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REVIEW 3 major objections 5 minor 18 references

Asymmetrical Latent Representation for Individual Treatment Effect Modeling

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper claims that CATE estimation requires two asymmetric latent spaces rather than one balanced space, and that the resulting ALRITE method comes with a guarantee linking its training loss to heterogeneous-effect error.

desk verdict Promising two-space CATE method with competitive results, but the advertised PEHE bound does not actually apply to the estimator being evaluated. read the letter →

arxiv 2501.14006 v1 pith:SWFGO2SA submitted 2025-01-23 cs.LG cs.AI

Armand Lacombe , Michèle Sebag This is my paper · ORCID
classification cs.LGcs.AI MSC 62D2068T07
keywords causalinferenceconditionalaveragetreatmenteffectcounterfactualregressionrepresentationlearninglatentmirrortwinheterogeneitydomainadaptationindividual
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 argues that estimating individual treatment effects is not one domain-adaptation problem but two intertwined ones: predicting outcomes for treated individuals requires control samples to be close neighbours in some latent space, and predicting outcomes for control individuals has the mirror requirement, which any single optimal space must compromise. It introduces ALRITE, a model with two asymmetric latent embeddings, one optimized so that treated samples are counterfactualizable and one optimized for controls, combined by a propensity-weighted average in the manner of X-learners. The paper proves that the within-sample error in heterogeneous effects is bounded by weighted factual residuals, squared mirror-twin distances, and irreducible outcome noise, and that this bound matches the terms in the training loss. On the IHDP and ACIC2016 benchmarks, ALRITE and its ensembles perform at or near the top of published methods. The authors caution that the method is designed for unbalanced treatment assignment; under uniform assignment the two problems collapse into one and the two pipelines risk overfitting.

What carries the argument

The load-bearing objects are the latent mirror twin and the counterfactual importance weight. For a sample $(x_i,t_i,y_i)$ under embedding $\phi$, its mirror twin is the nearest sample with the opposite treatment in latent space, and the counterfactualizability of $x_i$ is the squared distance $\|\phi(x_i)-\phi(x_i^m)\|^2$. The counterfactual importance weight $w_j$ of a sample $x_j$ is the number of samples for which $x_j$ is the mirror twin. These two quantities convert the unobservable counterfactual question into measurable geometric quantities: the mirror-twin distance controls the Lipschitz cost of extrapolating the outcome model across the treatment gap, and the importance weight directs factual accuracy to the samples that most influence counterfactual predictions. ALRITE trains two embeddings, each optimizing the symmetric version of the same geometry, and its PEHE bounds are expressed directly in these terms.

What would settle it

Settle it with a synthetic experiment where the true CATE is known and the two embeddings are forced to be asymmetric: choose potential outcome functions $\mu_0$ and $\mu_1$ that both depend on the same covariate $x_1$, then constrain $\phi_0$ to discard $x_1$ while $\phi_1$ preserves it, or vice versa. Under Theorem 2 the mirror-twin distances should no longer bound the within-sample PEHE, so ALRITE's error should degrade relative to a method using a single representation that keeps $x_1$; if the error does not degrade, the bound is not doing the work the paper claims.

Watch

Extended reading notes

Core claim

ALRITE's central claim is that a single balanced latent space is the wrong target for CATE estimation: making treated samples counterfactualizable and making control samples counterfactualizable pull the representation in different directions. The method therefore trains two pipelines. The treatment-driven pipeline $P_1$ uses embedding $\phi_1$ so that each treated sample is close to its latent mirror twin (nearest control in latent space) and weights the factual loss of control samples by how many treated samples use them as twins; $P_0$ does the symmetric job for controls. The two resulting estimates $\hat{\tau}_0$ and $\hat{\tau}_1$ are blended as $(1-\hat{\eta})\hat{\tau}_0+\hat{\eta}\hat{\tau}_1$. The main theoretical result, Theorem 2, upper-bounds the within-sample PEHE, computed with $\bar{\tau}_i$ using the observed factual outcome, by weighted factual residuals, squared mirror-twin distances, and the noise term $\kappa_Y$. Since these quantities are exactly what the compound training loss (Eq. 5) penalizes, the theorem connects the trainable objective to the estimation error of interest.

