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Doubly Robust Fusion of Many Treatments for Policy Learning

T0 review · 2 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Calibration-weighted fused lasso recovers latent treatment groupings whenever either the calibration model or the outcome model is correct, shrinking many-armed policy learning to a small interpretable action space.

desk verdict A practically promising combination of calibration weighting and treatment fusion, but the central recovery theorem rests on an essentially false completeness assumption and a penalty the implementation does not use. read the letter →

arxiv 2505.08092 v2 pith:T5HMUBFR submitted 2025-05-12 stat.ME stat.ML

Ke Zhu , Jianing Chu , Ilya Lipkovich , Wenyu Ye , Shu Yang This is my paper · ORCID
classification stat.MEstat.ML
keywords individualizedtreatmentrulesfusioncalibrationweightingfusedlassodoublerobustnesspolicylearningtreesmanytreatments
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

This paper tackles the problem of learning individualized treatment rules when the number of treatments is large and each treatment is observed on few, often covariate-imbalanced, patients. Its central proposal is calibration-weighted treatment fusion: reweight each treatment group so its covariates match the overall sample, then run a fused-lasso penalized linear model to identify which treatments share the same effect function. The paper proves that this fusion recovers the true latent grouping with probability tending to one if either the calibration weights or the outcome model is correctly specified, and that the resulting groups can be fed into any multi-armed policy learner. It also gives a regret bound for the resulting depth-D policy tree and demonstrates improved group recovery and policy value in simulations and a large electronic health record cohort.

What carries the argument

The operating machinery is the calibration-weighted fused-lasso objective (3). Calibration weights solve the constrained problem $\min \sum h_\gamma(w_i)$ subject to $\sum_{i:A_i=a} w_i X_i = \bar X$ and $\sum w_i = 1$; these weights enter weighted least squares $\min_\zeta \frac{1}{2n}\sum_a \sum_{i:A_i=a} \hat w_i(\tilde Y_i - X_i^\top \zeta_a)^2 + \sum_{a<a'} p_{\lambda_n}(\|\zeta_a-\zeta_{a'}\|_1)$. The identity doing the work is Lemma A.1, which shows calibration weighting zeroes the projection-residual bias term $E\{I(A_i=a)w_i^* X_{ij} \varepsilon_i(a)\}$ under either correct calibration or correct outcome model. The completeness assumption then identifies the partition: if $E[X h(X)]=0$ implies $h=0$ almost surely, then equal projections imply equal outcome means. The oracle-property argument uses the flatness of the penalty near zero, as in Assumption 3.10, to show the fused objective has a local minimum exactly at the oracle grouped estimator.

What would settle it

With $X \in \{0,1,2\}$ uniform, set $\mu_1(x)=x$ and $\mu_2(x)=x+h(x)$ where $h(0)=1$, $h(1)=-2$, $h(2)=1$; then $E[h]=0$ and $E[Xh]=0$, so $\zeta_1^*=\zeta_2^*=(0,1)$ even though $\mu_1 \neq \mu_2$, and calibration-weighted fusion will fuse the treatments with probability tending to 1 despite distinct oracle groups.

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Extended reading notes

Core claim

The central claim is that the oracle grouping $\cup_{b=1}^M G_b^*$, defined by equality of the conditional mean functions $\mu_a(X)=\mu_{a'}(X)$, is recoverable from equality of the best-linear-projection vectors $\zeta_a^*$ computed after calibration weighting. The paper proves (Theorem 3.8) that the oracle estimator $\hat\zeta^{\mathrm{or}}$ converges to $\zeta^*$ in $\ell^\infty$ at rate $\sqrt{p n\log n/N_{\min}}$ provided either the calibration weights limit to the true inverse propensity scores or the outcome model satisfies $E\{\varepsilon(a)|X\}=0$, and (Theorem 3.12) that with a fused-lasso penalty of sharp shape, the local minimizer of the penalized objective equals $\hat\zeta^{\mathrm{or}}$ with probability tending to 1. Because Assumption 3.1 turns $\zeta_a^*=\zeta_{a'}^*$ into $\mu_a=\mu_{a'}$ almost surely, Algorithm 1's output grouping recovers the oracle partition. Under that grouping, the CAIPWL policy-tree learner achieves regret $O_P\big(\sqrt{(2^D-1)\log p+2^D\log M+4^{3D}\sqrt{2D-1}}\sqrt{V_*/n}\big)$.

