Beyond the ATE: Interpretable Modelling of Treatment Effects over Dose and Time

Harry Amad; Julianna Piskorz; Krzysztof Kacprzyk; Mihaela van der Schaar

REVIEW 4 major objections 6 minor 14 references

Beyond the ATE: Interpretable Modelling of Treatment Effects over Dose and Time

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper argues that the average treatment effect should be modelled as a smooth, interpretable surface over both dose and time, and introduces SemanticATE, an adaptation of SemanticODE that fits such surfaces from surrogate treatment…

desk verdict A useful, honest adaptation of SemanticODE to dose-time treatment effects, with a standard pseudo-outcome caveat the authors should state explicitly rather than leave implicit. read the letter →

arxiv 2507.07271 v2 pith:PF7THXGA submitted 2025-07-09 cs.LG

Julianna Piskorz , Krzysztof Kacprzyk , Harry Amad , Mihaela van der Schaar This is my paper · ORCID

classification cs.LG

keywords treatmenteffectsurfacedose-timetrajectoriesSemanticODEsurrogateeffectsinterpretablecausalinferencecontinuoustreatmentsclinicaltrialanalysishorizontalasymptote

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 proposes to replace the static average treatment effect with a treatment effect surface $\tau_t(a)=\mathbb{E}[Y_t(a)-Y_t(0)]$ that varies smoothly over dose and time, and to keep that surface transparent enough for clinical use. Its central claim is that SemanticATE, an adaptation of SemanticODE to the causal setting, can fit such surfaces accurately by regressing surrogate treatment effects on dose and time rather than modelling outcomes directly. The payoff is that a clinician can read off answers the ATE cannot give — onset time, peak effect, duration above a threshold, sustained dose — from univariate functions of dose, and can verify or edit the fitted properties. If the claim holds, trial analysis gains the temporal dimension without giving up interpretability.

What carries the argument

The load-bearing machinery is SemanticATE's decomposition of a treatment-effect trajectory into a composition map and a property map, inherited from SemanticODE. The composition map assigns each dose $a$ a trajectory shape drawn from a library of motifs (segments labelled by monotonicity and convexity, ending in a bounded or unbounded motif such as a horizontal asymptote), while the property map expresses each shape's key quantities — transition times, function values at transitions, derivatives, and the asymptote — as univariate functions of dose. To feed this machinery, the paper constructs surrogate treatment effects $\tilde{\tau}_{i,j}=Y_{i,j}-\hat{\varphi}_0(X_i,T_{i,j})$ with a baseline trajectory model fitted only on untreated patients; the unbiasedness of that baseline model is what carries the causal content, and the dose takes over the role that the initial condition plays in the original SemanticODE.

What would settle it

Run SemanticATE on a synthetic trial where the true $\tau_t(a)$ is known and the fitted baseline model is deliberately misspecified (for example, the untreated outcome depends on an interaction that the baseline regressor cannot represent); if the resulting out-of-domain MISE jumps while an oracle-baseline version of SemanticATE stays accurate, the claim that the surrogate construction preserves unbiasedness is refuted.

Watch

Extended reading notes

Core claim

The paper's central claim is that the population treatment effect $\tau_t(a)=\mathbb{E}[Y_t(a)-Y_t(0)]$ can be estimated as a smooth, interpretable function of dose and time by fitting SemanticODE-style composition and property maps to surrogate treatment effects. Since $\tau_t(a)$ is never directly observed, each treated patient's measurement is converted into a pseudo-outcome $\tilde{\tau}_{i,j}=Y_{i,j}-\hat{\varphi}_0(X_i,T_{i,j})$, where $\hat{\varphi}_0$ is a baseline trajectory model trained only on untreated patients; the paper argues that under the RCT assumptions this surrogate is unbiased, so regressing it on dose and time recovers the true surface. The resulting model expresses the clinically meaningful features of the surface — maximum effect, time to peak, horizontal asymptote, transition points — as univariate functions of dose, making the two-dimensional object verifiable and editable. In the reported experiments, SemanticATE matches the best black-box methods in-domain and, with the inductive bias that trajectories end in a horizontal asymptote, achieves substantially lower out-of-domain error than SINDy, WSINDy, NeuralODE, XGBoost, and polynomial regression on all three benchmarks.