Load-bearing premise

The load-bearing premise is that each of the two learned embeddings is rich enough to recover both potential outcome functions, a factorization the paper acknowledges cannot be verified from observational data alone, and without which the mirror-twin bounds collapse.

Editorial extensions

If this is right

  • Within-sample PEHE is controlled by terms that appear in the training loss, namely weighted factual residuals, squared mirror-twin distances, and irreducible noise, so minimizing Eq. (5) is a principled proxy for minimizing the error that matters.
  • The two-pipeline architecture generalizes both T-learners and X-learners: each pipeline is a T-learner on its own embedding, and the propensity-weighted blend is the X-learner combination rule.
  • Errors in the propensity estimate enter the final CATE only as a product of two small errors, so a poorly calibrated propensity does not dominate the total error.
  • On IHDP, ALRITE ranks first on within-sample PEHE and second on out-of-sample PEHE; on ACIC2016 it ranks second behind one baseline, and both ensemble variants improve on it.
  • Under uniform treatment assignment the two counterfactualization problems coincide, and the two-pipeline design risks overfitting; the method is not designed for that regime.

Reading between the lines

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

  • A direct consequence the paper leaves implicit is that the mirror-twin distance per sample provides a diagnostic map of where CATE estimates are trustworthy; plotting $\|\phi_0(x_i)-\phi_0(x_i^m)\|$ and $\|\phi_1(x_i)-\phi_1(x_i^m)\|$ over the covariate distribution would flag low-overlap regions without needing counterfactual labels.
  • A testable extension is to replace the single nearest mirror twin with a kernel-weighted set of neighbours, which the paper lists as future work; the importance weights would become smoother and might remove the pathological incentive to distort $\phi$ so hard samples lose twin status.
  • The second-order sensitivity to propensity error suggests the method could tolerate misspecified propensity models, making it a candidate for settings where treatment assignment is only approximately modelled; one could verify this by comparing ALRITE's PEHE under an intentionally misspecified $\hat{\eta}$.
  • Because the method assumes unbalanced assignment, it implies a model-selection rule: run both ALRITE and a single-space T-learner and prefer ALRITE only when the propensity distribution deviates from $1/2$, an empirical comparison the paper does not carry out.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes ALRITE, a CATE estimator that learns two asymmetric latent representations: a control-driven pipeline P0 and a treatment-driven pipeline P1. Each pipeline is trained with the compound loss in Eq. (5), combining factual accuracy, counterfactual importance weighting, and a counterfactualizability term based on the distance to a latent mirror twin. The two pipeline estimates are aggregated in Eq. (4) via an estimated propensity score. The paper claims that Theorems 1–3 provide an upper bound on the within-sample PEHE and reports experiments on IHDP and ACIC2016 in which ALRITE and its ensemble variants perform at or near the state of the art.

Significance. The asymmetric two-space idea is original and clearly motivated: it correctly recognizes that counterfactual prediction for treated and control samples may require different representations, and the notions of mirror twin and counterfactual importance weight are intuitive. The paper is also transparent about its hyperparameter-selection protocol and ships public code. However, the central advertised contribution is the formal PEHE upper bound, and that bound is not for the estimator actually deployed: Theorem 2 bounds a pseudo-estimator that plugs in the observed factual outcome, while Eq. (4) is a propensity-weighted combination of two differences of learned outcome heads. The bound is also explicitly within-sample, whereas the empirical headline is out-of-sample PEHE. The empirical comparison, moreover, relies on baseline numbers taken from prior papers rather than re-run baselines. These issues make the significance conditional on a substantial reworking of the theoretical claim.

