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REVIEW 4 major objections 4 minor 69 references

Efficient and Scalable Estimation of Distributional Treatment Effects with Multi-Task Neural Networks

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A single multi-task neural network with a monotonic output layer estimates distributional treatment effects at all thresholds at once, cutting MSE by 50–65% and replacing many separate regressions.

desk verdict Solid applied paper: new monotonic multi-task NN for regression-adjusted DTE, backed by credible simulations and two real experiments; the main gap is that the efficiency theory covers only the oracle adjustment, not the feasible NN estimator. read the letter →

arxiv 2507.07738 v1 pith:22AE3FIY submitted 2025-07-10 cs.LG econ.EM

Tomu Hirata , Undral Byambadalai , Tatsushi Oka , Shota Yasui , Shingo Uto This is my paper
classification cs.LGecon.EM
keywords distributionaltreatmenteffectsmulti-tasklearningregressionadjustmentshapeconstraintsmulti-labelclassificationneuralnetworksrandomizedexperimentsconditionalcumulativedistributionfunctions
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

Randomized experiments usually report average treatment effects, but the distributional treatment effect (DTE) — the whole gap between the outcome distribution under treatment and control — gives a fuller picture of who is affected and how. The paper tries to establish that a single multi-task neural network can estimate all the points of this distributional gap at once, using a monotonicity-enforcing output layer and regression adjustment on pre-treatment covariates, and that this is both more precise and much cheaper than fitting a separate regression per threshold. In simulations the proposed estimator lowers mean squared error by 50 to 65 percent relative to the empirical DTE, with the largest gains in the tails, and runs about 80 percent faster than single-task neural-network adjustment; on two real experiments it lowers standard errors by up to 30 percent and cuts runtime by 71 to 93 percent. If true, this makes detailed distributional analysis feasible on the millions-of-users A/B tests common in industry.

What carries the argument

The load-bearing object is the regression-adjusted CDF estimator in equation (1), combined with a multi-task neural network that outputs all thresholds at once. The network's last hidden layer computes non-negative values \(g(h^H_m)\), forms cumulative sums \(\tilde h^H_j = \sum_{m\le j} g(h^H_m)\), and maps them through a monotone function \(f\), so the \(M\) output probabilities are automatically nondecreasing in the threshold. This cumulative-sum layer is the mechanism that enforces the shape constraint by construction rather than by post-hoc correction. The efficiency argument rests on Assumption 3, that the cost \(\tilde P\) of training one multi-output model is \(o(P\cdot M)\), the cost of training \(M\) separate models; the paper verifies this theoretically for linear regression and reports operation counts for several network architectures, while noting that boosting trees do not satisfy it.

What would settle it

On the same hardware, fold split, and threshold grid used in the paper's streaming-platform experiment, train the proposed multi-task network and \(M\) single-task networks with identical architecture and measure total wall-clock time; if the multi-task run is not cheaper than the sum of the single-task runs, Assumption 3 fails for the method as implemented.

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Extended reading notes

Core claim

The central claim is that distributional treatment effects can be estimated by rewriting the task as a single multi-label classification problem: for each treatment group, one neural network predicts the conditional probability \(\$gamma^{{(w)}}$_y(X) = \Pr($Y^{{(w)}}$\le y\mid X)\) at every threshold \(y\in\tilde{\mathcal Y}\) simultaneously, and these predictions are plugged into the regression-adjusted estimator \(\hat F_{$Y^{{(w)}}$}(y) = $n_w^{{-1}}$\sum_{i:W_i=w}(\mathbf{1}\{Y_i\le y\}-\hat\$gamma^{{(w)}}$_y(X_i)) + $n^{{-1}}$\sum_i\hat\$gamma^{{(w)}}$_y(X_i)\). The final layer accumulates non-negative hidden units with a cumulative sum before a monotone link, guaranteeing \(\hat F(y_s)\ge \hat F(y_t)\) whenever \(y_s\ge y_t\). The authors argue that joint training shares statistical strength across thresholds — helping where labels are imbalanced, such as at the 90th percentile — and that, under a sublinear-cost assumption on multi-output training, one network is far cheaper than \(M\) single-task networks. Their simulations show a 50–65% MSE reduction over the unadjusted empirical estimator and a roughly 80% runtime saving over single-task adjustment, and the two real experiments show standard-error reductions of 0–30% and 0–16%.

