that the network 'learns' weights that fully mitigate disparity. As it stands, the theoretical support is only a characterization of a global minimizer plus a heuristic multiple-initialization strategy; the claim should be re-scoped to avoid implying a convergence guarantee.

minor comments (4)

[Table 1, Case V] The text says LRD achieves 'similar disparity' to LFR in Case V, but for German Credit and Health, LFR reports smaller disparity than LRD (0.0148 vs. 0.0244 and 0.0022 vs. 0.0031, respectively). The statement should be made accurate.
[Appendix B.1.2, Table 2] The three configurations in this table are labeled 'Case 1', 'Case 2', and 'Case 3', which conflicts with the Cases I–V used in Section 5. Different labels would avoid confusion.
[Section 1, Introduction] The phrase 'an multi-objective optimization problem' should read 'a multi-objective optimization problem'.
[Section 4, Theorem 4.3] The theorem statement says 'including assumptions (A1)-(A5)' but Theorem 4.1 is stated under (A1)-(A6); the intended relaxation of (A6) should be stated explicitly to avoid ambiguity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: all theorems are derived from the explicitly stated loss function and assumptions, and no fitted values are presented as independent predictions.

full rationale

The paper's central claim is Theorem 4.2, which states that under assumptions (A1)-(A3) and (A6), the global minimum of the total loss Lw = aAw + bBw is attained at sparse, interpretable weights that make the desired decision independent of S and thus eliminate outcome disparity. This is a genuine mathematical consequence of the explicitly defined loss and the L1 penalty in Objective B; it is not assumed in the loss definition, and the proof in Appendix A derives the optimal weights by solving the constrained optimization. No fitted value is renamed as a prediction: the synthetic experiments in Appendix B generate data satisfying the theorem's preconditions and then check that the trained network recovers the predicted optimal weights, which is a consistency verification, and the paper explicitly notes that convergence to the global minimum is not guaranteed for Theorems 4.2 and 4.3. The only self-citation (reference [20]) appears in related work and is not load-bearing. One correctness caveat, not a circularity, is that Assumption (A3) (Y conditionally independent of S given H) excludes the empirically tested Cases I-IV where b ≠ 0, so the theorem's 'fully mitigate' guarantee does not formally cover those experiments; however, the paper does not claim the theorem predicts those empirical results. Therefore the derivation chain is self-contained and no circular step can be exhibited.

Assumptions & free parameters 6 free parameters · 8 assumptions · 1 invented entities

The central claim rests on the simplifying assumptions A1-A6 plus a constant-delta assumption. Among these, A3 is the most consequential because it removes the downstream outcome bias that the paper motivates. The free parameters are the hand-chosen loss weights and synthetic data generation settings; the model's internal weights are learned, not free in the ledger sense.

free parameters (6)

a (weight of disparity loss) = 0.99 (real-world); 0.9, 0.999, etc. in synthetic
Chosen by hand to prioritize disparity reduction; the theory requires a approximately 1.
b (weight of interpretability loss) = 0.01 (real-world)
Set to 1 - a to control sparsity of the disparity node.
c and d (weights for observed decision and outcome loss) = 1000
Chosen much larger than a and b to ensure accurate modeling of observed and outcome processes, as stated in Section 3.
m' (number of representation nodes for observed decision-maker) = 1 (German), 4 (Adult), 11 (Health)
Selected by 5-fold cross-validation on training data; affects the capacity of the observed decision model.
synthetic outcome parameter a = 0.6 (Cases I-IV), 1 (Case V)
Chosen to control the strength of the human decision's effect on the outcome in semi-synthetic experiments.
synthetic outcome parameter b = ac, -0.5ac, -ac, -1.5ac for Cases I-IV; 0 for Case V
Chosen to model different degrees of downstream outcome bias in the semi-synthetic experiments.