Load-bearing premise

The load-bearing premise is the completeness condition on the covariates: any function of $X$ uncorrelated with every covariate must be zero almost surely, a condition that discrete or categorical covariates typically violate.

Editorial extensions

If this is right

  • If the double-robustness claim holds, analysts can fuse treatments whenever they trust either the propensity or calibration model or a linear outcome model, rather than both, making many-armed policy learning practical in observational data with covariate shift.
  • The effective action space drops from $K$ to $M$ treatments, so standard multi-armed learners such as policy trees can be used with $M\ll K$; the paper's Proposition 3.18 gives a regret bound of order $\sqrt{(2^D-1)\log p+2^D\log M+4^{3D}\sqrt{2D-1}}\sqrt{V_*/n}$ for depth-$D$ trees.
  • Because grouping is estimated before policy learning, the decision tree may use a smaller, interpretable subset of covariates than the ones used for balancing, allowing protected attributes to be excluded from recommendations.
  • In the paper's $K=16$ simulation with misspecified nonlinear outcomes, calibration-weighted fusion raises the adjusted Rand index from 0.26 to 0.96 and improves policy value; under a misspecified weighting model with linear outcomes, it retains an ARI of 0.96.
  • The real-data application shows the procedure produces clinically coherent clusters (two monotherapies grouped together, chemotherapy alone separated) and a policy tree whose splits use age and time since diagnosis.

Reading between the lines

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

  • Beyond the paper: with categorical covariates the completeness assumption fails, so a practical safeguard is to enrich the covariate basis with splines, interactions, and indicator expansions until the empirical analogue of $E[X h(X)]=0$ holding for all estimated contrasts becomes implausible; this is directly testable in the CLL/SLL data by comparing groupings across bases.
  • Beyond the paper: the projection formulation implies the method groups treatments by shared best-linear predictor even when conditional mean functions are nonlinear; if a nonlinearity is orthogonal to all covariates, fusion is insensitive to it, which may be acceptable for linear or tree policies but not for policies that exploit that nonlinearity.
  • Beyond the paper: an iterative loop alternating calibration weighting and fusion, which the paper mentions as future work, could be evaluated as a remedy for instability with very small or empty treatment arms; a synthetic benchmark holding $n$ fixed while $K$ grows to 48 would quantify the gain.
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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

2 major / 5 minor

Summary. The paper proposes calibration-weighted treatment fusion for individualized treatment rule (ITR) learning with many treatment levels. The method first computes calibration weights that balance each treatment group's covariates to the overall sample mean, then fits a pairwise-penalized weighted linear working model to fuse treatment-specific projection vectors, and finally applies multi-armed policy-tree learning on the fused groups. The authors claim doubly robust recovery of the latent treatment group structure, consistency and the oracle property of the fusion estimator, and regret bounds for the integrated policy-tree learner, with supporting simulations and an EHR-based application.

Significance. If the central recovery claim were established, this would be a useful contribution to large-action policy learning. The paper addresses a real problem of data sparsity and covariate shift across many treatments, the double-robustness Lemma A.1 is clean and its proof is straightforward, and the paper gives explicit rates and regret bounds. The simulation comparison against Ma et al. (2022) and the real-data illustration are valuable. However, as detailed below, the bridge from projection fusion to the oracle group structure relies on an assumption that fails in the paper's own settings, and the oracle property is proved for a penalty class that does not include the L1 fused Lasso actually described and implemented. Both issues are load-bearing for the abstract's claims.