Load-bearing premise

The scalability claim rests on Assumption 3: that a single multi-task model for all thresholds can be trained at strictly less cost than one model per threshold; the paper proves this for linear regression and reports operation counts for generic architectures, but does not verify it for the actual networks used in its experiments, and notes that boosting trees violate it.

Editorial extensions

If this is right

  • Distributional treatment effects become practical at industrial scale: instead of \(M\) regression fits, one network fit supplies all threshold probabilities, and the runtime gap grows with \(M\).
  • Tail regions, where labels are imbalanced and single-task models struggle, receive the largest variance reduction, so the method is most useful when rare outcomes or extreme quantiles matter.
  • Because the monotonic constraint is enforced by construction, the fitted CDF estimates are always nondecreasing in the threshold, removing a common source of irregular estimates and improving interpretability.
  • The same estimator extends to any functional of CDFs, such as interval probabilities (PTE), so applied users get a whole distributional summary from one training run instead of separate analyses.

Reading between the lines

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

  • If Assumption 3 holds generally, the computational advantage should grow with the number of thresholds \(M\), making the method increasingly attractive for fine grids or continuous outcomes; for very small \(M\), the overhead of a multi-task network may offset the savings.
  • The cumulative-sum monotonic layer is a generic device that could be transplanted to other ordered-output problems, such as conditional quantile regression, survival curves, or calibration of probabilistic classifiers, where monotonicity is structural.
  • The streaming-platform experiment shows almost no gain from the monotonic constraint at roughly 4.3 million observations, suggesting the constraint's value is concentrated in smaller samples and tail regions; practitioners with very large data might reasonably drop it to save tuning effort.
  • A testable next step is to compare the calibration of the multi-task predictions against observed frequencies; if shared representations improve calibration as well as variance, the confidence bands would be expected to show better coverage than the standard-error comparison alone indicates.
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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

4 major / 4 minor

Summary. The paper proposes a multi-task neural network (NN) regression-adjustment estimator for distributional treatment effects (DTE) in randomized experiments. The method reformulates conditional CDF estimation at multiple outcome thresholds as multi-label classification, trains a single network for all thresholds, and enforces monotonicity across thresholds via a cumulative-sum construction. The authors present a theorem on variance reduction for an infeasible oracle estimator that uses the true conditional CDF, and they evaluate the feasible estimator in a Monte Carlo simulation and two real applications: a water conservation field experiment and a large-scale ABEMA streaming A/B test. They report 50-65% MSE reductions relative to the empirical estimator in simulation, 0-30% and 0-16% SE reductions in the two real applications, and computational speedups of roughly 71-93% over single-task NN adjustment.

Significance. If the empirical claims hold, the paper makes a useful practical contribution: a computationally cheaper regression-adjustment method for DTE in large randomized experiments, with an open-source Python implementation and a reproducible public-data experiment. The strengths include the clear randomized-experiment setting, the honest reporting of some negative results (e.g., the monotonic constraint's lack of benefit in the ABEMA data), and the use of cross-fitting and multiplier bootstrap in the empirical studies. However, the main theoretical support (Theorem 1) applies only to an infeasible oracle estimator, and no theoretical rate or finite-sample guarantee is provided for the neural-network nuisance estimator actually used. The efficiency claim therefore rests on empirical evidence that currently lacks uncertainty quantification, and the scalability claim rests on an assumption not directly verified for the deployed model.

