IGC-Net for conditional average potential outcome estimation over time
Authors: Konstantin Hess
Dennis Frauen
Valentyn Melnychuk
Stefan Feuerriegel
Venue: ICLR 2026 Poster (2026)
Keywords: causal inference
potential outcomes
treatment effects
healthcare
Primary area: causal reasoning
TL;DR: We develop a novel neural method that performs G-computation in an iterative end-to-end training algorithm for conditional average potential outcome estimation over time.

Abstract: Estimating potential outcomes for treatments over time based on observational data is important for personalized decision-making in medicine. However, many existing methods for this task fail to properly adjust for time-varying confounding and thus yield biased estimates. There are only a few neural methods with proper adjustments, but these have inherent limitations (e.g., division by propensity scores that are often close to zero), which result in poor performance. As a remedy, we introduce the iterative G-computation network (IGC-Net). Our IGC-Net is a novel, neural end-to-end model which adjusts for time-varying confounding in order to estimate conditional average potential outcomes (CAPOs) over time. Specifically, our IGC-Net is the first neural model to perform fully regression-based iterative G-computation for CAPOs in the time-varying setting. We evaluate the effectiveness of our IGC-Net across various experiments. In sum, this work represents a significant step towards personalized decision-making from electronic health records.

Published as a conference paper at ICLR 2026
IGC-NET FOR CONDITIONAL AVERAGE POTENTIAL OUTCOME ESTIMATION OVER TIME
Konstantin Hess!,", Dennis Frauen Valentyn Melnychuk 12, Stefan Feuerriege!!2
'LM Munich Munich Center for Machine Learning
"Corresponding author: k. hess@ 1mu. de
ABSTRACT
Estimating potential outcomes for treatments over time based observational data is important for personalized decision-makin making in medicine. However, many existing methods for this task fail to properly adjust for time-varying confounding and thus yield biased estimates. There are only a few neural methods with proper adjustments, but these have inherent limitations (e.g.. division by propensity scores that are often close to zero), which result in poor performance. As remedy, we introduce the iterative G-computation network (IGC-Net), Our IGC-Net is a novel, neural end-to-end model which adjusts for time-varying confounding in order to estimate conditional average potential outcomes (CAPOs) over time. Specifically, IGC-Net is the first neural model perform fully regression- based iterative G-computation for CAPOs in the time-varying setting. We evaluate the effectiveness of our IGC-Net across various experiments. In sum, this work represents significant step towards personalized Decision-making from electronic health records.
INTRODUCTION
Causal machine learning has large potential to personalize treatment decisions in medicine (Feuer ricgel et al., 2024). An important task for this is to estimate conditional average potential outcomes (CAPOs) from observational data over time. Recently, such data has become prominent in medicine
due to the growing prevalence of electronic health records (EHRs) (Allam et al., 2021 Bica et al. 202I) and wearable devices (Battalio et al. [202 Murray et al. 2016). However, estimating CAPOs over time is notoriously difficult due to time-naryig confounding: for several-step-ahead predic- tions, future time-varying confounders unobserved they depend both future treatments and outcomes that have not yet occurred, which forces inference to rely only on past information and model-based forecasts.
One stream of methods (i.c., CRN Bica et al. 2020), CT (Melnychuk et al. 2022), and TE-CDE (Seedat et al. 2022)) fails perform proper adjustments for time-varying confounding and, thus, do not target the correct estimand. Hence, methods from this stream have infinite-samee sample bias: i.e., irreducible estimation errors irrespective of the amount of available data, which renders these methods unsuitable for medical applications.
To the best of our knowledge, there are only two neural methods that perform proper adjustments for time-varying confounding. However, these have important limitations (see Table On the one hand, RMSNs (Lim et al., 2018) perform inverse propensity weighting, which, the time-varying setting, relies on products of inverse propensity scores and, hence, division by values close to zero. On the other hand, G-Net (Li et al. 2021) and G-transformer (Xiong et al. (0224) perform G-computation, yet by estimating the distribution of all time-varying confounders all time-steps the future, which inefficient due to two reasons: needs to estimate all moments of a high-dimensional random variable, and it requires indirect inference via Monte Carlo sampling.

---

Published as a conference paper at ICLR 2026
Category
Methodis)
Issue
CRN Bica et al.
2020
proper adjustmentt and thus infinite-data biss (i.e., inreducible estimation irrespective of the dataset size)
w/o proper adjustments
CT (Mllaychuk ct al
2023
TK-CDK Scodal
2022
RMSNs Lim
2018
Product of inverse propensity scores; division close to acto
@ proper adjustments
G-Net [i al.
2021
X Esrimation of the entire distribution (i.e., all higher-onder moments) of confounders
G-trandformer
Xiong et al.
2024
via MC, sampling
IGC-Net (ours)
/ Neural and-to-end iterative regression algorithm
Table Overview of key neural methods for estimating CAPOs over time. Existing methods that perform proper adjustments for time-varying confounding have important limitations: RMSNs rely on products of inverse propensity scores and unstable division by values close to zero, and G-Net estimates the entire distribution of all time-varying confounders in the future via MC sampling.
To fill the above research gap, we propose novel, neural method for estimating CAPOs over time, which we call iterative G-computation network (IGC-Nett) [ Our method allows for proper adjust- ments for time-varying confounding by leveraging the idea of G-computation. but where we develop a novel, regression- baase iterative approach to integrate G-computation into neural networks through an end-to-end training algorithm. As result, our IGC-Net overcomes the limitations of existing methods. Unlike RMSNs, we avoid inverse propensity scores, which makes our method robust, especially for longer time horizons. Unlike G-Net, we avoid estimating any probability distribution (i.e., any higher-order moments), but rather estimate CAPOs directly through our iterative regression algorithm in an end and-t--end manner. We demonstrate the effectiveness of our IGC-Net across various experiments. Our IGC-Net based on transformers achieves state-of of-the-art performance.
2 RELATED WORK
APOs over time:
Estimating average potential outcomes (APOs) over time has a long -ranging history
in classical statistics and epidemiology (Lok) 2008 Robins 1986 Rytgaard et al. [2022] van der
Laan & Gruber, 2012). Popular approaches are the G-methods (Robins & Hernán 2009), including
marginal structural models (MSMs) (Robins Hernán 2009: Robins et 2000), structural nested
models (Robins 1994 Robins & Hernán
2009), G-computation (Bang & Robins 2005 Robins
1999, Robins& & Hernán 2009), and TMLE
(van der Laan & Gruber
2012). Some of these have been
instantiated by neural models (Frauen et al.
2023a Shirakawa et al. 2024 However, these works do
not focus estimating CAPOs. Instead, they ignore individual patient characteristics.
CAPOs over time (Table I Existing neural methods have important limitations:
Limitation 1 proper adjustments: A number of neural methods for estimating CAPOs have been proposed that do not properly adjust for time-varying confounders. As a result, these methods are biased they do not target the correct estimand. Here, key examples are the counterfactual recurrent network (CRN) (Bica et al. 2020), the treatment effect neural controlled differential equation (TE-CDE) (Seedat et al.) 2022), and the causal transformer (CT) (Melnychuk et al. 2022). These methods try to account for timeviaying confounders through balanced representations. However, balancing was originally designed for redueing
estimation variance and not for mitigating confounding bias (Johansson et al.) 2016 [Shalit et al.) (017). Hence, this is a heuristic and may even introduce representation-induee these methods, our IGC-Net performs proper adjustments for time-varying confounders.
confounding bias (Melnychuk al., 2024). Unlike
Limitation 2 adjustment strategy: Existing neural methods with proper causal adjustments employ adjustment strategies that are in other ways problematic in empirical applications. On the one hand, the recurrent marginal structural networks (RMSNs) (Lim et al. 2018) construct pseudo outcomes through inverse propensity weighting (IPW). However, IPW constructs pseudo-outcomes with large variance compared to G-computation (+ we show this later in Proposition B). Specifically, for several-steps seeeaal-ttep-hhaade predictions. IPW relies on products of inverse propensity scores and, hence, division by values close to zero. In contrast, the G-Net (Li et al. 2021) and G-transformer (Xiong et al., 2024) use G-computation to adjust for time-varying confounding (see Supplement[D but proceeds by estimating the entire distribution of all confounders at several time-steps in the future (i.c., all moments of a dimeesiineiiooall random variable), which leads to poor empirical performance (see Section 4.4 for detailed discussion). Different from G-Net, we propose regression- based
Code is available at httppp////gtihiaacccccooossaaaaa GGCnnet
2