major comments (2)
  1. [Section 3.2.1, Assumption 3.1 and Eq. (9)] The completeness assumption is false for essentially every nondegenerate finite-dimensional covariate distribution. If X ~ N(0,1), then h(x)=x^2-1 satisfies E[Xh(X)]=0 but h != 0; with discrete covariates, the kernel of the map h -> E[Xh(X)] is nontrivial whenever the support size exceeds p+1, as is the case for the Bernoulli covariate X1 in Table 3 and for the discrete EHR covariates. Consequently, zeta*_a = zeta*_a' does not imply mu_a(X)=mu_a'(X), and the population objective (3) depends on zeta only through linear projections, so treatments with different conditional mean functions but identical best-linear projections will be fused by construction. Theorems 3.8 and 3.12 therefore establish recovery of projection-equivalence classes, not of the oracle group structure in Definition 2.2, and the abstract's central claim is not supported. Please either redefine the target as projection-based groups or impose a covariate setting in which Assumption 3.1 is actually plausible.
  2. [Section 3.2.3 and Appendix A.4, Assumption 3.10 vs Algorithm 1] The method is introduced as fused Lasso (Tibshirani et al., 2005), and Algorithm 1 implements P_n(zeta) = sum_{a<a'} lambda_n ||zeta_a - zeta_a'||_1, i.e., p_{lambda_n}(t)=lambda_n t. Assumption 3.10 requires the penalty to become constant for t >= c lambda_n/2, which the L1 penalty does not satisfy. In the proof of Statement 1, Eq. (18) asserts P_n(T(zeta)) = P_n(zeta_or) for all T(zeta), zeta_or in Z_or intersect Theta; this holds only if the penalty is constant over the cross-group distance range. With the L1 penalty, cross-group penalty terms differ, so the strict inequality for L_n can be offset by the penalty. Similarly, in Step 2.2 the claim that P_n(zeta)-P_n(zeta_bar) receives contributions only from within-group pairs is false for L1 because cross-group terms also change when moving from zeta to zeta_bar. Thus Theorem 3.12 does not cover the implemented estimator. The authors should either replace the implementation with a nonconvex penalty satisfying Assumption 3.10, or prove the oracle property for the L1 fused Lasso under the stated separation conditions.
minor comments (5)
  1. [Eq. (11)] The displayed AIPW estimator is ambiguous as typeset; the numerator should be written as I{B_i = d_B(X_i)}(Y_i - mu_hat_{B_i}(X_i)) + mu_hat_{d_B(X_i)}(X_i), with the division by the estimated propensity score applying to the first term.
  2. [Table 4] The notations X23 and X22 are unclear; they appear to denote X_2^3 and X_2^2, and should be written explicitly to avoid confusion.
  3. [Appendix A.1] The symbol 'b lambda' appears to be a typo for the estimator \hat\lambda; please correct it and check similar symbol substitutions in the Lagrange multiplier display.
  4. [Section 4.1 and Assumption 3.15] The simulation covariates X2 and X3 are Gaussian and the outcome mean functions in Table 4 involve exponentials, so Y and X are unbounded and Assumption 3.15 is violated; the paper should state that the Proposition 3.18 regret bound is not directly applicable to the reported simulation setting, or add a sub-Gaussian extension.
  5. [Section 4.2] The text says all 10 covariates are used in calibration weighting and nuisance estimation, but then states that 'the remaining six covariates' are used for fused Lasso and ITR; it should specify which six covariates are retained and why.

Circularity Check

0 steps flagged · score 0.0 of 10

No substantive circularity: the treatment-group oracle is defined independently, and the double-robustness and oracle-property theorems are proved from stated assumptions.

full rationale

I find no circular step in arXiv:2505.08092. The oracle group structure (Definition 2.2) is defined directly by equality of the conditional mean functions μ_a(X), independently of the proposed estimator. The target parameters ζ*_a are defined by population least-squares projections (4), and the forward implication μ_a = μ_a' ⇒ ζ*_a = ζ*_a' is immediate; the reverse implication is not assumed but is made conditional on the explicitly stated completeness Assumption 3.1. The double-robustness claim is proved in Lemma A.1 and Theorem 3.8 from the projection residual's construction and Assumption 3.3; it does not presuppose the group structure, since the oracle estimator uses the true groups only as a benchmark. Theorem 3.12 is a standard local-minimizer/oracle-property argument using Assumption 3.10's separation condition, not a re-statement of the conclusion. The calibration-weighting citations (Lee et al. 2023, Wu & Yang 2023) support a component method, and the proof of √n weight convergence in Appendix A.1 relies on textbook M-estimator conditions, so these citations are not load-bearing. The main weakness—Assumption 3.1 fails for discrete covariates and many continuous distributions—is a threat to the theorem's applicability, not circularity: the paper explicitly flags the assumption and does not define the estimator in terms of the oracle groups. Regret bounds in Propositions 3.17–3.18 are imported from the external CAIPWL/policy-tree framework with stated rate conditions, not derived from the paper's own fitted values.

Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

The central claim rests on standard causal assumptions, a strong completeness condition, regularity conditions on weights and errors, and a delicate penalty assumption. The most fragile items are the completeness assumption (likely false with discrete covariates) and the mismatch between the theoretical penalty condition and the implemented fused Lasso. No new physical or mechanistic entities are introduced.

free parameters (3)
  • Lambda_n (fusion penalty tuning parameter) = Selected by EBIC, value not reported
    Controls the strength of fusion between treatment-specific coefficient vectors. The theory requires it to lie between lower and upper bounds (Assumption 3.10), and simulations choose it data-adaptively.
  • Fusion grouping threshold = 0.25 (Euclidean distance)
    In simulations, treatments are declared grouped if the Euclidean distance between fused-lasso estimates is below 0.25. This post-hoc threshold is not part of the theoretical estimator, which uses exact equality.
  • Cressie-Read parameter gamma = Not specified in experiments
    The calibration weighting discrepancy family is indexed by gamma. The paper does not report which gamma is used in the numerical studies, though the theory allows any member under Assumption 3.2.
assumptions (7)
  • domain assumption Identification assumptions: consistency, unconfoundedness, and positivity (Assumption 2.1)
    Standard causal inference conditions needed to identify the value function from observational data.
  • ad hoc to paper Completeness: for any h, E[X h(X)] = 0 implies h(X) = 0 almost surely (Assumption 3.1)
    This bridges equality of projection coefficients to equality of conditional mean outcome functions. It is structurally necessary for group recovery and is questionable for discrete covariates.
  • domain assumption Calibration weights converge at sqrt(n) rate to bounded limits (Assumption 3.2)
    Asserted for entropy balancing under M-estimator regularity. If weights do not concentrate or are unbounded, the consistency argument in Theorem 3.8 fails.
  • domain assumption Either the calibration weighting model or the outcome model is correctly specified (Assumption 3.3)
    This is the core double robustness premise. If both models are misspecified, the bias term in Lemma A.1 does not vanish and fusion consistency is not guaranteed.
  • ad hoc to paper Penalty regularity: sharp derivative near zero and constant tail (Assumption 3.10)
    Required for the oracle property. The L1 fused lasso penalty described in the algorithm and simulations does not satisfy the constant-tail condition.
  • domain assumption Accurate estimation of the main effect M0(X), Section 3.1
    The paper defines transformed outcomes as Y minus M0(X) and assumes M0 is accurately estimated. Misspecification would shift the target projection vectors and could break recovery of the true group structure.
  • standard math Regularity conditions on X and sub-Gaussian errors (Assumptions 3.5 and 3.6)
    Typical high-dimensional statistical assumptions used in the proof of Theorem 3.8.

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Pith. "Pith review of Doubly Robust Fusion of Many Treatments for Policy Learning." pith.science (2026). https://pith.science/paper/T5HMUBFR

@misc{pith2026250508092,
  author       = {Pith},
  title        = {Pith review of: Doubly Robust Fusion of Many Treatments for Policy Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/T5HMUBFR}},
  note         = {Machine review of arXiv:2505.08092}
}
read the original abstract

Individualized treatment rules/recommendations (ITRs) aim to improve patient outcomes by tailoring treatments to the characteristics of each individual. However, when there are many treatment groups, existing methods face significant challenges due to data sparsity within treatment groups and highly unbalanced covariate distributions across groups. To address these challenges, we propose a novel calibration-weighted treatment fusion procedure that robustly balances covariates across treatment groups and fuses similar treatments using a penalized working model. The fusion procedure ensures the recovery of latent treatment group structures when either the calibration model or the outcome model is correctly specified. In the fused treatment space, practitioners can seamlessly apply state-of-the-art ITR learning methods with the flexibility to utilize a subset of covariates, thereby achieving robustness while addressing practical concerns such as fairness. We establish theoretical guarantees, including consistency, the oracle property of treatment fusion, and regret bounds when integrated with multi-armed ITR learning methods such as policy trees. Simulation studies show superior group recovery and policy value compared to existing approaches. We illustrate the practical utility of our method using a nationwide electronic health record-derived de-identified database containing data from patients with Chronic Lymphocytic Leukemia and Small Lymphocytic Lymphoma.