major comments (4)
  1. [Section 4.2, Eq. (1), Theorem 1] Theorem 1 establishes variance reduction only for the infeasible estimator that plugs in the true conditional distribution gamma; the feasible estimator in Eq. (1) replaces gamma with a multi-task neural network, and no theorem or rate condition shows that this replacement preserves the variance reduction or makes the multiplier bootstrap in Appendix C asymptotically valid. Standard DML theory requires the nuisance estimator to converge sufficiently fast (e.g., o(n^{-1/4}) in the relevant norm), and the paper neither verifies such a rate for the three-layer network nor cites NN-specific DML results. Because Sections 5.2 and 5.3 report bootstrap SE reductions as evidence, this gap is load-bearing for the central efficiency claim.
  2. [Section 4.2, Assumption 3, Table 1] The computational-efficiency and scalability claims rest on Assumption 3, that a single multi-task model can be trained at sublinear cost in the number of thresholds M compared with M separate models. Appendix G.1 proves this for multivariate linear regression and Table A8 reports MAC counts for generic architectures, but the actual multi-task NN used in Sections 5.2 and 5.3 is not tested for how its wall-clock training time scales with M under the cross-fitting scheme; Table 1 reports only fixed-M comparisons at one M per experiment. A direct measurement of training time versus M (with folds, epochs, and batch size held fixed) is needed to substantiate the 'scalable' characterization, especially because the text notes that boosting trees do not satisfy Assumption 3.
  3. [Sections 5.1-5.3, Figure 3, Table A3-A7] The reported MSE and SE reductions are point estimates without Monte Carlo confidence intervals. For the simulation with S=500, standard errors of the MSE reductions are directly computable; for the real-data SE reductions based on B=5,000 multiplier draws, the bootstrap itself has simulation error. Without uncertainty intervals, it is hard to judge whether the differences between methods (e.g., multi-task versus single-task) are statistically meaningful, particularly in the water data where the summary distributions overlap substantially.
  4. [Section 5.3, Table A7, Conclusion] The monotonic constraint provides no clear improvement in the ABEMA experiment (Table A7 shows nearly identical SE reductions for multi-task and monotonic multi-task), and the text concedes this. Nevertheless, the abstract and conclusion attribute precision enhancement to the monotonic shape constraint. The claim should be qualified to settings where the constraint actually helps, or presented as a secondary contribution rather than a general advantage.
minor comments (4)
  1. [Section 5.1] The sentence 'Since all estimators used in the experiment are unbiased' is asserted without proof for the NN-based estimators; under cross-fitting, unbiasedness is not immediate and should be either proven or replaced by a statement about approximate unbiasedness.
  2. [Appendix G.2] Table A8 reports MAC counts, which are an analytical proxy, but the text says the sub-linear assumption is 'empirically validate[d]'; MAC counts do not measure wall-clock training time and should be described as architectural complexity evidence rather than empirical validation.
  3. [Table A2] The relationship between the last hidden layer size h3 and the number of locations M should be stated explicitly: for the water experiment h3=200 and for ABEMA h3=51, which appear equal to M, but the simulation's h3=19 equals the number of quantiles; clarifying this avoids confusion about whether the architecture changes with M.
  4. [Figure 5] The pointwise SE reductions are computed across 200 locations in the water experiment, but no adjustment is made for multiple comparisons or for dependence across thresholds; a sentence acknowledging this would help the reader interpret the claimed improvements.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central estimator is benchmarked externally and the oracle theorem is proved in-appendix.

full rationale

The paper's central claim is empirical: the multi-task neural-network adjustment reduces DTE MSE/SE relative to the empirical estimator. That claim is tested against a Monte Carlo ground truth from 10^5 fresh samples, the public Ferraro and Price water data, and an internal ABEMA experiment; no parameter is fitted to the target DTE and then reported as a prediction. The only theoretical efficiency result, Theorem 1, concerns the infeasible oracle estimator that uses the true conditional CDF, and although its proof begins by citing the authors' prior work [8], the full proof is supplied in Appendix B using an elementary Lagrange/Bergstrom lemma, so the citation is not load-bearing. The feasible estimator's theoretical gap (no rate condition for the NN nuisance) and Assumption 3's lack of verification for the exact NN architecture are genuine correctness risks, but they are not circularity: they are missing support for an external benchmark claim, not an input redefined as an output. No equation in the paper reduces by construction to a fitted quantity or to a self-citation chain.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central derivation uses no new free parameters beyond standard NN hyperparameters; the key new premise is Assumption 3. No invented entities.