---

Published as a conference paper at ICLR 2026
approach to G-computation. Hence, our IGC-Net has two advantages in that (i) we do not attempt to learn the full distribution of all future time- varying confounders (i.e., all higher-order moments) but only estimate the first moments of much lower-dimensional random variable, and (ii) we do not need Monte Carlo sampling but can perform end-to-end regressions.
3 PROBLEM FORMULATION
Setup: We follow previous literature (Bica et al. 2020 Li et al. 2021 Melnychuk et al. 2022) and consider data that consist of realizations of the following random variables: (i) outcomes Y, E TR (ii) covariates X; E Id= and (iii) treatments A, E {0, 1) at time steps t E {o...., C No. where T is the time window that follows some unknown counting process. We are interested in estimating CAPOs for T steps in the future. For any random variable Ug E {Y, At). write Unt+r (Ut,..., Ultr) to refer to specific subsequence of random variable. We further write U.= = Un to denote the full trajectory of U including time L. Finally, we write Hi = (Y Xt+8, 11-1) for 0, and we let H, H2 denote the collective history of (i)-
Estimation task: We are interested in estimating the conditional average potential outcome (CAPO) for a future, interventional sequence of treatments, given the observed history. For this, we build upon the potential outcomes framework (Neyman 1923 Rubin 1978) for the vary-ng setting (Robins & Hernán 2009| Robins et al.) 2000). Hence, we aum to estimate the potential outcome Yt+r (+ttt-11 at future time L L-T, T E N, for an interventional sequence of treatments ā = a1str-1, conditionally on the observed history He = h2. That is, our objective is to estimate
E [Y44- [am4+-]] H. hu]
(I)
Identifiability: In order to estimate the causal quantity in Equation I from observational data, we make the following identifiability assumptions (Robins & Hernán 2009 Robins et al. 20000) that are standard in the literature (Bica et al. 2020 Li et al. [021]] Lim et al. 2018 Melnychuk et al. 2022aSeedat Seedat al. 2022):: (1) Consistency: For observed sequence of treatments A, Ôg. the
observed outcome Y.+1 equals the corresponding potential outcome Y(+1 (2) Positivity: For any history H, h2 that has non-zero probability P(H, h₂) O, there is positive probability
P(A, 0z| H, = he) > 0 of receiving any treatment A, = at, where de E {0, 1 1dd, (3) Sequential
ignorability: Given history H, h2s the treatment A, is independent of the potential outcome Y=+s that is, A, 1 Y++o [ara+8-1] H, = he for all apr+o-1 E {0, 10xd.
Why dealing with confounding is non-trivial in time-varying settings: Estimating CAPOs without confounding bias poses a non-trivial challenge in the time-vary time-narying setting. The issue lies in the plexity of handling future time-vare varying confounders. In particular, for future covariates X245 and outcomes Y:+5 5 may affect the probability of receiving certain treatments As+5' Importatll, the time-varying confounders are wnobserved during inference time, which is generally known as runtime confounding (Coston et al.) 2020). Therefore, in order to estimate the direct effect of an interventional treatment sequence, one needs to adjust for the time-varying confounders. That is, it in general insufficient to only adjust for the history (Frauen et al. 2025) via
and 1 < ô S. 8' S
[V+rr H. he]
* E Ye+ H, = he, Au = 0c2tr-1)
(2)
One way to adjust for mare-varying confounders is inverse propensity weighting (IPW), which is leveraged by RMSNs (Lim et al. 20118). However, show in Proposition] IPW is subject to large variance.
G-computation:
Instead, we leverage G-computation (Bang & Robins 2005 Robins 1999 Robins &
Hernán 2009), which provides a rigorous way to account for the time varevarying conlounders. Formally. G-computation identifies the causal quantity in Equation] l via
E| [am----]] H. hu]
E
E
... .B[E[(+ Fi Auetr-1 = austr-1] Hottr Autr- = (11-r-2)
(3)
Hi Auct1 = amt+1 |He = he, A az
We provide derivation of the G-computation formula for CAPOs in Supplement D Due to the nested structure of C-computation, estimating Equation 3 from data challenging.
3

---

Published as a conference paper at ICLR 2026
Why the approach by G-Net is problematic: So far, only G-Net (Li et al. 2021 and G-transformer
(Xiong et al. 2024) have used G-computation for estimating CAPOs in a neural model. For this, they estimate Equation through
J y44p 1 0u44r-1)))))
II dp(2)45, Bh48| he, Bo110- (4)
However, Equation requires estimating the entire distribution of all time-varying confounders at several time steps in the future. This has two drawbacks: (i) the distribution must be approximated (e.g.. through Monte Carlo sampling), which is inefficient; and (ii) all moments of a (T- x (dz + dyy) dimensional random variable need to be estimated. Importantly, (ii). We provide a detailed comparison to our IGC-Net in Section 4.4
IGC-Net addresses both (i) and
Our approach G-computation: We propose novel way to address the above challenges, and integrate G-computation into neural networks to offer better empirical performance. contrast to G-Net and G-transformer, our IGC-Net does not rely high-dimensional distribution estimation through Monte Carlo sampling. Further, our IGC-Net does not require estimating any probability distribution. Instead, performs regression-based iterative G-computation in an end-to-end training algorithm. Thereby, we perform proper adjustments for time-varying confounding through Equation while relying only on regressions of with low-variance pseudo-ous ggetoo-uutcomes.
ITERATIVE G-COMPUTATION NETWORK
In the following, we present our iterative G-computation network. Inspired by (Bang & Robins 2005: Robins] 1999] Robins & Hernán 2009) for APOs, we reframe G-computation for CAPOs time through recursive conditional expectations. Thereby, we precisely formulate the training objective of our IGC-Net through iterative regressions (->Proposition] Dp. We proceed below by first extending regression- based iterative G-computation account for the heterogeneous response to treatment intervention. We then detail the architecture of our IGC-Net and provide details on the end-to-end training and inference, which guarantees that we target the correct estimand and adjust for time-varying confounding (~Prrpositionn 2).
4.1
REGRESSION-BASEE ITERATIVE G- G-COMPUTATION FOR CAPOS
Our IGC-Net leverages G-computation as Equation 3 and, therefore, properly adjusts for time- varying confounders in Equation T However, do not attempt integrate over the estimated distribution all time-varying confounders. Instead, one our main novelties that our IGC-Net performs iterative regressions in neural end-to-end architecture. This allows us estimate Equa- tion D without approximating high nigh-dimensional probability distributions.
recursion of conditional expectations. Thereby, we can formulate the iterative regression objective of our IGC-Net. In particular, approach resembles an iterative pseudo- outcome regression. For this, let
We reframe Equation 3 equivalently
( = E[G M444 = M448, Austs = amata).
(5)
where the pseudo- outoomes are defined as
G YITT:
(6)
G (ff(s))
(7)
for 8 = 0,..,, 7 By reformulating the G-computation formula through recursions, the nested expectations in Equation 3 are now given by
G = B| Hi A = d1.
(8)
Gi+r-2 B E| Hl 11 Auc4--1 01447-1] Hitr-2 Austr 0u:44-22
(9)
and so on. Hence, the G-computation formula Equation 3 can be rewritten as
9 (h.) E[y++r H. he).
(10)
4

---

Published as a conference paper at ICLR 2026
To further illustrate regression- based iterative G-computation, provide two examples in Supplement where we show step-by-step how our approach adjusts for time-varying confounding.
We show in the following proposition that iterative pseudo-outcome, regression recovers the CAPO and thus performs proper adjustments for time-varying confounding, We summarize the iterative pseudo-outcome regression in the following proposition.
Proposition The regression- based iterative G-computation yields the CAPO in Equation 1
Proof. See Supplement C.I
In order correctly estimate Equation for a given history Hi h4 and an interventional treatment
sequence a = -1 all subsequent pseudo-outcomes in Equation 7 are required. However, the ground-truth realizations of the pseudo-outcomes G are not available in the data. Instead, only realizations of G++++ Yi++ in Equation 6 are observed during the training. Hence, when training our IGC-Net, it alternately generates predictions G of the pseudo-outcomes for ō = l.=....... I.... which it then uses for learning the estimator of Equation
Therefore, the training of our IGC-Net completes two steps in an iterative scheme: First, it runs A generation step, where it generates predictions of the pseudo-outcomes Equation 7 Then, runs a (8 learning step, where it regresses the predictions G for Equation and the observed G Y in Equation the history to update the estimator for Equation 5 Finally, the updated estimators are used again the next (A generation step. This procedure resembles an iterative pseudo- outcome regression. Thereby, our IGC-Net is designed to simultancously A generate predictions and L learn during the training. Importantly, we propose an implementation where both steps are performed in end-to-end architecture, ensuring that information is shared across time and data is used efficiently.
Ansuc
4.2 MODEL ARCHITECTURE
We first introduce the architecture of our IGC-Net. Then, we explain the iterative prediction and learning scheme inside our IGC-Net, which presents one of the main novelties. Fi- nally, we introduce the inference pro- cedure.
X
Our IGC-Net consists of two key com- ponents (see Figure []: (i) a neural backbone 2 (-), which can be, for ex- ample, be an LSTM or transformer, and (ii) several G-computation heads (1))) where denote the train- able weights. First, the neural back- bone encodes the entire observed history. Then, the G-computation heads take the encoded history and perform the iterative regressions according to Equation For all t 1,..., T and
gersuaion dey
gone aloak
gracs
cig
ang ski
Figure Iterative G-computation network. Neural end- to-end architecture of our iterative G-computation network.
d 0,..., 1, the components are designed follows:
Neural backbone: For our main experiments in Section 5 we use multi-input transformer (-) as our neural backbone, which consists of three connected encoder-only sub-transformers okk (.), k E 2, and is inspired by (Melnychuk et al. 2022). We provide details on the architecture Su provide additional ablations with an alternative I.STM backbone in Supplement F.1 At time i, the transformer =-)- receives data H; (Y,, X,, A,-1) as input and passes them to one corresponding sub- transformer. In particular, each uub-transformer zΦt one particular U. e (Y,, Xx, A in order to effectively process the different types of inputs. Further, we ensure that information shared between the sub-transformers. The output of the multi-input transformer are hidden states z,", which are then passed to the (ii) G- computation heads.
is responsible to focus
5