Load-bearing premise

The pipeline is unbiased only if the baseline trajectory model that imputes the untreated outcome is unbiased on average across the treated population, so a misspecified or small untreated cohort silently contaminates every estimated treatment effect.

Editorial extensions

If this is right

A two-dimensional treatment effect surface can be summarised and scrutinised through univariate dose-dependent properties, so interpretability is preserved despite the extra dimension.
Constraining trajectory shapes to end in a horizontal asymptote yields accurate extrapolation beyond the observed time window, giving SemanticATE an out-of-domain advantage over the compared methods.
Post-hoc edits, such as resetting the treatment effect to zero at time zero, align the model with domain knowledge without materially hurting in-domain accuracy.
The surrogate construction separates the untreated-outcome imputation from the transparent trajectory fit, so covariates can be used for accuracy without sacrificing interpretability of the final effect model.
SemanticATE reaches near-optimal performance with roughly fifteen outcome measurements per patient, and irregular measurement times help rather than hurt, which is actionable for trial design.

Reading between the lines

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

The unbiasedness of the whole pipeline is inherited from the baseline trajectory model, so in small or non-representative control arms the practical bottleneck shifts from the interpretable surface fitter to the untreated-outcome imputer; a doubly robust variant that also models treated outcomes could reduce that sensitivity.
Because the composition map assigns discrete shapes to dose intervals, SemanticATE can reveal dose thresholds where the qualitative response changes (for instance, where a peaking trajectory becomes a monotone rise), a feature the paper does not develop.
The strong out-of-domain results depend on the horizontal-asymptote prior; for treatments with genuinely non-saturating effects, such as cumulative toxicity, that constraint would need to be dropped and the extrapolation advantage would likely shrink.
A natural testable extension is to observational data under weak unconfoundedness, where the baseline model would have to be replaced by covariate-adjusted outcome models and the RCT exchangeability argument no longer applies.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Read the paper. The combination is genuinely new: SemanticODE's composition/property maps reparameterized so that dose, not initial condition, controls the trajectory, and the target is the never-observed treatment effect surface tau_t(a). The authors are clear about the estimand and the identifying assumptions, and the synthetic benchmarks are more careful than the field's default. The PK datasets are built from an actual pharmacometric model, and the IHDP-based generator separates baseline trajectory, heterogeneous effects, and the average surface. Code is promised. The transparency story is plausible: property maps for time-to-peak, peak value, and horizontal asymptote are exactly what a clinical trial analyst would want to inspect and edit. The paper is also honest about in-domain performance, reporting that black-box models often match or beat SemanticATE on in-domain MISE. That is a comfortable sign of fair benchmarking. The weak spot is the identification step in Section 4.3. The paper asserts that the surrogates tau_tilde_i,j = Y_i,j - phi_hat_0(X_i,T_i,j) satisfy E[tau_tilde|A=a,T=t] = tau_t(a). That equality holds only if phi_hat_0 is unbiased in the conditional sense E[phi_hat_0(X,t)|A=a,T=t] = E[Y_t(0)]. That is never stated as an assumption, and XGBoost or any finite-sample regressor does not guarantee it. This is not a technical nit: the paper's own Appendix C.1 shows MISE degrading as baseline-model validation loss grows, and improving as baseline sample size increases. So the main estimate inherits baseline-model bias, and the error is first-order. The fix is standard and cheap: state the unbiasedness assumption explicitly, or use cross-fitting / doubly robust pseudo-outcomes that make first-order bias removable. Second, the out-of-domain result in Table 1 is not apples-to-apples. SemanticATE is given the inductive bias that trajectories end in a horizontal asymptote; SINDy, WSINDy, NeuralODE, and polynomial regression are not. So the large out-domain errors of the competitors partly reflect the absence of that prior, not necessarily the superiority of the semantic model. That is a fair experiment only if the comparison is framed as 'with the correct prior, semantic modeling extrapolates well', which is a much weaker claim than the one the text suggests. Third, no real or semi-real RCT data. For a paper pitching clinical actionability, one benchmark with realistic model misspecification and informative baseline trajectories would substantially increase confidence. Bottom line: the central idea is sound, the presentation is honest, and the pseudo-outcome caveat is a known condition of the method the authors should explicitly own. It deserves a serious referee. I would not cite it in my own work this year, but I would bring it to a reading group and would engage seriously if the authors addressed the bias issue and reframed the extrapolation claim.