free parameters (1)
  • Neural network hyperparameters (learning rate, batch size, hidden sizes, folds) = See Table A2 (e.g., lr 0.01/0.001, batch 16/64/128, L=2)
    Chosen by hand per dataset; no sensitivity analysis is reported, so the observed MSE/SE reductions could depend on these choices.
assumptions (4)
  • domain assumption Assumption 1 and 2: unconfoundedness and overlap of treatment assignment
    Standard RCT conditions used throughout Section 3 to identify potential outcome CDFs.
  • ad hoc to paper Assumption 3: multi-task model training cost is sublinear in the number of target variables
    Introduced to justify the claimed computational advantage; verified for linear regression and a few NN architectures in Appendix G, but not for all models.
  • standard math DML regularity conditions from Chernozhukov et al. (2018)
    Used to claim unbiasedness and asymptotic normality of the cross-fitted regression-adjusted estimator; no specific rates are established for the multi-task NN estimator.
  • standard math Monotonicity of the true conditional CDF in y
    Guarantees the shape constraint in Section 4.2 does not exclude the truth.

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Cite this review

Pith. "Pith review of Efficient and Scalable Estimation of Distributional Treatment Effects with Multi-Task Neural Networks." pith.science (2026). https://pith.science/paper/22AE3FIY

@misc{pith2026250707738,
  author       = {Pith},
  title        = {Pith review of: Efficient and Scalable Estimation of Distributional Treatment Effects with Multi-Task Neural Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/22AE3FIY}},
  note         = {Machine review of arXiv:2507.07738}
}
read the original abstract

We propose a novel multi-task neural network approach for estimating distributional treatment effects (DTE) in randomized experiments. While DTE provides more granular insights into the experiment outcomes over conventional methods focusing on the Average Treatment Effect (ATE), estimating it with regression adjustment methods presents significant challenges. Specifically, precision in the distribution tails suffers due to data imbalance, and computational inefficiencies arise from the need to solve numerous regression problems, particularly in large-scale datasets commonly encountered in industry. To address these limitations, our method leverages multi-task neural networks to estimate conditional outcome distributions while incorporating monotonic shape constraints and multi-threshold label learning to enhance accuracy. To demonstrate the practical effectiveness of our proposed method, we apply our method to both simulated and real-world datasets, including a randomized field experiment aimed at reducing water consumption in the US and a large-scale A/B test from a leading streaming platform in Japan. The experimental results consistently demonstrate superior performance across various datasets, establishing our method as a robust and practical solution for modern causal inference applications requiring a detailed understanding of treatment effect heterogeneity.

Figures

Figures reproduced from arXiv: 2507.07738 by the authors.

Figure 1
Figure 1. Illustration: Multi-Task neural network estimating the conditional distribution function [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Illustration of the architecture of the proposed neural network model. The model accumulates the [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Pointwise MSE Reduction (%) relative to the empirical DTE in the Simulation Study. DTE is [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Distributional Treatment Effect (DTE) of a nudge (Strong Social Norm vs. Control) on water [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Pointwise SE reduction (%) relative to the empirical DTE of a nudge on water consumption. [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: Top-of-Screen promotion in ABEMA application. Screen captures showing the two treatment [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: Distributional Treatment Effect (DTE) of the content promotion on ABEMA. The left figure [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: Pointwise SE reduction (%) relative to empirical DTE of content promotion on 46-minute program [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]

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Works this paper leans on

69 extracted references · 66 canonical work pages

  1. [1]

    Bootstrap tests for distributional treatment effects in instrumental variable models

    Alberto Abadie. Bootstrap tests for distributional treatment effects in instrumental variable models. Journal of the American Statistical Association, 97:284–292, 2002

    work page 2002

  2. [2]

    Multi-task feature learning

    Andreas Argyriou, Theodoros Evgeniou, and Massimiliano Pontil. Multi-task feature learning. Ad- vances in Neural Information Processing Systems, 19:41–48, 2007

    work page 2007

  3. [3]

    Susan Athey and Guido W. Imbens. Identification and inference in nonlinear difference-in-differences models. Econometrica, 74:431–497, 2006

    work page 2006

  4. [4]

    Richard E. Barlow. Statistical inference under order restrictions : the theory and application of iso- tonic regression. Wiley, 1972

    work page 1972

  5. [5]