---

Published as a conference paper at ICLR 2026
G-computation
Aii 4
1887
mit (i. Mlt 111- R,.4
R. My. indenne -yn-
Hif jil sownull
IGC-Not
Figure 2: How our IGC-Net performs G-computation adjust for time-varying confounding.
G-computation heads: The G-computation heads {9] (-))zo are the read-out component of our IGC-Net. As input at time + 6, the G-computation heads receive the hidden state Z from the above neural backbone. Recall that we seek to perform the iterative regressions in Equation annd Equation 10 respectively. For this, we require estimators of G+++1 H++8, Ac+s). Hence, the G-computation heads compute
(11) for d = 0, 0,.., 1. As result, the G-computation heads and the neural backbone together form the estimators that are required for the pivression-based iterative G-computation. In particular, we
E[G Hess, Acta] o8 (Z Acts), with Z = (B
thereby ensure that, for 5 O. the last G-computation head (%) is trained as the estimator for the
CAPO as given in Equation I0 That is, as illustrated in Fig. 2 for fully trained neural backbone
and G-computation heads, our IGC-Net estimates the CAPÓ vIa
[[ H, h.] 90 (c))
(12)
4.3 ITERATIVE TRAINING AND INFERENCE
We now introduce the iterative training of our IGC-Net, which consists of (A generation step and a i learning step. Then, we show how inference for given history H, = h4 can be achieved. We summarize the iterative learning algorithm in Algorithm
Iterative training: Our IGC-Net is designed to estimate the CAPO gf (h+) in Equation 10 for given history HI hu and an interventional treatment sequence 0e.t+--1 via Equation 12 Therefore, the G-computation heads Equation 11 require the pseudo-outcomes {G+ 17 from Equation 7 during training. However, they are only available in the training data for ò That is, we only observe the factual outcomes G
17-1 in the A gener- As remedy, our IGC-Net first predicts the remaining pseudo-outcomes {G 84-88==1 8=1 ation step. Then, it can use these generated pseudo-outcomes and the observed G for learning the network weights in the B learning step. In the following, write (G /=1 for the generated oseudo-outeomes. Note that, since C Yi+r is observed during training, do not have to generate this target. Yet, for notational convenience, we write G = -
A Generation step: In this step, our IGC-Net generates G & gf+s((rits)) as substitutes for Equation [ which are the pseudo-outcomes in the iterative regression-based G-computation. Formally, our IGC-Net predicts these via
Gf+s (Z)4s
(13)
where
= = 2 am1+6-1)s
(14)
for 8 = 0, ..... 1. For this, all operations are detached from the computational graph. Hence, our IGC-Net now has pscudo-outcomes ( which it can use in the following B learning step. Of note, these generated pseudo-outcomes will be noisy for early training epochs. However, as training progresses, the G-computation heads perform increasingly more accurate predictions, explain below.
Learning step: This step is responsible for updating the weights of the neural backbone 20( and the G-computation heads {9/( (-))-)) For this, our IGC-Net learns the estimator for Equation via
B Hi Acatsl = o (2A Auts),
(15)

---

Published as a conference paper at ICLR 2026
where
7 = (
(16)
for 8 = T -- -1. 1. In particular, the estimator is optimized by backpropagating the squared error loss C for all 8 = .,..., -1 and ( 1,..., - via
9 (Z4 Acto) - G2 G(,s1))))
L
(17)
6=0
Then, after ø is updated, use the updated estimator in the next A generation step.
Here, it important that for ö T, the pseudo-outcome C% Y14r is available in the data. By learning Y2+r with
Algorithm 1: Training and inference
Training:
Inpot Dota (R Tr- Ar -1- Yr), sequence
=
Actr-1);
(18)
13 X Joaming rule
Outpus: Trained IOC.Nat (=", 16-0
it is ensured the last G-computation head oh (-) learned on a ground-truth quantity. Thereby, the weights of 1-) are gradually optimized during train-
for c = -...., T do
// initialize
6 -Y+++
Coneration stop do
ing. Hence, the predicted pstudo-
for
G
(2
(19)
Z (0 a1146-1) o + og (78+0:
in the next A generation step become mores accurate. Therefore, the G-computation head 2-) is learned on a more accurate prediction in the following @ learn-
and
11
Seasning step
for
D do
z - (Be44)
ing step, which thus leads to a better generated pseudo-
4 - (1 o1))
outcome G - and so on. As a result, the optimiza- tion of the G-computation heads gradually improves from & (.) up go (-).
end
Compute gradient update 160-Xet parametors
6- -V (TL Eh' (+ Eis of))
Inference: Finally, we introduce how inference is achieved with our IGC-Net. Given a history H, = h,
Inference:
and an interventional treatment sequence a = 0+:---1+ our IGC-Net is trained to estimate of Equation through Equation TO For this, our IGC-Net computes the CAPO via
Data BG, testment (0. 13 Output: of (Me) = EIG Ht, as]
Inpot
Initialize
Rut-r-1 t
Genecal Lon stup
of (hx) = B[G | H. = h., A. = as] = (2 (hi), ax).
88 (R.) 90 (At),
(20)
Legend: Operitoos
attsched the computatioonl
We summarize this in the following proposition.
graph, while operiioon with "t" are detnched from
Proposition 2. Our IGC-Net estimates the G-computation formula as in Equation 10 and, therefore, performs proper adjustments for time-varying confounding.
Proof. We provide an intuition in Figure 2
The full proof is in Supplement C.2
4.4 ADVANTAGES OVER EXISTING NEURAL METHODS
CT, CRN, and TE-CDE: Our IGC-Net
Method
Extimated mument
Moment dimenoou
Edimation strslegy
is vastly different from CT (Melnychuk
let al., (022), CRN (Bica et al. 2020) and
1) x dy) dy
2nd
( 1)xx (ds dg)
Mare Cado sumpling
TE-CDE (Seedat et al.) 2022). These meth- ods do not perform proper adjustments for time-varying confounding. In particular, they estimate [E[Y++r Hr = hı, Arettr a+:+++ which not the CAPO (Frauen) et al. 2025). Hence, they target an incor- rect estimand, leading irreducible bias, so deploying them to medical scenarios would be irresponsible.
Liet S02T
aed
(r 1)x (ds + dg)
Xiong al B004
1) (d. + 4,)
IGC-Nin (ourr)
Endeorecnl negracins
Table 2: Comparison: G-Net and G-transformer vs. our IGC-Net. G-Net and G-transformer require estimating the full distribution of all time-varyie con- founders in the future (i.e., estimating all moments).
RMSNs: RMSNs (Lim et al. 2018) rely on pseudo-outcome regressions in order to adjust for time-varying confounders. However, their pseudo-outeomes are constructed via inverse propensity weighting, which leads to pscudo-outcomes with larger variance than ours:
7