assumptions (8)

ad hoc to paper A1: The weights of the observed decision process and outcome process are learned from training data and fixed.
Simplifies proofs by ignoring objectives C and D; the authors claim similar weights are learned when c and d are large.
ad hoc to paper A2: Sensitive attribute S is independent of non-sensitive attributes X.
Used to prove Theorems 4.1-4.3; the paper says it is realizable by removing attributes correlated with S.
ad hoc to paper A3: Outcome Y is conditionally independent of S given H.
This excludes the downstream outcome bias that motivates the paper; the theoretical guarantee does not apply to the biased-outcome cases tested experimentally.
ad hoc to paper A4: No non-sensitive attributes (X empty).
Used in Theorems 4.1 and 4.3.
ad hoc to paper A5: Single representational disparity node.
Used in Theorems 4.1 and 4.3; Theorem 4.2 extends to multiple nodes.
ad hoc to paper A6: Disparity loss substantially outweighs interpretability loss (a approximately 1, b approximately 0).
Used to justify minimizing B subject to A = 0.
domain assumption The observed decision has constant logit difference delta across all x.
Assumed in Theorem 4.2; if delta varies with x, the simple one-node correction with w_XR' = 0 will not equalize decisions for all x.
standard math Standard results: convex optimization and sigmoid monotonicity.
Used in proofs of global minima, though some convexity claims in the paper are questionable.

invented entities (1)

Representational disparity node (R')
purpose: A hidden neuron whose incoming and outgoing weights encode the difference between observed and desired decision-makers' logits.
Introduced as a modeling construct; no independent cognitive or behavioral evidence is provided that such a node corresponds to a real mental representation. Its values are learned from the optimization objective.

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Cite this review

Pith. "Pith review of Learning Representational Disparities." pith.science (2026). https://pith.science/paper/NQP4PCRT

@misc{pith2026250517533,
  author       = {Pith},
  title        = {Pith review of: Learning Representational Disparities},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NQP4PCRT}},
  note         = {Machine review of arXiv:2505.17533}
}

read the original abstract

We propose a fair machine learning algorithm to model interpretable differences between observed and desired human decision-making, with the latter aimed at reducing disparity in a downstream outcome impacted by the human decision. Prior work learns fair representations without considering the outcome in the decision-making process. We model the outcome disparities as arising due to the different representations of the input seen by the observed and desired decision-maker, which we term representational disparities. Our goal is to learn interpretable representational disparities which could potentially be corrected by specific nudges to the human decision, mitigating disparities in the downstream outcome; we frame this as a multi-objective optimization problem using a neural network. Under reasonable simplifying assumptions, we prove that our neural network model of the representational disparity learns interpretable weights that fully mitigate the outcome disparity. We validate objectives and interpret results using real-world German Credit, Adult, and Heritage Health datasets.

Figures

Figures reproduced from arXiv: 2505.17533 by the authors.

**Figure 1.** Data Generation Process impacts a downstream outcome Y (e.g., whether the applicant is able to obtain housing). The decision could be based on the applicant’s values of a binary sensitive attribute S and other non-sensitive attributes X. Critically, the human decision Pr(H | S, X), the outcome model Pr(Y | H, S, X), or both, could be biased in a way that differentially impacts the protected class S = 1. For example,… view at source ↗

**Figure 2.** Architecture (left) with nodes used by the observed (middle) and desired human (right) The architecture is comprised of the following four layers: (1) Input layer, consisting of {S, X}. (2) Internal representation of the input, R = {R1, ..., Rm}. The weights from the first layer to the second layer are denoted by wij , where i is a node in the first layer, i ∈ {S, X}, and j is a node in the second layer, j ∈ {R1, ..… view at source ↗

**Figure 3.** Regions divided based on the signs of w, wSR′ , and biasR′ . Proof: Since a ≫ b, we minimize Bw under the constraint that Aw = 0. Let c(x) = Pr(X = x)(Y (x, 1) − Y (x, 0)), and enumerate all values x1, x2, ....., xn for which c(xi) ̸= 0. Now, we minimize Bw under the constraint that Aw = Pn i=1 c(xi) Dw(xi , 1) − Dw(xi , 0) = 0. There are two cases: I: Dw(x, 1) = Dw(x, 0), ∀x ∈ {x1, ..., xn}. Dw(x, 1) = Dw(x, 0) … view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Components of the multi-objective loss function as a function of [PITH_FULL_IMAGE:figures/full_fig_p023_4.png]