Referee Report

4 major / 6 minor

Summary. The paper proposes SemanticATE, a method for estimating the population average treatment effect as a smooth surface τ_t(a) = E[Y_t(a) − Y_t(0)] over continuous dose and time in a randomized trial with irregular longitudinal outcomes. The method constructs surrogate individual treatment effects by subtracting a baseline trajectory model φ̂_0(X,t) from observed treated outcomes, then fits a SemanticODE-style composition/property-map model to these surrogates with dose as the conditioning variable. The paper reports synthetic experiments on PK and IHDP-based datasets, including out-of-domain time extrapolation, interpretable property maps, editing, and a sample-efficiency study.

Significance. If the identification and surrogate-bias issues are resolved, this is a valuable contribution to interpretable time-varying causal inference: it defines a clinically meaningful estimand, provides a transparent functional representation, and includes an unusually careful synthetic evaluation with released code. The main empirical novelty—competitive in-domain accuracy plus extrapolation under a horizontal-asymptote prior—is plausible but currently depends on an unverified unbiasedness condition for the baseline model and on a comparison that does not fully isolate the inductive prior. The paper is honest about its scope (RCT setting, preliminary) and about remaining work on observational data and uncertainty quantification.

major comments (4)

[Section 4.3, Eq. (3)] The identifying claim E[τ̃_{i,j}|A=a,T=t]=τ_t(a) is not established by Assumptions 4.1 and 4.2 alone. Expanding the conditional expectation gives E[Y_t(a)|A=a,T=t] − E[φ̂_0(X,t)|A=a,T=t]. Under the assumptions, the first term equals E[Y_t(a)] only if the appropriate joint or conditional independence is stated (see next comment), and the second term equals E[Y_t(0)] only if E[φ̂_0(X,t)|A=a,T=t]=E[Y_t(0)] for all (a,t). The paper never states or verifies this baseline-unbiasedness condition, and it is not guaranteed for a regularized, finite-sample XGBoost trained on the untreated arm. Any bias δ(a,t)=E[φ̂_0(X,t)|A=a,T=t]−E[Y_t(0)] is inherited by SemanticATE because the subsequent regression of τ̃ on (a,t) cannot remove it. Figure 5 in Appendix C.1 is consistent with this: MISE grows with baseline-model validation loss and falls as the baseline sample size increases. Please either state baseline unbiasedness as an explicit assumption or replace the plug-in surrogate with a cross-fitted or doubly robust pseudo-outcome whose first-order bias vanishes.
[Section 4.1, Assumptions 4.1–4.2] The stated assumptions do not formally imply E[Y|A=a,T=t]=E[Y_t(a)], which is the basis of Eq. (3). Assumption 4.1 asserts Y_t(a)⊥A for each fixed T=t, and Assumption 4.2 asserts Y_t(a)⊥T for each fixed T=t. Pairwise independence of Y_t(a) from A and T does not imply joint independence of Y_t(a) from (A,T) without additional structure (e.g., A⊥T and no common causes, or a directly stated joint independence). The intended RCT structure may make this fixable by a small strengthening, but as written the identifiability argument has a formal gap. Please state Y_t(a)⊥(A,T) explicitly, or give the precise conditional independence version that supports Eq. (3).
[Section 6.3, Table 1] The out-domain comparison is confounded with the inductive prior. SemanticATE's composition library is restricted to trajectories ending in a horizontal asymptote (Section 6.2, inductive biases), while SINDy, WSINDy, NeuralODE, XGBoost, and PolyReg are not given an equivalent constraint. The claim of 'incomparable out-domain performance' therefore conflates the extrapolation prior with the SemanticODE representation. Please include an ablation of SemanticATE without the asymptote constraint, and where feasible impose the same monotone/asymptote prior on the neural or polynomial baselines, or at least report what each baseline receives as input. Without this, Table 1 does not separate the value of the prior from the value of the architecture.
[Section 6.3 and Appendix D.4–D.6] The experimental protocol for the black-box baselines is under-specified: it is not stated whether the XGBoost, NeuralODE, and polynomial baselines are trained on the same surrogate treatment effects τ̃_{i,j} as SemanticATE, or directly on raw outcomes. Since the surrogate construction is itself a modeling choice, this ambiguity makes the numerical comparisons in Table 1 hard to interpret. Please specify the exact input/output pairs, the loss function, and the training/validation split for each baseline.