    Program evalu- ation and causal inference with high-dimensional data

    Alexandre Belloni, Victor Chernozhukov, Ivan Fernandez-Val, and Christian Hansen. Program evalu- ation and causal inference with high-dimensional data. Econometrica, 85(1):233–298, 2017

    work page 2017

  6. [6]

    Covari- ance adjustments for the analysis of randomized field experiments

    Richard Berk, Emil Pitkin, Lawrence Brown, Andreas Buja, Edward George, and Linda Zhao. Covari- ance adjustments for the analysis of randomized field experiments. Evaluation review, 37:170–196, 2013

    work page 2013

  7. [7]

    On efficient estimation of distri- butional treatment effects under covariate-adaptive randomization

    Undral Byambadalai, Tomu Hirata, Tatsushi Oka, and Shota Yasui. On efficient estimation of distri- butional treatment effects under covariate-adaptive randomization. arXiv preprint arXiv:2506.05945, 2025

    arXiv 2025

  8. [8]

    Estimating distributional treatment effects in randomized experiments: Machine learning for variance reduction

    Undral Byambadalai, Tatsushi Oka, and Shota Yasui. Estimating distributional treatment effects in randomized experiments: Machine learning for variance reduction. 2024

    work page 2024

Show all 69 references
  1. [9]

    Quantile treatment effects in difference in differences models with panel data

    Brantly Callaway and Tong Li. Quantile treatment effects in difference in differences models with panel data. Quantitative economics, 10:1579–1618, 2019

    2019

  2. [10]

    Quantile treatment effects in difference in differences models under dependence restrictions and with only two time periods

    Brantly Callaway, Tong Li, and Tatsushi Oka. Quantile treatment effects in difference in differences models under dependence restrictions and with only two time periods. Journal of Econometrics , 206(2):395–413, 2018

    2018

  3. [11]

    Multitask learning

    Rich Caruana. Multitask learning. Machine Learning, 28(1):41–75, 1997

    1997

  4. [12]

    Double/debiased machine learning for treatment and structural parameters

    Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo, Christian Hansen, Whitney Newey, and James Robins. Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21(1):C1–C68, 01 2018

    2018

  5. [13]

    Locally robust semiparametric estimation

    Victor Chernozhukov, Juan Carlos Escanciano, Hidehiko Ichimura, Whitney K Newey, and James M Robins. Locally robust semiparametric estimation. Econometrica, 90(4):1501–1535, 2022

    2022

  6. [14]

    Inference on counterfactual distributions

    Victor Chernozhukov, Iv´an Fern´andez-Val, and Blaise Melly. Inference on counterfactual distributions. Econometrica, 81(6):2205–2268, 2013

    2013

  7. [15]

    Inference on counterfactual distributions

    Victor Chernozhukov, Iv´an Fern´andez-Val, and Blaise Melly. Inference on counterfactual distributions. Econometrica, 81:2205–2268, 2013

    2013

  8. [16]

    Generic inference on quantile and quantile effect functions for discrete outcomes

    Victor Chernozhukov, Iv ´an Fern ´andez-Val, Blaise Melly, and Kaspar W ¨uthrich. Generic inference on quantile and quantile effect functions for discrete outcomes. Journal of the American Statistical Association, 115:123–137, 2020. 14

    2020

  9. [17]

    An iv model of quantile treatment effects

    Victor Chernozhukov and Christian Hansen. An iv model of quantile treatment effects. Econometrica, 73:245–261, 2005

    2005

  10. [18]

    The econometrics of shape restrictions

    Denis Chetverikov, Andres Santos, and Azeem M Shaikh. The econometrics of shape restrictions. Annual review of economics, 10:31–63, 2018

    2018

  11. [19]

    Chipman, Edward I

    Hugh A. Chipman, Edward I. George, and Robert E. McCulloch. Bart: Bayesian additive regression trees. The Annals of Applied Statistics, 4(1), March 2010

    2010

  12. [20]

    Shape constraints for set functions

    Andrew Cotter, Maya Gupta, Heinrich Jiang, Erez Louidor, James Muller, Tamann Narayan, Serena Wang, and Tao Zhu. Shape constraints for set functions. In International conference on machine learning, pages 1388–1396. PMLR, 2019

    2019

  13. [21]