---

Published as a conference paper at ICLR 2026
Proposition 3. Pseudo-outcones constructed via inverse propensity weighting have larger variance than psendo-outcomes in our iterative G-computation network.
Proof. See Supplement
G-Net and G-transformer In order to estimate a r-step-ahead CAPO, G-Net (Li et al. 2021 and
G-transformer (Xiong et al. 2024) require (i) dy dy-dimensional regression as well as estimating the entire distribution of a (T 1) x (dy + ddddennnnio confounding variable. That is, it needs to estimate all moments of a high-dimensional random variable, which is inefficient. In contrast, our IGC-Ner Net only requires regressions of dy dimensioona outcome and, hence, only needs to estimate the first moment of a much lower-dimensional random variable. We provide a comparison in Table 2
5 EXPERIMENTS
We show the performance of our IGC-Net against key neural methods for estimating CAPOs over time (see Table D. Further details (e.g., implementation details, hyperparameter tuning, runtime) are given in Supplement
Confrendigg straghh
Bigus 2030
1
6.1
4:21 2:1.2
43311:0:1
1447
480
4.72::0555
C7 Moterc
5.012:002
137 0.15
5:55::0.75
357
4.3.2:0000
4.32
1.45:2005
RMSSS Lans
5:4 2:11
0.5
6:2
0:2
1.31
4.000::.:
4.4
0.52
1:7
1.70
0:00
1.66
6.7
0.07
6.50
6:00
IGONe (oor))
0.13
5:10
5.30::0.111
0:30
5.53
0.30
d: 0:20
5:007
13.3%
14.0%
Table 3: RMSE synthetic data. Based the tumor data with 2. Our IGC-Net consistently outperforms all baselines. We highlight the relative improvement over the best-performing baseline.
Synthetic data: First, we follow common practice in benchmarking for causal inference (Bica et al. 2020 Li et al. 2021 Lim al. 2018 Melnychuk et al. 2022) and evaluate the performance of our IGC-Net against other baselines on fully synthetic data. The use of synthetic data is beneficial as it allows us to simulate the outcomes under sequence of interventions, which are unknown in real-world datasets. Thereby, we able to evaluate the performance of all methods for estimating CAPOs over time. Here, our main aim is to show that our IGC-Net is robust against increasing levels of confounding.
For this, we use data based on the pharmacokinetic- phemmackkncic-plaaaaeaaaaa tumor growth model (Geng et al. 2017), which is a standard dataset for benchmarking causal inference methods in the time- varying setting (Bica et al. 2020: Li et al. 2021 Lim et al., 2018 Melnychuk et al., 2022). and allows for controlling the confounding strength with parameter y. Here, we interested in the performance of our IGC-Net for increasing levels of confounding. We thus increase the confounding parameter y from y = 10 ? 20, and the same parameterization as in (Melnychuk et al. 2022). We report details on the data-generating process in Supplement G.T
Results: Table shows the average RMSE over five different runs for a prediction horizon of Of note, we emphasize that our comparison is fair (see hyperparameter tuning in Supplement 1.2 We make the following observations:
(i) Our IGC-Net outperforms all baselines by a significant margin. Importantly, as our IGC-Net performs proper adjustments for time-varying confounding, it is robust against increasing y- In particular, our IGC-Net achieves performance improvement over the best-performing baseline of up to 17.4%.
(ii) The ① baselines that do not perform proper adjustments (i.e., CRN (Bica et al. 2020 TE-CDE (Seedat et al. 2022), and CT |Meinychuk al., 2022) exhibit large variations performance and are thus highly unstable. This expected, they do not target the correct causal estimand and, accordingly, suffer from the increasing confounding.
(iii) The baselines with 2 problematic adjustment strategies (i.e., RMSNs (Lim al. 2018 G-Net
(Li et al. (02T)) are slightly more stable than the no-adjustment baselines. This can be attributed to that the tumor growth model has time- varying covariates X, and to that we are only focusing on
T = 2-step ahead predictions, both of which reduce the variance, However, the RMSNs and G-Net
still significantly worse than IGC-Net.
8

---

Published as a conference paper at ICLR 2026
K- 1800
Siger
E:0.0001
6212/M
155.11
02:13112
031 K17
345:4144
1:3 20
011-113
137
060
205-812
00:13
140
108-1
20--22
1404-30
0N
077
030
10:1000
0722
13123000
Ed aqprecee
1996
2.9
10.4
Table 4: RMSE on semi-synthetic data based the MIMIC-III extract. Our IGC-Net consistently outperforms all baselines. We highlight the relative improvement over the best-performing baseline.
Next, we study how our IGC-Net performs when (i) the covariate space is high-dimensional and when (ii) the prediction windows become larger. For this, we use semi- synthetic data, which, similar to the fully-synthetic dataset, allows us to access the ground-truth outcomes under an interventional sequence of treatments for benchmarking.
Semi-synthetic data:
Our data- aata-generatiig process is taken from (Mennychuk et al., 2022). which builds upon the MIMIC- extract (Wang et al. 2020) based on the MIMIC-III dataset (Johnson et al.) (016)) In short, we use d₂ 25 different vital signs as time-varying covariates, and simulate observational outcomes for training, and interventional outcomes for testing, respectively. As the covariate space is high- dimensional, we thereby study how robust our IGC-Net with respect to estimation variance. We further increase the prediction windows from T 2 up T 6. We report details on the data-generating process in Supplement G.1
Results: Table 4
shows the average RMSE over five different runs. Again, we emphasize that our comparison is fair (see hyperparameter tuning in Supplement[] [.. We make three observations:
(i) Our IGC-Net consistently outperforms all baselines by large margin. The performance of IGC-Net is robust across all sample sizes N. Further, it is stable across different prediction windows. We observe that our IGC-Net has better performance compared to the best baseline of up to 7%.
(ii) The 1 baselines that do not perform proper adjustments (i.e., CRN (Bica et al. 2020 CT (Melnychuk al.||202. )022 tend perform better than baselines with problematic adjustment strategies (i.e., RMSNs (Lim et al. 2018), G-Net (Li et al. 202T)). The reason is that the former baselines (ii) do not require IPW pseudo-outcomes. Hence, they can better handle the high-dimensional covariate space. They are, however, biased as they do not adjust for time-varying confounders and thus still perform significantly worse than our IGC-Net.
are (i) regression-
(iii) The baselines with ? problematic adjustment strategies (i.e., RMSNs (Lim et al. 2018 G-Net (Li et al. 202T), G-transformer (Xiong al. 2024)) struggle with the high-dimensional covariate space and larger prediction windows This can be expected, as RMSNs suffer from overlap violations and thus produce unstable inverse propensity weights. Similarly, G-Net suffers from the curse of dimensionality, it requires estimating (dz dy) x (r 1) dimeesiooal distribution.
Ablation studies We now compare IGC-Net against two ablations: (i) an IGC-LSTM ablation and (ii) a biased transformer ablation. For the former, we substitute the multi-input transformer in our IGC-Net with a simple LSTM. For the latter, we use the same transformer backbone as in our main results but directly learn the G-computation heads the factual data. Thereby, we omit the iterative generation and learning steps and do not perform proper adjustments for time-varying confounding.
Figure g shows the performance of both ablations. (i) We can see that the IGC-LSTM ablation has competitive performance due to our approach to G- computation. Of note, the ICG-LSTM is proposed in this work and thus presents a key novelty by itself. (ii) The biased transformer clearly has poor performance due to the absence of proper adjust- ments, which further highlights the importance of our iterative generation and learning algorithm.
Dieiic
64
We additionally evaluate on the MIMIC-III ICU dataset in T following the setup of Meinychuk et al.) (2022). where the goal is to predict factual patient outcomes (c.g.,
Real-world data:
Prodider
Figure 3: Ablations. IGC-LSTM has competi- tive performance. while the biased transformer without proper adjustments is inferior.
effects of vasopressors and ventilation on diastolic