minor comments (6)

[Section 6.1] The text reads 'a sensitivity analysis ... is presented in in the Appendix C.1'; the duplicated 'in' should be removed.
[Section 6.4] The text reads 'presented in Figure Figure 4'; the duplicated 'Figure' should be removed.
[Figure 3 caption] The caption contains incomplete labels 'Transition points ( -coordinates)' and '( -coordinates)', with the variable names missing.
[Appendix D.1.2] The ground-truth equations use ϕ(x) in Eq. (8) but then apply ϕ to t in Eq. (9); please make the time variable notation consistent.
[Table 4] The table lists 'TRANS2(t0) 0.0' twice; one row appears to be a typo for TRANS3(t0).
[Section 4.3] The statement 'by assumption τ̃_t(0)=0' introduces a substantive modeling assumption about the treatment effect at time zero; it should be listed as an inductive bias or assumption rather than presented as a consequence of the surrogate definition.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: SemanticATE's surrogate-outcome regression is checked against external synthetic ground truth, and the SemanticODE self-citations are not load-bearing.

full rationale

The paper's central derivation is not circular. Section 4.3 constructs surrogate treatment effects as tau_tilde_{i,j}=Y_{i,j}-phi_hat_0(X_i,T_{i,j}), where phi_hat_0 is fit only on untreated patients; the final estimator is then compared against ground-truth tau_t(a) generated by external ODE/simulator models (PK dataset and IHDP-based dataset in Section 6.1 and Appendix D.1). The identification claim E[tau_tilde|A=a,T=t]=tau_t(a) requires an unstated regularity condition on phi_hat_0 (roughly, E[phi_hat_0(X,t)|A=a,T=t]=E[Y_t(0)]); this is a potential bias/correctness limitation, not a circularity, because the target estimand is not defined in terms of phi_hat_0 and the benchmarks are independent of the fitted baseline. The out-of-domain extrapolation in Table 1 is explicitly attributed to the imposed horizontal-asymptote inductive bias, and the asymptotic level itself is learned from data; the constraint is stated in Section 6.2 rather than smuggled in. Self-citations to Kacprzyk & Van Der Schaar (2024) supply the SemanticODE machinery, but no load-bearing mathematical claim reduces to those citations; the paper's predictions are falsifiable against the synthetic ground truth. No equation in the claimed derivation chain is equivalent to its inputs by construction.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

No new physical entities are introduced. The load-bearing assumptions are the standard RCT exchangeability conditions, an unstated unbiasedness condition on the baseline trajectory model, and a hand-chosen inductive bias about trajectory shape. The free parameters are model configuration choices, not fitted constants in a derivation.

free parameters (3)

Composition library restriction = Up to 4 motifs; final segment type 'h' (horizontal asymptote)
Chosen by hand to constrain the trajectory shape; it matches the synthetic benchmarks' true trajectories and drives the out-domain performance.
Property map basis functions = Constant, linear, and four B-spline basis functions of degree 3
Chosen by hand for the SemanticODE property maps.
Regularization penalties = Derivative difference penalty 0.05; first-derivative penalty tuned in [1e-9, 0.1]
Hand-set or tuned regularization that shapes the fitted trajectories.

assumptions (6)

standard math Potential outcomes framework and consistency: Y = Y_T(A).
Invoked in Section 4.1 to define τ_t(a).
domain assumption Assumption 4.1: treatment dose is randomly assigned, so Y_t(a) ⊥ A for all a, t.
RCT design; ensures no confounding by dose.
domain assumption Assumption 4.2: measurement times are completely at random, Y_t(a) ⊥ T and T independent of patient characteristics.
Ensures no informative sampling bias; load-bearing for the exchangeability argument in Section 4.1.
domain assumption The fitted baseline trajectory model \hatφ_0(X,t) is unbiased for E[Y_t(0)|X].
Needed for E[\tildeτ|A=a,T=t]=τ_t(a) in Section 4.3; not proven for XGBoost or any finite-sample regression.
domain assumption Smoothness of τ_t(a) in a and t.
Required for interpolation to unobserved doses and times, stated in Section 4.1.
ad hoc to paper Composition library constrained to trajectories ending in a horizontal asymptote.
Inductive bias added in Section 6.2; matches the synthetic benchmarks by construction, but is not universally valid.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Beyond the ATE: Interpretable Modelling of Treatment Effects over Dose and Time." pith.science (2026). https://pith.science/paper/PF7THXGA