    Multi-task learning with deep neural networks: A survey

    Michael Crawshaw. Multi-task learning with deep neural networks: A survey. CoRR, abs/2009.09796, 2020

    2009 arXiv

  14. [22]

    On label depen- dence and loss minimization in multi-label classification

    Krzysztof Dembczy ´nski, Willem Waegeman, Weiwei Cheng, and Eyke H¨ullermeier. On label depen- dence and loss minimization in multi-label classification. Machine Learning, 88:5–45, 2012

    2012

  15. [23]

    Improving the sensitivity of online controlled ex- periments by utilizing pre-experiment data

    Alex Deng, Ya Xu, Ron Kohavi, and Toby Walker. Improving the sensitivity of online controlled ex- periments by utilizing pre-experiment data. In Proceedings of the Sixth ACM International Conference on Web Search and Data Mining, pages 123–132. Association for Computing Machin...

    2013

  16. [24]

    Shape-constrained statistical inference

    Lutz D ¨umbgen. Shape-constrained statistical inference. Annual review of statistics and its application, 11:373–391, 2024

    2024

  17. [25]

    Ferraro and Michael K

    Paul J. Ferraro and Michael K. Price. Using nonpecuniary strategies to influence behavior: Evidence from a large-scale field experiment. The review of economics and statistics, 95:64–73, 2013

    2013

  18. [26]

    Efficient semiparametric estimation of quantile treatment effects

    Sergio Firpo. Efficient semiparametric estimation of quantile treatment effects. Econometrica, 75(1):259–276, 2007

    2007

  19. [27]

    The design of experiments

    Ronald Aylmer Fisher. The design of experiments. Oliver and Boyd, 2nd ed. edition, 1937

    1937

  20. [28]

    Decomposition methods in economics

    Nicole Fortin, Thomas Lemieux, and Sergio Firpo. Decomposition methods in economics. 4:1–102, 2011

    2011

  21. [29]

    Freedman

    David A. Freedman. Statistical models for causation: What inferential leverage do they provide? Evaluation review, 30:691–713, 2006

    2006

  22. [30]

    Unconditional quantile treatment effects under endogeneity.Journal of Business & Economic Statistics, 31(3):346–357, 2013

    Markus Fr ¨olich and Blaise Melly. Unconditional quantile treatment effects under endogeneity.Journal of Business & Economic Statistics, 31(3):346–357, 2013

    2013

  23. [31]

    Diminishing returns shape constraints for interpretability and regularization

    Maya Gupta, Dara Bahri, Andrew Cotter, and Kevin Canini. Diminishing returns shape constraints for interpretability and regularization. Advances in neural information processing systems, 31, 2018

    2018

  24. [32]

    Monotonic calibrated interpolated look-up tables

    Maya Gupta, Andrew Cotter, Jan Pfeifer, Konstantin V oevodski, Kevin Canini, Alexander Mangylov, Wojciech Moczydlowski, and Alexander Van Esbroeck. Monotonic calibrated interpolated look-up tables. Journal of Machine Learning Research, 17(109):1–47, 2016

    2016

  25. [33]

    Trevor. Hastie. Generalized additive models. Chapman and Hall, 1st ed edition, 1990

    1990

  26. [34]

    Horowitz and Sokbae Lee

    Joel L. Horowitz and Sokbae Lee. Nonparametric estimation and inference under shape restrictions. Journal of econometrics, 201:108–126, 2017. 15

    2017

  27. [35]

    Improving regression performance with distributional losses

    Ehsan Imani and Martha White. Improving regression performance with distributional losses. 2018

    2018

  28. [36]

    Imbens and Donald B

    Guido W. Imbens and Donald B. Rubin. Causal Inference for Statistics, Social, and Biomedical Sci- ences. Cambridge University Press, 2015

    2015

  29. [37]

    Regression-adjusted estimation of quantile treatment effects under covariate-adaptive randomizations

    Liang Jiang, Peter CB Phillips, Yubo Tao, and Yichong Zhang. Regression-adjusted estimation of quantile treatment effects under covariate-adaptive randomizations. Journal of Econometrics , 234(2):758–776, 2023

    2023

  30. [38]