Figures

Figures reproduced from arXiv: 2505.08092 by the authors.

Figure 1
Figure 1. The fusion results and the learned optimal policy tree assigns patients to grouped treatments based on covariate splits. time is the time from diagnosis to the first LOT; age is the age at the start of the first LOT; lymphadenopathy false=1 indicates no lymph node swelling, and lymphadenopathy false=0 indicates its presence; raistage 0=1 indicates Rai stage 0 (low risk), and raistage 0=0 indicates stages I-IV (inter… view at source ↗

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Works this paper leans on

60 extracted references · 52 canonical work pages

  1. [1]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION format.date year duplicate empty "emp...

  2. [2]

    Synthetic combinations: A causal inference framework for combinatorial interventions

    Agarwal, A., Agarwal, A., and Vijaykumar, S. Synthetic combinations: A causal inference framework for combinatorial interventions. Advances in Neural Information Processing Systems, 36: 0 19195--19216, 2023

    work page 2023

  3. [3]

    Bayesian off-policy evaluation and learning for large action spaces

    Aouali, I., Brunel, V.-E., Rohde, D., and Korba, A. Bayesian off-policy evaluation and learning for large action spaces. arXiv preprint arXiv:2402.14664, 2024

    arXiv 2024

  4. [4]

    and Wager, S

    Athey, S. and Wager, S. Policy learning with observational data. Econometrica, 89 0 (1): 0 133--161, 2021

    work page 2021

  5. [5]

    Model-assisted cohort selection with bias analysis for generating large-scale cohorts from the EHR for oncology research

    Birnbaum, B., Nussbaum, N., Seidl-Rathkopf, K., Agrawal, M., Estevez, M., Estola, E., Haimson, J., He, L., Larson, P., and Richardson, P. Model-assisted cohort selection with bias analysis for generating large-scale cohorts from the EHR for oncology research. arXiv preprint arXiv:2001.09765, 2020

    arXiv 2001

  6. [6]

    Boos, D. D. and Stefanski, L. A. Essential statistical inference: theory and methods, volume 120. Springer Science & Business Media, 2013

    work page 2013

  7. [7]

    Bruns-Smith, D., Dukes, O., Feller, A., and Ogburn, E. L. Augmented balancing weights as linear regression. Journal of the Royal Statistical Society Series B: Statistical Methodology, pp.\ qkaf019, 2025

    work page 2025

  8. [8]

    Deep jump learning for off-policy evaluation in continuous treatment settings

    Cai, H., Shi, C., Song, R., and Lu, W. Deep jump learning for off-policy evaluation in continuous treatment settings. Advances in Neural Information Processing Systems, 34: 0 15285--15300, 2021

    work page 2021

Show all 60 references
  1. [9]

    Carranza, A. G. and Athey, S. Robust offline policy learning with observational data from multiple sources. arXiv preprint arXiv:2410.08537, 2024

    2024 arXiv

  2. [10]

    Estimation of a non-parametric variable importance measure of a continuous exposure

    Chambaz, A., Neuvial, P., and van der Laan, M. Estimation of a non-parametric variable importance measure of a continuous exposure. Electronic Journal of Statistics, 6: 0 1059--1099, 2012

    2012

  3. [11]

    and Chen, Z

    Chen, J. and Chen, Z. Extended bayesian information criteria for model selection with large model spaces. Biometrika, 95 0 (3): 0 759--771, 2008

    2008

  4. [12]

    and Yang, S

    Cheng, Y. and Yang, S. Inference for optimal linear treatment regimes in personalized decision-making. In Kiyavash, N. and Mooij, J. M. (eds.), Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, volume 244 of Proceedings of Machine Learning Resea...