@misc{pith2026250707271,
  author       = {Pith},
  title        = {Pith review of: Beyond the ATE: Interpretable Modelling of Treatment Effects over Dose and Time},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PF7THXGA}},
  note         = {Machine review of arXiv:2507.07271}
}

read the original abstract

The Average Treatment Effect (ATE) is a foundational metric in causal inference, widely used to assess intervention efficacy in randomized controlled trials (RCTs). However, in many applications -- particularly in healthcare -- this static summary fails to capture the nuanced dynamics of treatment effects that vary with both dose and time. We propose a framework for modelling treatment effect trajectories as smooth surfaces over dose and time, enabling the extraction of clinically actionable insights such as onset time, peak effect, and duration of benefit. To ensure interpretability, robustness, and verifiability -- key requirements in high-stakes domains -- we adapt SemanticODE, a recent framework for interpretable trajectory modelling, to the causal setting where treatment effects are never directly observed. Our approach decouples the estimation of trajectory shape from the specification of clinically relevant properties (e.g., maxima, inflection points), supporting domain-informed priors, post-hoc editing, and transparent analysis. We show that our method yields accurate, interpretable, and editable models of treatment dynamics, facilitating both rigorous causal analysis and practical decision-making.

Figures

Figures reproduced from arXiv: 2507.07271 by the authors.

**Figure 1.** Despite being a two-dimensional function, τtpaq can be visualised and analysed by scrutinising the univariate functions which describe the dependence of its key properties on the dose of the treatment assigned. ments (e.g., the treatment effect should be zero initially) – a requirement which existing modelling methods rarely satisfy. Our solution. To satisfy the above requirements of interpretability and robustness… view at source ↗

**Figure 2.** The causal graph characterising the RCT setting considered in this work. Given Assumption 4.1 and Assumption 4.2, for fixed values of A “ a and T “ t, there are no backdoor paths between the treatment dose, measurement time, and outcome. As a result, patients assigned different doses and measured at different time points remain exchangeable, allowing models trained on subsets of the population (conditioned on A “ a… view at source ↗

**Figure 4.** Performance of SemanticATE with the changing number of outcome measurements. for τtpaq estimation setting, we fix the timing of the first observation t0 across all individuals, and fit an additional model to predict τt0 paq based on the dose a. τt0 paq is then used as an initial condition for the trajectory. Because of the requirements of the NeuralODE method, for this experiment we rely on regular sampling of the o… view at source ↗

Figures from the paper (2 more)

**Figure 5.** Figure 5: Comparison of the performance of the different baseline trajectory models. The error bars denote the confidence intervals, computed over 10 seeds. where µpa, t, xq “ ErY |A “ a, T “ t, X “ xs. This estimation method would require us to obtain a model µpa, t, xq. Even i…

**Figure 6.** Figure 6: Comparison of the performance of the different trajectory models, as a function of the number of treated patients. The error bars mark the confidence intervals, computed over 5 seeds. utilising the information available if the times of measurement are misaligned betwee…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

14 extracted references · 7 canonical work pages

[7]

doi: 10.1137/ 20M1343166

ISSN 1540-3459, 1540-3467. doi: 10.1137/ 20M1343166. URL http://arxiv.org/abs/ 2005.04339. arXiv:2005.04339 [math]. Moodie, E. E. M. and Stephens, D. A. Estimation of dose- response functions for longitudinal data using the gener- alised propensity score. Statistical Methods in Medical Research, 21(2):149–166, April 2012. ISSN 1477-0334. doi: 10.1177/0962...

arXiv 2005
[8]

URL http://arxiv.org/abs/2103. 07861. arXiv:2103.07861 [cs]. Qian, Z., Zhang, Y ., Bica, I., Wood, A., and van der Schaar, M. SyncTwin: Treatment Effect Estima- tion with Longitudinal Outcomes. In Advances in Neural Information Processing Systems , vol- ume 34, pp. 3178–3190. Curran Associates, Inc.,

arXiv
[9]

No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs

doi: 10.1002/0470090456.ch7. URL https: //onlinelibrary.wiley.com/doi/abs/ 10.1002/0470090456.ch7. Section: 7 eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/0470090456.ch7. Kacprzyk, K. and Van Der Schaar, M. No Equations Needed: Learning System Dynamics Without Relying on Closed- Form ODEs. October 2024. URL https://arxiv. org/abs/2501.18563. Ka...