**Figure 5.** Figure 5: Losses L1 and L2 (top), Case 1 (bottom left), 2 (bottom middle), and 3 (bottom right). Loss L1 is shown in red, and Loss L2 is shown in blue. The x-axis is the regularization loss Bw = |w3| + |wSR3 | + |biasR3 | for representational disparity node R3, with correspondin…

**Figure 6.** Figure 6: Selection of number of nodes m′ used to model the observed decision-maker by crossvalidation. (a) and (b) are the training and validation results respectively for the German Credit dataset. (c) and (d) are the training and validation results respectively for the Adult…

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Exchange xi and xj. When δ <0, we show that the minimum loss attained with Dw(xi, 1) − Dw(xi, 0) > 0 is strictly greater than 2 p |δ|. Dw(xi, 1) − Dw(xi, 0) > 0 ⇐ ⇒ kX i=1 wi ReLU(wT XR′ i xi + biasR′ i ) − ReLU(wT XR′ i xi + wSR′ i + biasR′ i ) = δ − γ, γ >0. 15 Now, we find ...
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Further, σ′(x) is an increasing function for x < 0, and x0 − k B2 w 4 ≤ x1 + (1 − 2k) B2 w 4 ∀k ∈ [0, 1] as δ >0

≈ 1.76 (Note that for y = σ′(x) = σ(x)(1 − σ(x)), x = ± ln((1 + √1 − 4y)/(1 − √1 − 4y))). Further, σ′(x) is an increasing function for x < 0, and x0 − k B2 w 4 ≤ x1 + (1 − 2k) B2 w 4 ∀k ∈ [0, 1] as δ >0. Hence, 2σ′ x1 + (1 − 2k) B2 w 4 = σ′ x0 − k B2 w 4 cannot have a solution...
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≈ 1.76, only x1 + (1 − 2k) B2 w 4 ≥ ln(3 + 2 √
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needs to be considered for analyzing f ′(k) = 0. Now, we look at the second derivative, f ′′(k) = −4 B4 w 16 σ′ x1 + (1 − 2k) B2 w 4 g x1 + (1 − 2k) B2 w 4 + B4 w 16 σ′ x0 − k B2 w 4 g x0 − k B2 w 4 , where g(x) = (ex − 1)/(ex + 1), which is an increasing function of x. When t...
[35]

(16) 19 Using Eq

≈ 1.76 and f (x) > 0 ∀x >0, g x1 + (1 − 2k) B2 w 4 > 0. (16) 19 Using Eq. 15 and 16, one can easily show that f ′′(k) ≤ 0. Hence, f (k) attains a local maximum when f ′(k) = 0. In other words, σ x1 + (1 − 2k) B2 w 4 − σ x0 − k B2 w 4 attains the minimum at k = 0 or k = 1 as f ...
[36]

Here, Bopti = 3 .47, w = −1.735, wSR′ = 1 .735, biasR′ = 0

Loss L1 is globally optimal when a = 0 .9, logit(O(0)) = −4.595, δ= 5 , α= 1 as loss L1 = 0 .4 and loss L2 = 0 .531. Here, Bopti = 3 .47, w = −1.735, wSR′ = 1 .735, biasR′ = 0
[37]

Here, Bopti = 4.418, w = 2.209, wSR′ = 0, biasR′ = 2.209

Loss L2 is globally optimal when a = 0.9, logit(O(0)) = −2, δ= 10, α= 1 as loss L1 = 0.597 and loss L2 = 0.49. Here, Bopti = 4.418, w = 2.209, wSR′ = 0, biasR′ = 2.209
[38]