    2024

  5. [13]

    Semi-parametric efficient policy learning with continuous actions

    Chernozhukov, V., Demirer, M., Lewis, G., and Syrgkanis, V. Semi-parametric efficient policy learning with continuous actions. Advances in Neural Information Processing Systems, 32, 2019

    2019

  6. [14]

    Targeted optimal treatment regime learning using summary statistics

    Chu, J., Lu, W., and Yang, S. Targeted optimal treatment regime learning using summary statistics. Biometrika, 110 0 (4): 0 913--931, 2023

    2023

  7. [15]

    and Read, T

    Cressie, N. and Read, T. R. Multinomial goodness-of-fit tests. Journal of the Royal Statistical Society: Series B (Methodological), 46 0 (3): 0 440--464, 1984

    1984

  8. [16]

    S., and van der Laan, M

    Ertefaie, A., Hejazi, N. S., and van der Laan, M. J. Nonparametric inverse-probability-weighted estimators based on the highly adaptive lasso. Biometrics, 79 0 (2): 0 1029--1041, 2023

    2023

  9. [17]

    Causal customer churn analysis with low-rank tensor block hazard model

    Gao, C., Zhang, Z., and Yang, S. Causal customer churn analysis with low-rank tensor block hazard model. In International Conference on Machine Learning, pp.\ 14920--14953. PMLR, 2024

    2024

  10. [18]

    Gates, A. J. and Ahn, Y.-Y. The impact of random models on clustering similarity. Journal of Machine Learning Research, 18 0 (87): 0 1--28, 2017

    2017

  11. [19]

    Flexible inference of optimal individualized treatment strategy in covariate adjusted randomization with multiple covariates

    Ghosh, T., Ma, Y., Song, R., and Zhong, P. Flexible inference of optimal individualized treatment strategy in covariate adjusted randomization with multiple covariates. Electronic Journal of Statistics, 17 0 (1): 0 1344--1370, 2023

    2023

  12. [20]

    Goplerud, M., Imai, K., and Pashley, N. E. Estimating heterogeneous causal effects of high-dimensional treatments: Application to conjoint analysis. The Annals of Applied Statistics, in press, 2025

    2025

  13. [21]

    J., and Silva, R

    Kaddour, J., Zhu, Y., Liu, Q., Kusner, M. J., and Silva, R. Causal effect inference for structured treatments. Advances in Neural Information Processing Systems, 34: 0 24841--24854, 2021

    2021

  14. [22]

    Laber, E. B. and Zhao, Y.-Q. Tree-based methods for individualized treatment regimes. Biometrika, 102 0 (3): 0 501--514, 2015

    2015

  15. [23]

    Improving trial generalizability using observational studies

    Lee, D., Yang, S., Dong, L., Wang, X., Zeng, D., and Cai, J. Improving trial generalizability using observational studies. Biometrics, 79 0 (2): 0 1213--1225, 2023

    2023

  16. [24]

    Estimating individualized optimal combination therapies through outcome weighted deep learning algorithms

    Liang, M., Ye, T., and Fu, H. Estimating individualized optimal combination therapies through outcome weighted deep learning algorithms. Statistics in medicine, 37 0 (27): 0 3869--3886, 2018

    2018

  17. [25]

    A., and Zhao, Y.-Q

    Liang, M., Choi, Y.-G., Ning, Y., Smith, M. A., and Zhao, Y.-Q. Estimation and inference on high-dimensional individualized treatment rule in observational data using split-and-pooled de-correlated score. Journal of Machine Learning Research, 23 0 (262): 0 1--65, 2022

    2022

  18. [26]

    Learning individualized treatment rules with many treatments: A supervised clustering approach using adaptive fusion

    Ma, H., Zeng, D., and Liu, Y. Learning individualized treatment rules with many treatments: A supervised clustering approach using adaptive fusion. Advances in Neural Information Processing Systems, 35: 0 15956--15969, 2022

    2022

  19. [27]

    Learning optimal group-structured individualized treatment rules with many treatments

    Ma, H., Zeng, D., and Liu, Y. Learning optimal group-structured individualized treatment rules with many treatments. Journal of Machine Learning Research, 24 0 (102): 0 1--48, 2023

    2023

  20. [28]

    and Huang, J

    Ma, S. and Huang, J. A concave pairwise fusion approach to subgroup analysis. Journal of the American Statistical Association, 112 0 (517): 0 410--423, 2017

    2017

  21. [29]