    Localized debiased machine learning: Efficient inference on quantile treatment effects and beyond

    Nathan Kallus, Xiaojie Mao, and Masatoshi Uehara. Localized debiased machine learning: Efficient inference on quantile treatment effects and beyond. Journal of Machine Learning Research, 25(16):1– 59, 2024

    2024

  31. [39]

    Trustworthy online controlled experiments : a practical guide to A/B testing

    Ron Kohavi. Trustworthy online controlled experiments : a practical guide to A/B testing. Cambridge University Press, 2020

    2020

  32. [40]

    Quantile-optimal treatment regimes

    Rui Song Lan Wang, Yu Zhou and Ben Sherwood. Quantile-optimal treatment regimes. Journal of the American Statistical Association, 113(523):1243–1254, 2018. PMID: 30416233

    2018

  33. [41]

    The unfavorable economics of measuring the returns to advertising

    Randall A Lewis and Justin M Rao. The unfavorable economics of measuring the returns to advertising. The Quarterly Journal of Economics, 130(4):1941–1973, 2015

    1941

  34. [42]

    Bondell, and Brian J

    Rui Li, Howard D. Bondell, and Brian J. Reich. Deep distribution regression, 2019

    2019

  35. [43]

    Agnostic notes on regression adjustments to experimental data: Reexamining freedman’s critique

    Winston Lin. Agnostic notes on regression adjustments to experimental data: Reexamining freedman’s critique. The annals of applied statistics, 7:295–318, 2013

    2013

  36. [44]

    List, Ian Muir, and Gregory Sun

    John A. List, Ian Muir, and Gregory Sun. Using machine learning for efficient flexible regression adjustment in economic experiments. Econometric reviews, pages 1–39, 2024

    2024

  37. [45]

    Rosa L. Matzkin. Chapter 42 Restrictions of economic theory in nonparametric methods , volume 4, pages 2523–2558. Elsevier B.V , 1994

    1994

  38. [46]

    Regression adjustment for estimating distributional treatment effects in randomized controlled trials

    Tatsushi Oka, Shota Yasui, Yuta Hayakawa, and Undral Byambadalai. Regression adjustment for estimating distributional treatment effects in randomized controlled trials. 2024

    2024

  39. [47]

    Pytorch: An imperative style, high-performance deep learning library, 2019

    Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas K ¨opf, Edward Yang, Zach DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu F...

    2019

  40. [48]

    Rosenbaum

    Paul R. Rosenbaum. Covariance adjustment in randomized experiments and observational studies. Statistical science, 17:286–304, 2002

    2002

  41. [49]

    Simple, efficient estimators of treatment effects in randomized trials using generalized linear models to leverage baseline variables

    Michael Rosenblum and Mark J van der Laan. Simple, efficient estimators of treatment effects in randomized trials using generalized linear models to leverage baseline variables. The International Journal of Biostatistics, 6:13–Article 13, 2010

    2010

  42. [50]

    Nonparametric estimation of distributional policy effects

    Christoph Rothe. Nonparametric estimation of distributional policy effects. Journal of Econometrics, 155(1):56–70, 2010

    2010

  43. [51]

    Estimating causal effects of treatments in randomized and nonrandomized studies

    Donald B Rubin. Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of educational psychology, 66:688–701, 1974. 16

    1974

  44. [52]

    Randomization analysis of experimental data: The fisher randomization test com- ment, 1980

    Donald B Rubin. Randomization analysis of experimental data: The fisher randomization test com- ment, 1980

    1980

  45. [53]

    An overview of multi-task learning in deep neural networks

    Sebastian Ruder. An overview of multi-task learning in deep neural networks. arXiv preprint arXiv:1706.05098, 2017

    2017 arXiv

  46. [54]

    Zlpr: A novel loss for multi-label classification, 2022

    Jianlin Su, Mingren Zhu, Ahmed Murtadha, Shengfeng Pan, Bo Wen, and Yunfeng Liu. Zlpr: A novel loss for multi-label classification, 2022

    2022

  47. [55]

    Single-model uncertainties for deep learning

    Nadezhda Tagasovska and David Lopez-Paz. Single-model uncertainties for deep learning. In Ad- vances in Neural Information Processing Systems 32, pages 6417–6428, 2019