major comments (3)
  1. [3.4, Thm. 2–3 vs. Eq. (4)] The advertised theoretical guarantee does not cover the deployed estimator. Theorem 2 bounds the within-sample error of the pseudo-estimator τ̄_i, which for a treated sample is y_i − h^0_1(φ1(x_i)) and for a control sample is h^1_0(φ0(x_i)) − y_i; that is, it plugs the observed factual outcome y_i into the counterfactual branch. The ALRITE estimator defined in Eq. (4) is τ̂(x) = (1−η̂(x))τ̂_0(x) + η̂(x)τ̂_1(x), where each τ̂_t is the difference of two learned outcome heads and no y_i appears. The bound M2 contains no term for the factual error of h^0_0 on controls or h^1_1 on treated, which would be needed to control Eq. (4), and it also ignores the η̂ weighting. Theorem 3 repeats the same τ̄_i target. Section 3.4 further restricts the results to the within-sample setting, while Tables 1–2 report out-of-sample PEHE as a main metric. Consequently, the abstract's claim that ALRITE admits an upper bound on PEHE is not established for the estimator whose performance is reported, either within-sample or out-of-sample.
  2. [3.4–3.5, double-factorization assumption] Theorem 2 assumes that each embedding is sufficient for both outcome functions: μ0 = ν^0_0∘φ0 = ν^0_1∘φ1 and μ1 = ν^1_0∘φ0 = ν^1_1∘φ1. The proof uses this assumption to replace τ(x_i) by a function of the same embedding used to form τ̄_i. Section 3.5 explicitly acknowledges that such sufficiency cannot be verified from observational data alone. If this double-factorization fails, the mirror-twin distance term does not control the PEHE and the formal guarantee collapses. Since this assumption is unverifiable and the paper provides no practical check or sensitivity analysis, the formal result is conditional in a way that should be stated much more prominently, and ideally accompanied by an empirical diagnostic (for example, holdout factual accuracy of each pipeline's outcome heads).
  3. [3.4, Thm. 3; Tables 1–2] The scope of the formal claims is narrower than the paper's presentation suggests. Section 3.4 states that the results do not generalize to the out-of-sample setting, yet the abstract and the experimental section present out-of-sample PEHE as a headline result. Moreover, Theorem 3 is non-constructive: it only asserts the existence of hyperparameters (α0, α1, β0, β1) for which the bound holds. The values actually used in the experiments, listed in Table 3, are selected by a proxy metric and are not shown to satisfy the theorem's condition. Thus even the within-sample guarantee, if it were stated for Eq. (4), would not automatically cover the configuration whose numbers are reported. The paper should state precisely which claims are formal and which are empirical, and either provide a constructive out-of-sample argument or clearly restrict the theoretical conclusions.
minor comments (5)
  1. [3.4, Thm. 2 statement] In the definition of w_j, the set notation reads "(xi, ti, yj) ∈ D"; this should be "(xi, ti, yi) ∈ D" to be consistent with the data notation.
  2. [3.4, Thm. 3 statement] The M3 formula contains a typographical error: the term "−γ∥P1∥" should be "−γ1∥P1∥" to match the proof and the stated hyperparameter tuple.
  3. [4.2 and Tables 1–2] The baseline numbers are taken from prior papers rather than re-run under a shared protocol; the paper acknowledges this in Section 4.2, but the limitation should also be stated in the results section and in the conclusion so that the comparative rankings are not over-interpreted.
  4. [4.4, ensemble significance test] The reported p-value of 1.3e−3 for the ensemble improvement over ALRITE is from a one-sided paired t-test on the IHDP instances; please report the number of instances used, the effect size, and whether any multiple-comparison correction was applied, since several ensemble hyperparameters were examined.
  5. [Throughout] The name of the method is written both as "Alrite" and "ALRITE" in different places; please unify the capitalization.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation; the only self-citation is minor and non-load-bearing, while the theorem/estimator target mismatch is a soundness concern, not circularity.