    J., and Baxi, S

    Ma, X., Long, L., Moon, S., Adamson, B. J., and Baxi, S. S. Comparison of population characteristics in real-world clinical oncology databases in the US : Flatiron health, SEER , and NPCR . Medrxiv, 2020

    2020

  22. [30]

    G., Morstatter, F., Galstyan, A., and Ver Steeg, G

    Marmarelis, M. G., Morstatter, F., Galstyan, A., and Ver Steeg, G. Policy learning for localized interventions from observational data. In International Conference on Artificial Intelligence and Statistics, pp.\ 4456--4464. PMLR, 2024

    2024

  23. [31]

    Learning optimal distributionally robust individualized treatment rules

    Mo, W., Qi, Z., and Liu, Y. Learning optimal distributionally robust individualized treatment rules. Journal of the American Statistical Association, 116 0 (534): 0 659--674, 2021

    2021

  24. [32]

    Murphy, S. A. Optimal dynamic treatment regimes. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65 0 (2): 0 331--355, 2003

    2003

  25. [33]

    Zero-shot causal learning

    Nilforoshan, H., Moor, M., Roohani, Y., Chen, Y., S urina, A., Yasunaga, M., Oblak, S., and Leskovec, J. Zero-shot causal learning. Advances in Neural Information Processing Systems, 36: 0 6862--6901, 2023

    2023

  26. [34]

    Learning robust decision policies from observational data

    Osama, M., Zachariah, D., and Stoica, P. Learning robust decision policies from observational data. Advances in Neural Information Processing Systems, 33: 0 18205--18214, 2020

    2020

  27. [35]

    Offline policy evaluation in large action spaces via outcome-oriented action grouping

    Peng, J., Zou, H., Liu, J., Li, S., Jiang, Y., Pei, J., and Cui, P. Offline policy evaluation in large action spaces via outcome-oriented action grouping. In Proceedings of the ACM Web Conference 2023, pp.\ 1220--1230, 2023

    2023

  28. [36]

    and Liu, Y

    Qi, Z. and Liu, Y. D-learning to estimate optimal individual treatment rules. Electronic Journal of Statistics, 12 0 (2), 2018

    2018

  29. [37]

    and Murphy, S

    Qian, M. and Murphy, S. A. Performance guarantees for individualized treatment rules. The Annals of Statistics, 39 0 (2): 0 1180--1210, 2011

    2011

  30. [38]

    U., Luckett, D

    Rashid, N. U., Luckett, D. J., Chen, J., Lawson, M. T., Wang, L., Zhang, Y., Laber, E. B., Liu, Y., Yeh, J. J., Zeng, D., et al. High-dimensional precision medicine from patient-derived xenografts. Journal of the American Statistical Association, 116 0 (535): 0 1140--1154, 2021

    2021

  31. [39]

    Rubin, D. B. Bayesian inference for causal effects: The role of randomization. The Annals of Statistics, 6 0 (1): 0 34--58, 1978

    1978

  32. [40]

    Off-policy evaluation for large action spaces via policy convolution

    Sachdeva, N., Wang, L., Liang, D., Kallus, N., and McAuley, J. Off-policy evaluation for large action spaces via policy convolution. In Proceedings of the ACM Web Conference 2024, pp.\ 3576--3585, 2024

    2024

  33. [41]

    and Joachims, T

    Saito, Y. and Joachims, T. Off-policy evaluation for large action spaces via embeddings. In International Conference on Machine Learning, pp.\ 19089--19122. PMLR, 2022

    2022

  34. [42]

    Off-policy evaluation for large action spaces via conjunct effect modeling

    Saito, Y., Ren, Q., and Joachims, T. Off-policy evaluation for large action spaces via conjunct effect modeling. In international conference on Machine learning, pp.\ 29734--29759. PMLR, 2023

    2023

  35. [43]

    Estimating the dimension of a model

    Schwarz, G. Estimating the dimension of a model. The annals of statistics, pp.\ 461--464, 1978

    1978

  36. [44]

    Reliable off-policy learning for dosage combinations

    Schweisthal, J., Frauen, D., Melnychuk, V., and Feuerriegel, S. Reliable off-policy learning for dosage combinations. Advances in Neural Information Processing Systems, 36: 0 67900--67924, 2023

    2023

  37. [45]