---

Published as a conference paper at ICLR 2026
A-300
1+1
200
00-30
03
Table 5: RMSE on real-world data based on the MIMIC-III extract (best in bold, second-best underlined. We conduct sanity check, and evaluate all methods on real-world data for factual outcome prediction. Of note, methods that perform adjustments for time-varying confounding are not primarily tailored for factual outcome prediction, as there are no causal interventions. Predicting factuals only requires simple history-adjustmen highly competitive, and is the best-perforning method along with CT.
in CT. CRN and TE-CDE. Yet, our IGC-Net is
blood pressure). Because no counterfactuals are observed, this experiment serves only as a sanity check rather than an evaluation of causal accuracy. Nevertheless, our method achieves state-of-the-art factual prediction performance, which demonstrates that our IGC-Net remains highly effective even when no vime-narying adjustment required, and is directly applicable to real-world clinical data.
Overlap sensitivity analysis: We further evaluate the robustness to overlap violations using the synthetic tumor dataset in Table [ Therein, we scale the treatment-assinnment logits with a factor p. Smaller values of p produce well-balanced treatment overlap, whereas larger values push the assignment probabilities toward Our IGC-Net outperforms all baselines, which demonstrates strong robustness even when overlap deteriorates.
1, which induces increasingly severe overlap violations.
Ohertip CRN
115
0.6
07
P-BB 11.
P- 1.B
P-11 1.1
1.2
1.3
P-11
1.5
mipuural 1030
2:59 1 0.36
313:1
355 1:035
100 D:533
3:31 1.51
5:7 1.99
5.5 1141
5 0:33
3.5
0.55
1:51
0.00
2003
2:35
3.251:0.55
110:1:45
125:1000
0.3.10522
426- 1157
1.77
2:00
2.71
053
0:5
-91=133)
0.370000
0.31-000
1:90
1.1:1:337
5.511188
490 1.30
1.0
5.3.1.85
6.0-111877
5,60 1:91
0.50
3.74
6.70 1:21
G-Na
Lidt
3.16-110.33
4.3-2:0074
410 0:45
1/11
1136
4,33
0::45
5,00 3.000
4.50
0.31
3,00 0487
1.57 11.0
5,00 1144
IGl--Net (ser))
2:53 3.53.10.11
2.761.0.88
3.07 J. 0.20
3.16 1
0.32
5,36
0.27
3.24
0.12
3.08 0.32
3.39 1 0.38
3.55 0.53
3:48
0.19
3.65 0.29
Rd.
0,355
2,138
2.7%
6,83
11.8%
1007E
7.0%
16.155
13.05
20.4%
11.28
Table 6: RMSE with overlap violations. Based on the tumor data with T = 2 and varying levels of overlap. Lower values of the overlap parameter indicate more balanced overlap, whereas larger values of p skew the overlap towards extreme values close to 0 or 1. Our IGC-Net outperforms all baselines. We highlight the relative improvement over the pereoorrff baseline.
Unobserved confounding: We perform robust- ness checks under unobserved confounding in Ta- ble Hence, we introduce an unobserved con- founder U₁ (N00 1) for each patient in the tumor dataset. The confounder is omitted from the observed state, but influences both treatment assignment and tumor evolution. Treatment logits for chemotherapy and radiotherapy are shifted by an additive term 0.2 x U, and therefore systematic hidden bias is injected into the assignment policy. Additionally, the tumor growth is perturbed by adding w x U; inside the multiplicative growth factor. The scalar coefficients w controls the strength of the unobserved confounding. Of note, none of the baselines is designed to handle unobserved confounding. Our results show that our IGC-Net remains fairly robust, and performance does not deteriorate any worse than the baselines.
1.00
4.3.
X01
G.
530-1.5
6554157
116
600-1.0
657
4.7
4.7--000
3:41 -6-27
3 2.11
Table 7: RMSE under unobserved confound- ing. Our IGC-Net maintains the best perfor- mance under increasing confounding w.
Additional results: We report additional ablation studies, a sensitivity analysis of our pseudo- outcomes, uncertainty quantification with MC dropout and kernel smoothing, and the coefficient of variation in Supplement
Conclusion: In this paper, we propose the IGC-Net, a novel end-to-end method that adjusts for time- varying confounding. Therefore, expect our IGC-Net be important step toward personalized medicine with machine learning.
10

---

Published as a conference paper at ICLR 2026
ACKNOWLEDGMENTS
This work has been supported by the German Federal Ministry of Education and Research (Grant: 011S24082). This paper is supported by the DAAD program "Konrad Zuse Schools of Excellence in Artificial Intelligence", sponsored by the Federal Ministry of Education and Research.
REFERENCES
Ahmed M. Alaa and Mihaela van der Schaar. Bayesian inference of individualized treatment effects using multi-task Gaussian processes. In NewrlPS, 2017.
Ahmed Allam, Stefan Feuerriegel, Michael Rebhan, and Michael Krauthammer. Analyzing patient trajectories with artificial intelligence. Journal of Medical Internet Research, 23(12))e29812, 2021.
Per Kragh Andersen and Maja Pohar Perme. Pseudo observvibssssnsonns in survival analysis. Staristical Method in Medical Research, 19(1):71-99) 2010.
Per Kragh Andersen, Elisavet Syriopoulou, and Erik T Parner. Causal inference in survival analysis using pseudo-observation Statistics Medicine, 36( (6(17):2669-260 2017.
2017.
Ellen M. Apperloo, Jose L. Gorriz, Maria Jose Soler, Secundino Cigarrán Guldris, Josep M. Cruzado, Maria Jesús Puchades, Marina Lépez-Martínez, Femke Waanders, Gozewijn D. Laverman, An- nemarie van der Aart-van der Beek, Klaas Hoogenberg, André P. van Beek, Jacobien Verhave, Sofia Ahmed, Roland E. Schmieder, Christoph Wanner, David Z. I. Cherney, Niels Jongs, and Hiddo J. L. Heerspink. Semaglutide in patients with overweight or obesity and chronic kidney disease without diabetes: a randomized double-blind control-cn clinical trial. Nature Medicine, 2024.
Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E. Hinton. Layer normalization. arXiv preprint, 1607.06450, 2016.
Heejung Bang and James M. Robins. Doubly robust estimation in missing data and causal inference models. Biometrics, 61(4):962-973 2005.
Samuel L. Battalio, David E. Conroy, Walter Dempsey, Peng Liao, Marianne Menictas, Susan Murphy, Inbal Nahum Nahum-Shani, Tianchen Qian, Santosh Kumar, and Bonnie Spring. Sense2Stop: A micro- randomized trial using wearable sensors to optimize just-in- just-in-times time-adaptive stress management intervention for smoking relapse prevention. Contemporary Clinical Trials, 109:106534, 2021.
Ioana Bica, Ahmed M. Alaa, James Jordon, and Mihaela van der Schaar. Estimating counterfactual treatment outcomes over time through adversarially balanced representations. In ICLR, 2020.
Ioana Bica, Ahmed M. Alaa, Craig Lambert, and Mihaela van der Schaar. From real-world patient data to individualized treatment effects using machine learning: Current and future methods to address underlying challenges. Clinical Pharmacology and Therapeutics, 109(1):87-100, 2021.
Yevgen Chebotar, Quan Vuong, Alex Irpan, Karol Hausman, Fei Xia, Yao Lu, Aviral Kumar, Tianhe Yu, Alexander Herzog, Karl Pertsch, Keerthana Gopalakrishnan, Julian Ibarz, Ofir Nachum, Sumedh Sontakke, Grecia Salazar, Huong T Tran, Jodilyn Peralta, Clayton Tan, Decksha Manju- nath, Jaspiar Singht, Brianna Zitkovich, Tomas Jackson, Kanishka Rao, Chelsea Finn, and Sergey Levine. O-transformer: Scalable CoRL, 2023.
learning via autoregressive f-funtiions. In
Amanda Coston, Edward H. Kennedy, and Alexandra Chouldechova. Counterfactual predictions under runtime confounding. In NeurIPS, 2020.
Leon Deng. Hong Xiong, Feng Wu, Sanyam Kapoor, Zach Gosh, Soumya Shahn, and Li-wei Lehman. Uncertainty quantification for conditional treatment effect estimation under dynamic treatment regimes. In ML4H, 2025.
Guilherme Duarte, Noam Finkelstein, Dean Knox, Jonathan Mummolo, and llya Shpitser. An automated approach to causal inference discrete settings. Journal of the American Staristical Association, 119:1778-1798 2023.
11

---

Published as a conference paper at ICLR 2026
Stefan Feuerriegel, Dennis Frauen, Valentyn Melnychuk, Jonas Schweisthal, Konstantin Hess, Alicia Curth, Stefan Bauer, Niki Kilbertus, Isaac S. Kohane, and Mihaela van der Schaar. Causal machine learning for predicting treatment outcomes. Nature Medicine, 30:958-960 2024.
Dennis Frauen, Tobias Hatt, Valentyn Melnychuk, and Stefan Feuerriegel. Estimating average causal effects from patient trajectories. In AAAI, 2023a.
Dennis Frauen, Valentyn Melnychuk, and Stefan Feuerriegel. Sharp Bounds for Generalized Causal Sensitivity Analysis. In NeurlPS, 2023b.
Dennis Frauen, Konstantin Hess, and Stefan Feuerriegel. Model-agnostic meta-learners for estimating heterogeneous treatment effects over time. In ICLR, 2025.
Hiroki Furuta, Yutaka Matsuo, and Shixiang Shane Gu. Generalized decision transformer for offline hidnsight information matching. In ICLR, 2022.
Yarin Gal and Zoubin Ghahramani. Dropout as a Bayesian approximation: Representing model uncertainty in deep learning. In ICML, 2016.
Changran Geng, Harald Paganetti, and Clemens Grassberger. Prediction of treatment response for combined chemo- and radiation therapy for non-small cell lung cancer patients using a bio- mathematical model. Scientific Reports, 7(1):13542, 2017.
Konstantin Hess and Stefan Feuerriegel. Stabilized neural prediction of potential outcomes in continuous time. In ICLR, 2025.
Konstantin Hess, Valentyn Melnychuk, Dennis Frauen, and Stefan Feuerriegel. Bayesian neural controlled differential equations for treatment effect estimation. In ICIR, 2024.
Konstantin Hess, Dennis Frauen, Mihaela van der Schaar, and Stefan Feuerriegel. Overlap-weighted orthogonal meta-learner for treatment effect estimation over time. In ICLR, 2026.
Sepp Hochreiter and Jürgen Schmidhuber. Long short-term memory. Neural Computation, 9(8): 1780- 1997.
Yuongsoo Jang, Jongmin Lee, and Kee-Fung Kim. Gpt-critic: Offline reinforcement learning for end-to-end task-oriented dialogue systems. In ICLR, 2022.
Emil Javurek, Valentyn Melnychuk, Jonas Schweisthal, Konstantin Hess, Dennis Frauen, and Stefan Feuerriegel. An orthogonal learner for individualized outcomes in Markov decision processes, In ICI.R, 2026.
Fredrik Johansson, Uri Shalit, and David Sonntag. Learning representations for counterfactual inference. In ICML, 2016.
Alistair E. W. Johnson, Tom J. Pollard, Lu Shen, Li-wei H. Lehman, Mengling Feng, Mohammad Ghassemi, Benjamin Moody, Peter Szolovits, Leo Anthony Celi, and Roger G. Mark. MIMIC-III, freely accessible critical care database. Scientific Data, 311: 2016.
Nathan Kallus and Masatoshi Uehara. Intrinsically efficient, stable, and bounded off off-po evaluation for reinforcement learning. In NeurIPS, 2019.
Nathan Kallus and Masatoshi Uchara. Double reinforcement learning for efficient off off-policy evalua- tion in markov decision processes. Journal of Machine Learning Research, 21:1-63, 2020.
Nathan Kallus and Masatoshi Uehara. Efficiently breaking the curse of horizon in off- policy evaluation with double reinforcement learning. Operations Reseurch, 70(6):3282-3300 2022.
Patrick Kidger, James Morrill, James Foster, and Terry Lyons. Neural controlled differential equations for irregular time series. In NewrIPS, 2020.
Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In ICLR, 2015.
Aviral Kumar, Justin Fu. George Tucker, and Sergey Levine. Stabilizing off- off-policy q-learning via bootstrapping error reduction. In NeurIPS, 2019.
12