full rationale

The derivation chain of Theorems 1-3 is self-contained: each bound is proven in Appendix A.1 from the stated Lipschitz and factorization assumptions, and Eq. (5) is deliberately assembled from the terms appearing in those bounds. That alignment is a design choice, not a circular reduction—the bound is not assumed equal to the loss, and Theorem 3 explicitly constructs the hyperparameter setting rather than taking the conclusion as an input. The only self-citation is Lacombe (2024) in Section 4.5, a pointer to complementary experiments confirming the regularization interpretation; it is not load-bearing for any theoretical or benchmark claim. The paper also candidly limits Theorem 2 to the within-sample setting and acknowledges the unverifiability of the sufficiency assumption in Section 3.5. A genuine soundness concern exists—Theorem 2 bounds a within-sample pseudo-outcome tau-bar_i, not the Eq. (4) estimator actually evaluated—but that is a target mismatch and correctness issue, not an instance of the derivation reducing to its own inputs, so no circularity score is added for it.

Assumptions & free parameters 4 free parameters · 3 assumptions · 2 invented entities

The central claim rests on standard causal assumptions plus a strong, unverifiable sufficiency condition on the two embeddings. The method introduces no physical entities, but it does introduce internal constructs such as the mirror twin and counterfactual importance weights. Hyperparameters α and β are fitted per benchmark by validation search, and γ and the ensemble hyperparameters are also selected rather than derived.

free parameters (4)
  • α (counterfactualizability regularization strength) = IHDP: P0=10^1, P1=10^1.5; ACIC2016: 10^-2 for both
    Selected by random search over {0} ∪ {10^{k/2}}_{k=-4}^{4} using a validation proxy (Appendix B, Table 3); it controls the distance-to-mirror-twin term in Eq. (5).
  • β (counterfactual importance reweighting) = IHDP: P0=10^-1.5, P1=0; ACIC2016: 0 for both
    Selected by random search over {0} ∪ {10^{k/2}}_{k=-4}^{2}; it reweights factual accuracy by mirror-twin importance w_i in Eq. (5).
  • γ (L2 regularization weight) = not reported in Table 3
    Appears in Eq. (5) as γ||P||^2; the paper attributes the ATE bias to this term but does not report its selected value.
  • Ensemble hyperparameters K and λ = K=4 and λ=100 on IHDP; ACIC selected via validation µ-risk as described in Appendices B and C
    Top-K and softmax ensemble variants beat the single ALRITE model; K and λ are selected on the validation set using the µ-risk proxy.
assumptions (3)
  • domain assumption Conditional exchangeability, positivity, and SUTVA (Y = (1-T)Y0 + TY1)
    Stated in Section 1 as the standard Neyman-Rubin assumptions; all counterfactual claims depend on them.
  • domain assumption Sufficiency of each embedding: there exist ν_i^j such that μ0 = ν_0^0 ∘ φ0 = ν_0^1 ∘ φ1 and μ1 = ν_1^0 ∘ φ0 = ν_1^1 ∘ φ1
    Invoked in Theorem 2 (Section 3.4) and discussed in Section 3.5; cannot be verified from observational data alone.
  • domain assumption The learned outcome functions have known finite Lipschitz constants
    Used in the upper bounds M1 and M2; the paper notes in Section 3.5 that estimating Lipschitz constants for neural networks requires additional care.
invented entities (2)
  • Latent mirror twin
    purpose: The nearest sample with the opposite treatment assignment in latent space; supplies the counterfactual reference outcome and defines counterfactualizability in Eq. (3).
    It is an internal modeling construct. The bounds and the loss both measure distance to this twin, but the construct has no independent observable support outside the paper.
  • Counterfactual importance weight w_j
    purpose: Counts how many samples have sample j as their mirror twin; used to reweight factual accuracy in Eq. (5).
    Derived from the mirror-twin construct and used inside the training loss and the theoretical bounds; no external evidence.