work page Pith review arXiv
[10]

Using Noisy or Incomplete Data to Discover Models of Spatiotemporal Dynamics

URL https://proceedings.neurips. cc/paper_files/paper/2021/hash/ 19485224d128528da1602ca47383f078-Abstract. html. Reinbold, P. A. K., Gurevich, D. R., and Grigoriev, R. O. Using Noisy or Incomplete Data to Discover Models of Spatiotemporal Dynamics. Physical Review E, 101(1): 010203, January 2020. ISSN 2470-0045, 2470-0053. doi: 10.1103/PhysRevE.101.01020...

work page Pith review arXiv 2021
[11]

doi: 10.1609/aaai.v34i04

ISSN 2374-3468. doi: 10.1609/aaai.v34i04

doi:10.1609/aaai.v34i04
[13]

ISSN: 2640-3498

URL https://proceedings.mlr.press/ v162/seedat22b.html. ISSN: 2640-3498. Silva, B. M. d., Champion, K., Quade, M., Loiseau, J.-C., Kutz, J. N., and Brunton, S. L. PySINDy: A Python package for the sparse identification of nonlinear dynam- ical systems from data. Journal of Open Source Soft- ware, 5(49):2104, May 2020. ISSN 2475-9066. doi: 10.21105/joss.02...

doi:10.21105/joss.02104 2020
[14]

cc/paper_files/paper/2022/hash/ 390bb66a088d37f62ee9fb779c5953c2-Abstract-Conference

URL https://proceedings.neurips. cc/paper_files/paper/2022/hash/ 390bb66a088d37f62ee9fb779c5953c2-Abstract-Conference. html. Woillard, J.-B., de Winter, B. C. M., Kamar, N., Mar- quet, P., Rostaing, L., and Rousseau, A. Population pharmacokinetic model and Bayesian estimator for two tacrolimus formulations–twice daily Prograf and once daily Advagraf. Brit...

work page arXiv 2000
[2004]

doi: 10.1111/j.1467-9868

ISSN 1369-7412. doi: 10.1111/j.1467-9868. 2004.b5543.x. URL https://doi.org/10.1111/ j.1467-9868.2004.b5543.x. Melnychuk, V ., Frauen, D., and Feuerriegel, S. Causal Transformer for Estimating Counterfactual Outcomes. In Proceedings of the 39th International Conference on Machine Learning, pp. 15293–15329. PMLR, June

arXiv 2004

Show all 14 references

[2019]

Right to Explanation

URL https://openreview.net/forum? id=BJg866NFvB. Brunton, S. L., Proctor, J. L., and Kutz, J. N. Dis- covering governing equations from data by sparse identification of nonlinear dynamical systems. Pro- ceedings of the National Academy of Sciences , 113 (15):3932–3937, April 2...

2016
[2020]

URL http:// arxiv.org/abs/2001.02478

doi: 10.1145/3313831.3376590. URL http:// arxiv.org/abs/2001.02478. arXiv:2001.02478 [cs]. Lin, H., Scharfstein, D. O., and Rosenheck, R. A. Analysis of Longitudinal Data with Irregular, Outcome-Dependent Follow-Up. Journal of the Royal Statistical Society Se- ries B: Statisti...

2001
[2021]

ISSN: 2640-3498

URL https://proceedings.mlr.press/ v158/li21a.html. ISSN: 2640-3498. Liao, Q. V ., Gruen, D., and Miller, S. Questioning the AI: Informing Design Practices for Explainable AI User Experiences. In Proceedings of the 2020 CHI Conference on Human Factors in Computing Systems, pp....

2020
[2022]

ISSN: 2640-3498

URL https://proceedings.mlr.press/ v162/melnychuk22a.html. ISSN: 2640-3498. Messenger, D. A. and Bortz, D. M. Weak SINDy: Galerkin-Based Data-Driven Model Selection. Multi- scale Modeling & Simulation, 19(3):1474–1497, January
[5364]

Publisher: Institute of Mathematical Statis- tics

URL https://www.jstor.org/stable/ 2240995. Publisher: Institute of Mathematical Statis- tics. Schwab, P., Linhardt, L., Bauer, S., Buhmann, J. M., and Karlen, W. Learning Counterfactual Repre- sentations for Estimating Individual Dose-Response Curves. Proceedings of the AAAI C...
[6014]

php/AAAI/article/view/6014

URL https://ojs.aaai.org/index. php/AAAI/article/view/6014. Number: 04. Seedat, N., Imrie, F., Bellot, A., Qian, Z., and Schaar, M. v. d. Continuous-Time Modeling of Counterfactual Out- comes Using Neural Controlled Differential Equations. In Proceedings of the 39th Internatio...