---

Published as a conference paper at ICLR 2026
Rui Li, Stephanie Hu, Mingyu Lu, Yuria Utsumi, Prithwish Chakraborty, Daby M. Sow, Piyush Madan, Jun Li, Mohamed Ghalwash, Zach Shahn, and Li-wei Lehman. G-Net: A recurrent network approach to G-computation for counterfactual prediction under dynamic treatment regime. In MI4H, 2021.
Bryan Lim, Ahmed M. Alaa, and Mihaela van der Schaar. Forecasting treatment responses over time using recurrent marginal structural networks. In NewrIPS, 2018.
Roderick Little and Donald Rubin. Causal effects in clinical and epidemiological studies via potential outcomes: Concepts and analytical approaches. Annual Review of Public Health, 21:121 1-54, 02 2000.
Judith J. Lok. Statistical modeling of causal effects in continuous time. Annals of Statistics, 36(3). 2008.
Christos Louizos, Uri Shalit, Joris Mooij, David Sontag, Richard Zemel, and Max Welling. Causal effect inference with deep latent-variable models. In NeurIPS, 2017.
Haorui Ma, Dennis Frauen, and Stefan Feuerriegel. DeepBlip: Estimating Conditional Average Treatment Effects Over Time. arXiv preprint, 2511.14545, 2025.
Valentyn Melnychuk, Dennis Frauen, and Stefan Feuerriegel. Causal transformer for estimating counterfactual outcomes. ICML, 2022.
Valentyn Melnychuk, Dennis Frauen, and Stefan Feuerriegel. Normalizing flows for interventional density estimation. ICML, 2023.
Valentyn Melnychuk, Dennis Frauen, and Stefan Feuerriegel. Bounds on representation-indien inducce confounding bias for treatment effect estimation. In ICLR, 2024.
Krikamol Muandet, Montonobu Kanagawa, Sorawit Saengkyongam, and Sanparith Marukatat. Coun- terfactual mean embeddings. Journal of Machine Learning Research, 22:1-71, 2021.
Susan A. Murphy. Optimal dynamic treatment regimes. Journal of the Royal Statistical Society: Series B, 65(2):331-355 2003.
Elizabeth Murray, Eric B. Hekler, Gerhard Andersson, Linda M. Collins, Aiden Doherty, Chris Hollis, Daniel E. Rivera, Robert West, and Jeremy C. Wyatt. Evaluating Digital Health Interventions: Key Questions and Approaches. American Journal of Preventive Medicine, 51(5):843-855 851, 2016.
Jerzy Neyman. On the application of probability theory to agricultural experiments. Annals of Agricultural Sciences, 10:1-51, 1923.
Miruna Oprescu, Jacob Dorn, Marah Ghoummaid, Andrew Jesson, Nathan Kallus, and Uri Shalit. B-Leamer: Quasi-oracle bounds heterogeneous causal effects under hidden confounding. In ICML., 2023.
Yilmazcan Özyurt, Mathias Kraus, Tobias Hatt, and Stefan Feuerriegel. AtDMM: An attentive deep Markov model for risk scoring in intensive care units. In KDD. 2021.
Alexander Pashevich, Schmid, Cordelia, and Chen Sun. Episodic transformer for vision-and-language navigation. IEFF/CVF, 2021.
James M. Robins. A new approach to causal inference in mortality studies with a sustained exposure period: Application to control of the healthy worker survivor effect. Mathematical Modelling, 1512-1 1986.
James M. Robins. Correcting for non-compliance in randomized trials using structural nested mean models. Communications in Statistics Theory and Methods, 23(8):2379-24133 1994.
James M. Robins. Robust estimation in sequentially ignorable missing data and causal inference models. Proceedings of the American Statistical Association on Bayesian Statistical Science, pp. 6- 10, 1999.
13

---

Published as a conference paper at ICLR 2026
James M. Robins and Miguel A. Hernán. Estimation of the causal effects of time-varying exposures. Chapman & Hall/CRC handbooks of modern statistical methods. CRC Press, Boca Raton, 2009. ISBN 9781584886587.
James M. Robins, Miguel A. Hernán, and Babette Brumback. Marginal structural models and causal inference in epidemiology. Epidemiology, 11(5):50-550, 2000.
Donald B. Rubin. Bayesian inference for causal effects: The role randomization. Annals of Statistics, 6(1):34-58, 1978.
Helene C. Rytgaard, Thomas A. Gerds, and Mark J. van der Laan. Continuous-time targeted minimum loss-based estimation of intervention-specffi mean outcomes. The Annals of Statistics, 2022.
Peter Schulam and Suchi Saria. Reliable decision support using counterfactual models. In NeurIPS, 2017.
Nabeel Seedat, Fergus Imrie, Alexis Bellot, Zhaozhi Qian, and Mihaela van der Schaar. Continuous- time modeling of counterfactual outcomes using neural controlled differential equations. In ICML, 2022.
Uri Shalit, Fredrik D. Johansson, and David Sontag. Estimating individual treatment effect: General- ization bounds and algorithms. In ICML, 2017.
Peter Shaw, Jakob Uszkoreit, and Ashish Vaswani. Self-attention with relative position representations. In Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, 2018.
Yi Shirakawa, Toru; Li, Yulun Wu, Sky Qiu, Yuxuan Li, Mingduo Zhao, Hiroyasu Iso, and Mark van der Laan. Longitudinal targeted minimum bass-based estimation with temporal-differee heterogeneous transformer. In ICML, 2024.
Hossein Soleimani, Adarsh Subbaswamy, and Suchi Saria. Treatment- models for counter- factual reasoning with continuous-timg continuous-valle interventions. In UAI, 2017.
Chien-Lin Su, Robert W Platt, and Francorasçoos Plante. Causal inference for recurrent event data using pseudo-observations. Biostatistics, 23(1):189-200 2022.
Masatoshi Uehara, Chengehun Shi, and Nathan Kallus. A review of off-policy evaluation in rein- forcement learning. arXiv preprint, 2212.06355, 2022.
Mark J. van der Laan and Susan Gruber. Targeted minimum loss based estimation of causal effects of multiple time point interventions. The International Journal of Biostatistics, 8(1), 2012.
Toon Vanderschueren, Alicia Curth, Wouter Verbeke, and Mihaela van der Schaar. Accounting for informative sampling when learning to forecast treatment outcomes over time. In ICML, 2023.
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention all you need. NeurlPS, 2017.
Haotian Wang, Haoxuan Li, Hao Zou, Haoang Chi, Long Lan, Wanrong Huang, and Wenjing Yang. Effective and efficient time-varying counterfactual prediction with state-space models. In ICLR, 2025a.
Shirly Wang, Matthew B.A. McDermott, Geeticka Chauhan, Marzyeh Ghassemi, Michael C. Hughes, and Tristan Naumann. MIMIC-extract: A data extraction, preprocessing, and representation pipeline for MIMIC-III In CHIL, 2020.
Xin Wang, Shengfei Lyu, Chi Luo, Xiren Zhou, and Huanhuan Chen. Variational counterfactual intervention planning achieve target outcomes. In ICML, 2025b.
Shenghao Wu, Wenbin Zhou, Minshuo Chen, and Shixiang Zhu. Counterfactual generative models for time-varying treatments. In KDD), 2024.
Hong Xiong. Feng Wu, Leon Deng, Megan Su, and Zach Shan. G-transformer: Counterfactual outcome prediction under dynamic and time-varying treatment regimes. In MI.HC, 2024.
14