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Cite this review

Pith. "Pith review of Asymmetrical Latent Representation for Individual Treatment Effect Modeling." pith.science (2026). https://pith.science/paper/SWFGO2SA

@misc{pith2026250114006,
  author       = {Pith},
  title        = {Pith review of: Asymmetrical Latent Representation for Individual Treatment Effect Modeling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SWFGO2SA}},
  note         = {Machine review of arXiv:2501.14006}
}
read the original abstract

Conditional Average Treatment Effect (CATE) estimation, at the heart of counterfactual reasoning, is a crucial challenge for causal modeling both theoretically and applicatively, in domains such as healthcare, sociology, or advertising. Borrowing domain adaptation principles, a popular design maps the sample representation to a latent space that balances control and treated populations while enabling the prediction of the potential outcomes. This paper presents a new CATE estimation approach based on the asymmetrical search for two latent spaces called Asymmetrical Latent Representation for Individual Treatment Effect (ALRITE), where the two latent spaces are respectively intended to optimize the counterfactual prediction accuracy on the control and the treated samples. Under moderate assumptions, ALRITE admits an upper bound on the precision of the estimation of heterogeneous effects (PEHE), and the approach is empirically successfully validated compared to the state-of-the-art

Figures

Figures reproduced from arXiv: 2501.14006 by the authors.

Figure 1
Figure 1. Average counter-factualizability (definition in section 3.2.1) for [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Contrasting the T- and X-learner architectures. 3.2 Overview of Alrite 3.2.1 Counter-factualizability Extending (Johansson et al., 2016; Wu et al., 2023a), with ϕ an embedding from the covariate space X onto latent space Z we define the latent mirror twin of sample (xi , ti , yi) noted (x m,ϕ i , 1 − ti , y m,ϕ i ) as the nearest sample with different treatment assignment in latent space: (x m,ϕ i , 1 − ti , y m,ϕ i… view at source ↗
Figure 3
Figure 3. Treated and control samples in latent space. Left: the treated xi has a far mirror twin; the control xj has a close mirror twin. Right: the treated xℓ has counter-factual importance weight 0; the control sample xk has wk=3. Formally, a pipeline P = (ϕ, h0 , h1 ) is defined as the triplet formed by an embedding ϕ mapping the instance space on some latent space (ϕ : X → Z ⊂ R d ) and models h 0 and h 1 of the treated … view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Alrite architecture: Top: control-driven pipeline P0. Middle: propensity estimate ˆη. Bottom: treatment-driven pipeline P1. Right: overall CATE estimate. loss enforcing: i) the accuracy5 of model h 0 on the control samples; ii) the accuracy of model h 1 on the treated …
Figure 5
Figure 5. Figure 5: Distribution of the control and treated samples. Top: covariate space R 2 . Bottom left: distribution of distances to mirror twins for ϕ =Id. Bottom right: distribution of distances to mirror twins for ϕ =projection on the x-axis. Another potential weakness of the appr…
Figure 6
Figure 6. Figure 6: Diversity of the 100 problem instances in [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]
Figure 7
Figure 7. Figure 7: Ensemble models in the out-of-sample setting: PEHE vs factual error on the validation set sensitivity, depending on the hyper-parameter. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_7.png]
Figure 8
Figure 8. Figure 8: PEHE value (test set) vs proxy metrics (validation set) for IHDP. These experiments validate a posteriori the relevance of µ-risk as best proxy metrics, as it achieves the lowest PEHE and lowest ATE. The quality of the proxy metrics is also confirmed by its high Spearm…

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Works this paper leans on

18 extracted references · 13 canonical work pages

  1. [1]

    G., Steiner, B., Tucker, P., Vasudevan, V., Warden, P., Wicke, M., Yu, Y., and Zheng, X