    2019

  48. [56]

    Overlapping experiment infrastruc- ture: More, better, faster experimentation

    Diane Tang, Ashish Agarwal, Deirdre O’Brien, and Mike Meyer. Overlapping experiment infrastruc- ture: More, better, faster experimentation. In Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining, pages 17–26, 2010

    2010

  49. [57]

    Deep learning for multi-label learning: A comprehensive survey, 2024

    Adane Nega Tarekegn, Mohib Ullah, and Faouzi Alaya Cheikh. Deep learning for multi-label learning: A comprehensive survey, 2024

    2024

  50. [58]

    Tsiatis, Marie Davidian, Min Zhang, and Xiaomin Lu

    Anastasios A. Tsiatis, Marie Davidian, Min Zhang, and Xiaomin Lu. Covariate adjustment for two- sample treatment comparisons in randomized clinical trials: A principled yet flexible approach. Statis- tics in medicine, 27:4658–4677, 2008

    2008

  51. [59]

    Nonparametric estimation of conditional quantiles using neural networks

    Halbert White. Nonparametric estimation of conditional quantiles using neural networks. In Com- puting Science and Statistics: Statistics of Many Parameters: Curves, Images, Spatial Models , pages 190–199. Springer, 1992

    1992

  52. [60]

    Dnet: Distri- butional network for distributional individualized treatment effects

    Guojun Wu, Ge Song, Xiaoxiang Lv, Shikai Luo, Chengchun Shi, and Hongtu Zhu. Dnet: Distri- butional network for distributional individualized treatment effects. In Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining , KDD ’23, page 5215–5224, N...

    2023

  53. [61]

    Improving the sensitivity of online controlled experiments: Case studies at netflix

    Huizhi Xie and Juliette Aurisset. Improving the sensitivity of online controlled experiments: Case studies at netflix. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 645–654, 2016

    2016

  54. [62]

    Improving the sensitivity of online controlled experiments: Case studies at netflix

    Huizhi Xie and Juliette Aurisset. Improving the sensitivity of online controlled experiments: Case studies at netflix. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 645–654. ACM, 2016

    2016

  55. [63]

    Daniels, and Almut G

    Dandan Xu, Michael J. Daniels, and Almut G. Winterstein. A bayesian nonparametric approach to causal inference on quantiles. Biometrics, 74(3):986–996, 2018

    2018

  56. [64]

    Efficiency study of estimators for a treatment effect in a pretest- posttest trial

    Li Yang and Anastasios A Tsiatis. Efficiency study of estimators for a treatment effect in a pretest- posttest trial. The American statistician, 55:314–321, 2001

    2001

  57. [65]

    Deep lattice networks and partial monotonic functions

    Seungil You, David Ding, Kevin Canini, Jan Pfeifer, and Maya Gupta. Deep lattice networks and partial monotonic functions. In I Guyon, U V on Luxburg, S Bengio, H Wallach, R Fergus, S Vish- wanathan, and R Garnett, editors, Advances in Neural Information Processing Systems , v...

    2017

  58. [66]

    Multilabel neural networks with applications to functional genomics and text categorization

    Min-Ling Zhang and Zhi-Hua Zhou. Multilabel neural networks with applications to functional genomics and text categorization. IEEE Transactions on Knowledge and Data Engineering , 18(10):1338–1351, 2006. 17

    2006

  59. [67]

    A review on multi-label learning algorithms

    Min-Ling Zhang and Zhi-Hua Zhou. A review on multi-label learning algorithms. IEEE Transactions on Knowledge and Data Engineering, 26(8):1819–1837, 2014

    2014

  60. [68]

    An overview of multi-task learning

    Yu Zhang and Qiang Yang. An overview of multi-task learning. National Science Review, 5(1):30–43, 2018

    2018

  61. [69]

    A survey on multi-task learning

    Yu Zhang and Qiang Yang. A survey on multi-task learning. IEEE Transactions on Knowledge and Data Engineering, 34(12):5586–5609, 2021. 18 Appendix The Appendix is structured as follows. Appendix A summarizes the notations used in the main text and the Appendix. Appendix B prov...

    2021

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.