    High-dimensional a-learning for optimal dynamic treatment regimes

    Shi, C., Fan, A., Song, R., and Lu, W. High-dimensional a-learning for optimal dynamic treatment regimes. Annals of statistics, 46 0 (3): 0 925, 2018

    2018

  38. [46]

    Song, R., Wang, W., Zeng, D., and Kosorok, M. R. Penalized Q -learning for dynamic treatment regimens. Statistica Sinica, 25 0 (3): 0 901, 2015

    2015

  39. [47]

    F., Ton, J.-F., Cornish, R., Teh, Y

    Taufiq, M. F., Ton, J.-F., Cornish, R., Teh, Y. W., and Doucet, A. Conformal off-policy prediction in contextual bandits. Advances in Neural Information Processing Systems, 35: 0 31512--31524, 2022

    2022

  40. [48]

    Sparsity and smoothness via the fused lasso

    Tibshirani, R., Saunders, M., Rosset, S., Zhu, J., and Knight, K. Sparsity and smoothness via the fused lasso. Journal of the Royal Statistical Society Series B: Statistical Methodology, 67 0 (1): 0 91--108, 2005

    2005

  41. [49]

    Wainwright, M. J. High-dimensional Statistics: A Non-asymptotic Viewpoint, volume 48. Cambridge University Press, 2019

    2019

  42. [50]

    Watkins, C. J. and Dayan, P. Q-learning. Machine Learning, 8 0 (3-4): 0 279--292, 1992

    1992

  43. [51]

    Wooldridge, J. M. Introductory Econometrics: A Modern Approach. South-Western Cengage Learning, Mason, OH, 5th edition, 2012. ISBN 978-1-111-53104-1

    2012

  44. [52]

    and Yang, S

    Wu, L. and Yang, S. Transfer learning of individualized treatment rules from experimental to real-world data. Journal of Computational and Graphical Statistics, 32 0 (3): 0 1036--1045, 2023

    2023

  45. [53]

    Multi-label residual weighted learning for individualized combination treatment rule

    Xu, Q., Cao, X., Chen, G., Zeng, H., Fu, H., and Qu, A. Multi-label residual weighted learning for individualized combination treatment rule. Electronic Journal of Statistics, 18 0 (1): 0 1517--1548, 2024 a

    2024

  46. [54]

    Optimal individualized treatment rule for combination treatments under budget constraints

    Xu, Q., Fu, H., and Qu, A. Optimal individualized treatment rule for combination treatments under budget constraints. Journal of the Royal Statistical Society Series B: Statistical Methodology, 86 0 (3): 0 714--741, 2024 b

    2024

  47. [55]

    A., Laber, E

    Zhang, B., Tsiatis, A. A., Laber, E. B., and Davidian, M. A robust method for estimating optimal treatment regimes. Biometrics, 68 0 (4): 0 1010--1018, 2012

    2012

  48. [56]

    B., Tsiatis, A., and Davidian, M

    Zhang, Y., Laber, E. B., Tsiatis, A., and Davidian, M. Using decision lists to construct interpretable and parsimonious treatment regimes. Biometrics, 71 0 (4): 0 895--904, 2015

    2015

  49. [57]

    Conformal off-policy prediction

    Zhang, Y., Shi, C., and Luo, S. Conformal off-policy prediction. In International Conference on Artificial Intelligence and Statistics, pp.\ 2751--2768. PMLR, 2023

    2023

  50. [58]

    Minimax regret estimation for generalizing heterogeneous treatment effects with multisite data

    Zhang, Y., Huang, M., and Imai, K. Minimax regret estimation for generalizing heterogeneous treatment effects with multisite data. arXiv preprint arXiv:2412.11136, 2024

    2024 arXiv

  51. [59]

    J., and Kosorok, M

    Zhao, Y., Zeng, D., Rush, A. J., and Kosorok, M. R. Estimating individualized treatment rules using outcome weighted learning. Journal of the American Statistical Association, 107 0 (499): 0 1106--1118, 2012

    2012

  52. [60]

    Offline multi-action policy learning: Generalization and optimization

    Zhou, Z., Athey, S., and Wager, S. Offline multi-action policy learning: Generalization and optimization. Operations Research, 71 0 (1): 0 148--183, 2023

    2023

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.