    Abadi, M., Barham, P., Chen, J., Chen, Z., Davis, A., Dean, J., Devin, M., Ghemawat, S., Irving, G., Isard, M., Kudlur, M., Levenberg, J., Monga, R., Moore, S., Murray, D. G., Steiner, B., Tucker, P., Vasudevan, V., Warden, P., Wicke, M., Yu, Y., and Zheng, X. (2016). TensorFlow: a system for 23 Asymmetrical Latent Representation For ITE Modeling large-sc...

    work page 2016

  2. [3]

    Cuturi, M. (2013). Sinkhorn Distances: Lightspeed Computation of Optimal Transport. In Advances in Neural Information Processing Systems, volume

    work page 2013

  3. [5]

    We underline that this comparison can only be done in retrospect, for in real-life cases no evaluation of the PEHE is possible. (a) µ-risk (b) µ-risk IPTW (c) R-risk (d) π-risk IPTW (e) π-risk DR (f) τ -risk 1NNI (g) τ -risk naive (h) τ -risk IPTW (i) τ -risk U (j) τ -risk DR Figure 8: PEHE value (test set) vs proxy metrics (validation set) for IHDP. Thes...

    work page 2017

  4. [8]

    Kuang, K., Cui, P., Zou, H., Li, B., Tao, J., Wu, F., and Yang, S. (2022). Data-Driven Variable Decomposition for Treatment Effect Estimation. IEEE Transactions on Knowledge and Data Engineering, 34(5):2120–2134. Confer- ence Name: IEEE Transactions on Knowledge and Data Engineering. K¨ unzel, S. R., Sekhon, J. S., Bickel, P. J., and Yu, B. (2019). Meta- ...

    arXiv 2022

  5. [10]

    H., Hastie, T., and Tibshirani, R

    Powers, S., Qian, J., Jung, K., Schuler, A., Shah, N. H., Hastie, T., and Tibshirani, R. (2018). Some methods for heterogeneous treatment effect estimation in high dimensions. Statistics in Medicine, 37(11):1767–1787. Rezende, D. J., Mohamed, S., and Wierstra, D. (2014). Stochastic Backpropaga- tion and Approximate Inference in Deep Generative Models. In ...

    arXiv 2018

  6. [14]

    Cycle-Balanced Representation Learning For Counterfactual Inference

    Curran Associates, Inc. Yao, L., Li, S., Li, Y., Huai, M., Gao, J., and Zhang, A. (2019). ACE: Adaptively Similarity-Preserved Representation Learning for Individual Treatment Effect Estimation. In 2019 IEEE International Conference on Data Mining (ICDM), pages 1432–1437. ISSN: 2374-8486. Yoon, J., Jordon, J., and Schaar, M. v. d. (2018). GANITE: Estimati...

    work page Pith review arXiv 2019

  7. [15]

    31 Asymmetrical Latent Representation For ITE Modeling A.1.3 Proof of Thm

    in D, it comes: 1 n X ti=1 ¯τi − τ (xi) 2 ≤ 5 n X ti=1 (L2 + ˆL2)∥ϕ(xi) − ϕ(xj)∥2 + µ1(xi) − yi 2 + 5 n X tj =0 wj h0 1 ◦ ϕ1(xj) − yj 2 + µ0(xj) − yj 2 Adding the control samples sum yields M2. 31 Asymmetrical Latent Representation For ITE Modeling A.1.3 Proof of Thm. 3 Proof. Set the loss hyper-parameters values α0, α1, β0, β1 to α0, α1, β0, β1 = (1 − p)...

    work page 2017

  8. [16]

    Finally, P ∥ϕ0(xi) − ϕ0(xm i )∥ > ϵ = P ∀j ∈ J1, nK, tj = 1 = ⇒ ϕ0(xj) ̸∈ B(ϕ0(xi), ϵ) ≤ P ∀i ∈ J1, nK, tj = 1 = ⇒ xj ̸∈ ϕ−1 0 (B(ϕ0(xi), ϵ)) ≤ P ∀j ∈ J1, nK, tj = 1 = ⇒ xj ̸∈ A ≤ 1 − P(T = 1, X∈ A) n n→+∞ − − − − − →0 B Hyper-parameter selection in causal inference Alrite hyper-parameters are summarized in Table 3, together with their range of variation ...

    work page 2016

Show all 18 references
  1. [19]

    Bengio, Y., Courville, A., and Vincent, P

    MIT Press. Bengio, Y., Courville, A., and Vincent, P. (2013). Representation Learning: A Review and New Perspectives. IEEE transactions on pattern analysis and machine intelligence, 35:1798–1828. Breiman, L. (2001). Random Forests. Machine Learning, 45(1):5–32. Brooks-Gunn, J....