---

Published as a conference paper at ICLR 2026
Yanbo Xu, Yanxun Xu, and Suchi Saria. A non-parametric bayesian approach for estimating treatment-response curves from sparse time series. In ML4H, 2016.
Jinsung Yoon, James Jordon, and Mihaela van der Schaar. GANITE: Estimation of individualized treatment effects using generative adversarial nets. In ICLR, 2018.
Yao Zhang, Alexis Bellot, and Mihaela van der Schaar. Learning overlapping representations for the estimation of individualized treatment effects. In AISTATS, 2020.
15

---

Published as a conference paper at ICLR 2026
A EXTENDED RELATED WORK
Estimating CAPOs in the static setting: Extensive work on estimating potential outcomes focuses
on the static setting (e.g.. Alaa & van der Schaar 2017 Frauen et al. 2023b Johansson et al. 2016
Louizos et al. 2017 Melnychuk et al. 2023; Yoon et al. 2018 Zhang et al., 2020)). However,
observational data such as electronic health records (EHRs) clinical settings are typically measured over time (Allam et al., [021] Bica et al. (02T). Additionally, treatments are rarely applied all at once but rather sequentially over time (Apperloo al., 2024). Therefore, the underlying assumption of these methods prohibitive and does not properly reflect medical reality, Hence, static methods are not tailored accurately estimate potential outcomes when (i) time series data is observed and (ii) multiple treatments in the future are of interest.
Additional literature on estimating CAPOs over time: Recently, |rauen et al. (2025); Hess et al.)
(2026) proposed model-agnostic meta-learners for heterogeneous treatment effect estimation over time. Therein, they analyze theoretically the advantages and disadvantages of several adjustment strategies such regression adjustment, IPW, and DR estimators. Our IGC-Net uses similar identification
(RA) approach, in the sense that both rely on the G-formula and estimate the conditional mean of the next outcome given the observed history. However, the core innovation of our IGC-Net lies not in adopting RA as an identification strategy, but in developing a novel end-to-end learning algorithm that implements the full multi-step G-computation recursion within a single neural architecture. Instead of fitting a separate model at each time step, our method couples representation learning with iterative pseudo-outcome leaming+generation, which enables joint optimization across all time-steps.
There are some non-parametric methods for this task (Schulam & Saria 2017 Soleimani et al. 2017] Xu et al. 2016), yet these suffer from poor scalability and have limited flexibility regarding the outcome distribution, the dimension of the outcomes, and static covariate data; because of that, we do not explore non- -on-aaametriic methods further but focus on neural methods instead.
Other works are orthogonal to ours. For example, (Hess et al. 2024 Vanderschueren et al. 2023) are approaches for informative sampling and uncertainty quantification, respectively. However, they do not focus on the causal structure, and are therefore not primarily designed for our task of interest. (2025) propose the first neural method for proper causal adjustments in continuous time, which is different stream of literature, and is not tailored for our discrete time setting. Ma et al. (2025) propose a neural method that imposes parametric assumptions on the DGP.
Further, /Hess& & Feuerriegel
Deng et al. (025)) do not introduce a new estimator for time-varying conditional treatment effects and CAPOs; instead, they take existing models as fixed bases and add approximate Bayesian uncertainty quantification layers (deep ensembles, variational dropout, SWAG) on top. Their focus is on improving calibration and decision underlying CAPO estimand or addressing bias/variance trade-offs of the point estimates themselves. As such, their work is orthogonal ours and could be applied on top of our IGC-Net as well.
by modeling parameter uncertainty, not on changing the
Further, Wang et al. 20025b) and Wu et al. (2024) try to estimate the entire distribution of CAPOs over time, which is different task from ours: their estimand is the counterfactual density, not the conditional mean potential outcome (CAPO) that our paper targets. This task fundamentally differs from ours, as they require learning nigh-dimmnssooal conditional distributions and sampling trajectories and are therefore unsuitable for our task.
Finally, Wang et al. (2025a) propose a state-space-moe propose a framework with decorrelation regularization. However, its learning objective is different in two essential ways: It does not perform proper adjustments and therefore does not identify the CAPO under sequential ignorability. Instead, it regularizes correlations between hidden states and treatments, which does not correspond to any identified estimand in longitudinal causal inference. directly predicts outcomes from hidden states learned under de-correlation penalties. As a result, its outputs are not guaranteed to estimate the CAPO.
Andersen al. 2017. Su et al. 2022) employ pseudo-outcomes, which is similar to our approach. However, these works different in that they aimed survival outcomes and not CAPOs for sequences of treatments. Further, they do not consider neural networks as estimators. Additionally, (Andersen
Survival analysis: Some works in survival analysis (Andersen & Perme 2010
et al. 2017) only considers single, static treatment, and (Andersen & Perme 2010) only uses
16

---

Published as a conference paper at ICLR 2026
linear estimators. Finally, (Su al. 2022) focuses average causal effects and is therefore not applicable to personalized medicine.
Kallus & Uchara 2019) from the reinforcement learning literature (Furuta et al., 2022] ang et al. 2022 Kumar et al. 2019 Pashe vich et al., 2021 Javurek et al.) (2266) is closely related G-computation, although both have different purpose. They are similar in that they share a common goal of understanding the effect of treatments/actions, but operate in complementary domains: G-computation grounded in causal inference for evaluating potential outcomes, whereas Q-learning is rooted in reinforcement learning to derive policies that maximize long-tew term rewards. We show more details on the two in the following:
G-computation and Q-learning:
Q-lcarning (Murphy 2003
G-computation can be written as the iterative update
c = -E [[ H6+5 = hi+5: Autto = 0c4+5l.
(21)
In our setting, we aim to estimate E (Y+r [01 H, = h..]
However, could also consider the expected cumulative rewards E ((+t|anatril) H, hr]. where we define [ Σi= y'Y++oluuuee- and where y < is so-called discount factor that weighs the importance of immediate and future rewards. One can show that the G- computation update becomes
ge g = E| 90
Hi h4445 Attts a1:-5).
(22)
If only care about the optimal treatment sequence a" (i.e., the that maximizes the cumulative reward), we can write
Le Pito E{22+8 + max G94841 66661
H24 Ni4 Austs d2.+4))
(23)
Eq. equation 23 is known Q-learning in the literature on dynamic treatment regimes (Murphy 2003 Kallus & Uehara 2019) and can be used to compute an optimal dynamic policy.
In reinforcement learning, often makes additional Markov and stationarity assumptions such that the history hi4 simplifies to a single state St455 and the function g"i (s:) is not dependent time. These assumptions allow us to consider infinite time-horizons and break the so-called curse of horizon (Kallus & Uehara 2022 Uehara et al. 2022). Then, Q-learning simplifies
d (st) EY + max G" 62+1
S = st, A = at).
(24)
which is often called fitted Q- Q-iteration in the RL literature (Kallus Uchara 2020 Uchara et al. 2022). In contrast, our work does not make these assumptions.
State-of- the-art neural instantiations such as (Chebotar et al. 2023) are different to our work in that they (i) serve the purpose of learning long-term rewards, and (ii) rely restrictive Markov assumptions. In contrast, our IGC-Net is designed to estimate CAPOs for sequences of treatments, conditionally the entire individual patient history.
17