Pith tools

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

[1] [7]

doi: 10.1137/ 20M1343166

ISSN 1540-3459, 1540-3467. doi: 10.1137/ 20M1343166. URL http://arxiv.org/abs/ 2005.04339. arXiv:2005.04339 [math]. Moodie, E. E. M. and Stephens, D. A. Estimation of dose- response functions for longitudinal data using the gener- alised propensity score. Statistical Methods in Medical Research, 21(2):149–166, April 2012. ISSN 1477-0334. doi: 10.1177/0962...

arXiv 2005

[2] [8]

URL http://arxiv.org/abs/2103. 07861. arXiv:2103.07861 [cs]. Qian, Z., Zhang, Y ., Bica, I., Wood, A., and van der Schaar, M. SyncTwin: Treatment Effect Estima- tion with Longitudinal Outcomes. In Advances in Neural Information Processing Systems , vol- ume 34, pp. 3178–3190. Curran Associates, Inc.,

arXiv

[3] [9]

No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs

doi: 10.1002/0470090456.ch7. URL https: //onlinelibrary.wiley.com/doi/abs/ 10.1002/0470090456.ch7. Section: 7 eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/0470090456.ch7. Kacprzyk, K. and Van Der Schaar, M. No Equations Needed: Learning System Dynamics Without Relying on Closed- Form ODEs. October 2024. URL https://arxiv. org/abs/2501.18563. Ka...

work page Pith review arXiv

[4] [10]

Using Noisy or Incomplete Data to Discover Models of Spatiotemporal Dynamics

URL https://proceedings.neurips. cc/paper_files/paper/2021/hash/ 19485224d128528da1602ca47383f078-Abstract. html. Reinbold, P. A. K., Gurevich, D. R., and Grigoriev, R. O. Using Noisy or Incomplete Data to Discover Models of Spatiotemporal Dynamics. Physical Review E, 101(1): 010203, January 2020. ISSN 2470-0045, 2470-0053. doi: 10.1103/PhysRevE.101.01020...

work page Pith review arXiv 2021

[5] [11]

doi: 10.1609/aaai.v34i04

ISSN 2374-3468. doi: 10.1609/aaai.v34i04

doi:10.1609/aaai.v34i04

[6] [13]

ISSN: 2640-3498

URL https://proceedings.mlr.press/ v162/seedat22b.html. ISSN: 2640-3498. Silva, B. M. d., Champion, K., Quade, M., Loiseau, J.-C., Kutz, J. N., and Brunton, S. L. PySINDy: A Python package for the sparse identification of nonlinear dynam- ical systems from data. Journal of Open Source Soft- ware, 5(49):2104, May 2020. ISSN 2475-9066. doi: 10.21105/joss.02...

doi:10.21105/joss.02104 2020

[7] [14]

cc/paper_files/paper/2022/hash/ 390bb66a088d37f62ee9fb779c5953c2-Abstract-Conference

URL https://proceedings.neurips. cc/paper_files/paper/2022/hash/ 390bb66a088d37f62ee9fb779c5953c2-Abstract-Conference. html. Woillard, J.-B., de Winter, B. C. M., Kamar, N., Mar- quet, P., Rostaing, L., and Rousseau, A. Population pharmacokinetic model and Bayesian estimator for two tacrolimus formulations–twice daily Prograf and once daily Advagraf. Brit...

work page arXiv 2000

[8] [2004]

doi: 10.1111/j.1467-9868

ISSN 1369-7412. doi: 10.1111/j.1467-9868. 2004.b5543.x. URL https://doi.org/10.1111/ j.1467-9868.2004.b5543.x. Melnychuk, V ., Frauen, D., and Feuerriegel, S. Causal Transformer for Estimating Counterfactual Outcomes. In Proceedings of the 39th International Conference on Machine Learning, pp. 15293–15329. PMLR, June

arXiv 2004