Here, Bopti = 3.47, w = 1.735, wSR′ = 1.735, biasR′ = 0

Loss L3 is globally optimal when a = 0.9, logit(O(0)) = 4 .595, δ= −5, α= 1 as loss L3 = 0.4 and loss L4 = 0.531. Here, Bopti = 3.47, w = 1.735, wSR′ = 1.735, biasR′ = 0
[39]

no change

Loss L4 is globally optimal when a = 0.9, logit(O(0)) = 2, δ= −10, α= 1 as loss L3 = 0.597 and loss L4 = 0.49. Here, Bopti = 4.418, w = −2.209, wSR′ = 0, biasR′ = 2.209. 21 B Experiments In Appendix B.1, we present several proof-of-concept experiments on simple, synthetic data...
[40]

Each record has 20 attributes classifying account holders into a Good or Bad class

German Credit: The dataset has 1,000 records. Each record has 20 attributes classifying account holders into a Good or Bad class. We consider Age as the sensitive attribute, following [26, 12]. We preprocess the data in the same manner as [26], with 13 categorical attributes o...
[41]

Each record has 14 attributes classifying whether or not an individual’s income is larger than $50,000

Adult income: The dataset has 45,222 records. Each record has 14 attributes classifying whether or not an individual’s income is larger than $50,000. We considerGender as the sensitive attribute, following [26, 15, 13]. We preprocess the data in the same manner as [26] with 8 ...
[42]

We use features similar to the winning team, Market Makers [5]

Heritage Health: The dataset is from the Heritage Health Prize milestone challenge. We use features similar to the winning team, Market Makers [5]. The dataset has 184,308 records. The goal is to classify whether or not each individual will spend any days in the hospital that ...

1945

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

Machine bias

Julia Angwin, Jeff Larson, Surya Mattu, and Lauren Kirchner. Machine bias. propublica, may 23, 2016, 2016

work page 2016

[2] [2]

Fairness in machine learning

Solon Barocas, Moritz Hardt, and Arvind Narayanan. Fairness in machine learning. Nips tutorial, 1:2017, 2017

work page 2017

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Toward operationalizing pipeline-aware ml fairness: A research agenda for developing practical guide- lines and tools

Emily Black, Rakshit Naidu, Rayid Ghani, Kit Rodolfa, Daniel Ho, and Hoda Heidari. Toward operationalizing pipeline-aware ml fairness: A research agenda for developing practical guide- lines and tools. In Proceedings of the 3rd ACM Conference on Equity and Access in Algorithms, Mechanisms, and Optimization, pages 1–11, 2023

work page 2023

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Convex optimization

Stephen P Boyd and Lieven Vandenberghe. Convex optimization. Cambridge university press, 2004

2004

[5] [5]

market makers

Phil Brierley, David V ogel, and Randy Axelrod. Heritage provider network health prize round 1 milestone prize how we did it – team "market makers".foreverdata.org/1015/content/milestone1- 2.pdf, 2011

work page 2011

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Clinically applicable deep learning for diagnosis and referral in retinal disease

Jeffrey De Fauw, Joseph R Ledsam, Bernardino Romera-Paredes, Stanislav Nikolov, Nenad Tomasev, et al. Clinically applicable deep learning for diagnosis and referral in retinal disease. Nature Medicine, 24(9):1342–1350, 2018

work page 2018

[7] [7]

Can we reconcile the declarative memory and spatial navigation views on hippocampal function? Neuron, 83(4):764–770, 2014

Howard Eichenbaum and Neal J Cohen. Can we reconcile the declarative memory and spatial navigation views on hippocampal function? Neuron, 83(4):764–770, 2014

work page 2014

[8] [8]

stop-and-frisk

Andrew Gelman, Jeffrey Fagan, and Alex Kiss. An analysis of the new york city police department’s “stop-and-frisk” policy in the context of claims of racial bias. Journal of the American Statistical Association, 102(479):813–823, 2007

work page 2007