    2013 arXiv

  2. [26]

    Dorie, V., Hill, J., Shalit, U., Scott, M., and Cervone, D

    Curran Associates, Inc. Dorie, V., Hill, J., Shalit, U., Scott, M., and Cervone, D. (2017). Automated versus Do-It-Yourself Methods for Causal Inference: Lessons Learned from a Data Analysis Competition. Statistical Science,

    2017

  3. [27]

    Gouk, H., Frank, E., Pfahringer, B., and Cree, M

    Curran Associates, Inc. Gouk, H., Frank, E., Pfahringer, B., and Cree, M. J. (2021). Regularisa- tion of neural networks by enforcing Lipschitz continuity. Machine Learning, 110(2):393–416. Gretton, A., Borgwardt, K. M., Rasch, M. J., Sch¨ olkopf, B., and Smola, A. (2012). A K...

    2021

  4. [30]

    Curran Associates, Inc. Nie, X. and Wager, S. (2021). Quasi-oracle estimation of heterogeneous treatment effects. Biometrika, 108(2):299–319. Oprescu, M., Dorn, J., Ghoummaid, M., Jesson, A., Kallus, N., and Shalit, U. (2023). B-learner: quasi-oracle bounds on heterogeneous ca...

    2021

  5. [31]

    Wager, S

    Curran Associates, Inc. Wager, S. and Athey, S. (2018). Estimation and Inference of Heteroge- neous Treatment Effects using Random Forests. Journal of the American Statistical Association, 113(523):1228–1242. Publisher: Taylor & Francis eprint: https://doi.org/10.1080/01621459...

    2018

  6. [34]

    Du, X., Sun, L., Duivesteijn, W., Nikolaev, A., and Pechenizkiy, M. (2021). Adversarial balancing-based representation learning for causal effect inference 25 Asymmetrical Latent Representation For ITE Modeling with observational data. Data Mining and Knowledge Discovery, 35(4):1713–

    2021

  7. [1738]

    Foster, D. J. and Syrgkanis, V. (2023). Orthogonal statistical learning. The Annals of Statistics, 51(3):879–908. Publisher: Institute of Mathematical Statistics. Ganin, Y., Ustinova, E., Ajakan, H., Germain, P., Larochelle, H., Laviolette, F., March, M., and Lempitsky, V. (20...

    2023

  8. [1988]

    (Eq. 2), that approximates E Y − m(X) − (T − η(X))ˆτ (X) 2 through approximating the mean conditional outcome m(x) = E[Y |X = x] and the propensity η; • the τ -risks, leveraging an independent approximation of the ground-truth CATE, that is most often based on a plug-in referr...

    2018

  9. [2024]

    Lechner, M. (1999). Earnings and Employment Effects of Continuous Gff- the-Job Training in East Germany After Unification. Journal of Business & Economic Statistics, 17(1):74–90. Publisher: Taylor & Francis eprint: https://doi.org/10.1080/07350015.1999.10524798. Light, I. J. (...

    1999

  10. [3498]

    Wu, A., Yuan, J., Kuang, K., Li, B., Wu, R., Zhu, Q., Zhuang, Y., and Wu, F. (2023b). Learning Decomposed Representations for Treatment Ef- fect Estimation. IEEE Transactions on Knowledge and Data Engineering, 35(5):4989–5001. Conference Name: IEEE Transactions on Knowledge an...

    2023

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