---

Published as a conference paper at ICLR 2026
B DISCUSSION ON IDENTIHABILITY ASSUMPTIONS AND CLINICAL RELEVANCE
In this work, present novel neural network, the iterative G-computation network, for estimating conditional average potential outcomes (CAPOs) from observational data such as electronic health records (EHRs). Our IGC-Net addresses a crucial question in personalized medicine: "What would the outcome be for patient X if they were administered treatments A, B. and C sequentially over the next days, given their unique clinical history?" Unlike many existing methods that focus on static or single-ponn point interventions (Alaa & van der Schaar 2017: Johansson et al.) [016: Zhhng et al.) 2020), our method specifically designed to hundle the sequential nature of treatments in medical practice feature that is both realistic and necessary, as treatments are rarely applied all at once but rather sequentially over time (Apperloo et al. 2024). With the growing availability of scale observational data from EHRs (Allam al. [021] Feuerriegel et al.) 2024 Bica et al. [202] l) and wearable devices (Battalio et al., 2021). there is an increasing need for robust methods that estimate the effect of multiple treatments, given the individual patient history.
Our framework builds on three key assumptions: (i) consistency, (ii) positivity, and (iii) sequential
ignorability (see Section 3). These assumptions are the standard assumptions for estimating CAPOs over time (Bica et al. 2020; ei et al. 2021 Melnychuk et al., 2022; Seedat et al. 2022). Notably, compared other methods that rely even stricter assumptions, such as additional Markov or independence assumptions (Özyurt et al. 2021). our assumptions are less restrictive. Furthermore, these assumptions are the dynamic analogues of the standard causal inference assumptions static settings (Alaa & van der Schaar 2017: Muandet et al. [021 Johansson et al., 2016). Importantly, methods for the static setting implicitly impose unrealistic assumption that treatments occur only once and that covariates and outcomes remain static over time. Such limitations can introduce significant bias sequential ceziiioonmaaingg contexts. In contrast, our approach models the time-varying nature of clinical interventions and patient evolution, making it less restrictive and far more aligned with real-world medical scenarios.
Further, argue that these assumptions are both plausible and practical in medical applications. First, consistency is generally satisfied as long as EHR data is accurately and systematically recorded. Second, positivity be ensured through thoughtful data nre-proeessing such filtering obser- vations or applying propensity clipping. Additionally, as the scale of observational datasets grows, this assumption becomes less restrictive. Third, the sequential ignorability assumption is a standard assumption in epidemiology (Little & Rubin (2000), and studies in digital health interventions may satisfy this assumption by design. Furthermore, advances in sensitivity analysis (Frauen al.) 2023b. Oprescu et al. (202)) and partial identification (Duarte et al. (202)) offer complementale pathways to relax this assumption. That is, these literature streams are orthogonal to our work. In practice, our IGC-Net thus integrates into established workflows that include point estimation, uncertainty quantification, and sensitivity analysis.
From practical perspective, our IGC-Net addresses key challenges in estimating CAPOs for se- quences of treatments. Specifically, our IGC-Net provides a neural end-to-end solution that adjusts for time-varying confounding. On top, it neither relies on large-variance pseudo-outcomes (Proposition 3) nor on estimating high- -igh--imennional probability distributions. Therefore, we are convinced that our IGC-Net is an important step towards reliable personalized medicine.
18

---

Published as a conference paper at ICLR 2026
C PROOFS
C.I UNBIASED ESTIMAND
Proposition Our regression-based iterative G-computation yields the CAPO in Equation
Proof. For the proof. only need to apply the definition of the pseudo-outcomes G2+5'
E| [ 1] He -he]
(25)
E
B[E[Y++T -1: A = 01:t+7-1] H. H Aua+7-2 = 0
He = Ar = =at] }
Auct1 = Arot1
(26)
E
B[E|GH+ 1
AuAT-1 = a++++-1]
Hitr-2 A2147-2 = -
Hit Art+1 = am++1
=1= A: = =a1
(27)
E
1 (11(+-1) 11 A = a1:
Hi = h2g A: = }
Hit Aut+1 = 0c:41
(28)
E
E G G
Acctr-2 = -1:
Hi Aut+1 = ac:+1
Hi = hrg Ar = aD
(29)
1
=E
E
git 2( (H
A0041 = a1s+1
Hg = hr, A: = at)
(30)
(31)
=E G
H. h4, Ar at
(32)
(ht)
(33)
where Equation 26 holds due the G-computation formula (see Supplement D
19

---

Published as a conference paper at ICLR 2026
C.2 TARGET OF OUR IGC-NET
Proposition 2. Our IGC-Net estimates the G-computation formula as in Equation 10 and therefore, performs proper adjustments for time-varying confounding.
Proof. For the proof, we perform the steps as in Supplement 0 1 1+r [0114--1]
He = he]
(34)
B
B( Hi+r-1. 1 Acstr-1 -0:14--1] -itt--2 Auttr-2 0cctr-2)
Hi == heg :he A. = a1 )
Hith = a0141
(35)
B
B[BIC H1tT-11AActT- a1:44-11 21 A =6144-22
Hi Artt1 = 01:4+1
H-= h4g As at
(36)
Auttr-2 = 0c:+r-2
F Artt1 = acst1]
Hr =h,, A: at
(37)
B(G 21
Auatt-2
a1:
H Art+1 = 01:411
H7 = hi, A, at
(38)
of (0-2(ar7-22. (1 ... H H Ac41 act+1
H. h, A. at
(39)
(40)
=B
G(+1
H. h4, A, at
(41)
= 3 (a):=011))
(42)
20

---

Published as a conference paper at ICLR 2026
C.3 VARIANCE OF INVERSE PROPENSITY WEIGHTING
In this section, we compare two possible approaches to adjust for time-varying confounders: G- computation and inverse propensity weighting (IPW) (Robins & Hernán 2009; Robins et al. 2000), which is leveraged by the existing baselines, namely, the RMSNs (Lim et al. 2018), and continuous time versions as in (Hess & Feuerriegel, 2025).
For a fair comparison of G-computation and IPW, we compare the variance of the ground-truth pseudo-outcomes that each method relies on that is, the G of our IGC-Net and the inverse propensity weighted outcomes of RMSNs. Importantly, a larger variance of the -seudo-outcomes will directly translate into larger variance of the respective estimator. We find that IPW leads to a larger variance, which is why we prefer G-computation in our IGC-Net.
Proposition 3. Pseudo-outcomes constructed via inverse propensity weighting have larger variance than pseudo-outcomes in our iterative G-computation network.
Proof. To simplify notation, we consider the variance of the pseudo-outcomes in the static setting. The analog directly translates into the time-varying setting.
Let Y be the outcome, X the covariates, and A the treatment. Without loss of generality, we consider the potential outcome for A = 1.
For G-computation, the variance of the pseudo-outcome (X) is given by
Varlg (X)] Var[E[|
X, I]]
(43)
E BIY
X, A 1|2 E E[Y
X, A =1] 11]
(44)
=
E
X = 113 - E r
(45)
For IPW, the variance of the pseudo-outcome
YA
YA
] - R
YA 2
Var
R
(46)
(X)
(X)
Y
[x] E [r1]]
E
E
(47)
(X)
(²)(X)
X, $11 R -F[YI1]] 2
E
I
(48)
(X)
E
E
|x,= 11 - B [[1]
(49)
and, with
E|Y X, = 1]2 + Var Y
= 1
| X, A == 1).
(50)
20
we have that
YA
Var
Varlg((X)):
(51)
(X))
T
Therefore, we conclude that G-computation leads to lower variance than IPW, and, hence, our IGC-Net has a lower variance than RMSNs
Remarks:
The inverse propensity weight is what really drives the difference in variance between the approaches. Note that, in the vime-varying setting, IPW relies on products of inverse propensities, which can lead to even more extreme weights for multi-step ahead predictions. This is expected: propensity weights are typically small and close to zero, especially in time-series settings. Hence, by diving to a quantity close to zero, the variance can naturally explode.
21

---

Published as a conference paper at ICLR 2026
IPW is particularly problematic when there overlap violations in the data, this implies propensity scores close to zero and thus division by values that are close to zero. However, as the imput history H, in the time- time-narying setting is very high-dimensional (i.e., t (dz d dimensional), overlap violations are even more problematic. This is another advantage of method.
22

---

Published as a conference paper at ICLR 2026
D DERIVATION OF G-COMPUTATION FOR CAPOS
Hony
Fiaa Veatree
Dneet of Hibeed
Figure During inference, future time- tireiigyiigg confounders are unobserved (here: (X+11, Y(-1)). In order to estimate CAPOs for an interventional treatment sequence without time-varying confounding bias, proper causal adjustments such as G-computation are required.
In the following, we provide a derivation of the G-computation formula (Bang & Robins 2005
Robins 1999 Robins & Hernán 2009) for CAPOs over time. Recall that G-computation for CAPOS
is given by
B
++r (Qustr-1 He he]
= E
E
E
00:4+-11] 1
Ac147-1
- Autrr2 0xa+r-2] (52)
Hit Autt1 = 04s41 Hr = hi A,
The following derivation follows the steps in FFauen et al. 2023a) and extends them to CAPOs:
H. he]
=E =E Y++ [11++-1]
H. = h4g A a:l
(53)
-E Y 6+ [1]
Hi At = az}
(54)
H, h4, At orl
M1 A 01.+11
(55)
H, h At arl
EE (a 1]
2 A a+:++1
(56)
Hi4 A am411
H, = h,,
A, = dr)
=E -E (0+
H2 Aut42 = a1:122
(57)
A1141 = a1:41]
H. = h4 orl
-E (0cet4
H 11 A 0ut4T-1]
(58)
11 11 Au4tr-2 01:47-2)
...
H. h4, Ar arl
=E E(
H. H 11 A Autr-1 0
(59)
11 A 01:47-23
H. h4, Ar =a),
23

---

Published as a conference paper at ICLR 2026
where Equation 53 follows from the positivity and sequential ignorability assumptions, Equation 54 holds due to the law of total probability. Equation [55 again follows from the positivity and sequential ignorability assumptions, Equation [6 the tower rule, Equation [ is again due to the positivity and sequential ignorability assumptions, Equation (58 follows by iteratively repeating the previous steps, and Equation 59 follows from the consistency assumption.
24

---

Published as a conference paper at ICLR 2026
E EXAMPLES
To illustrate how regression-bend based iterative G-computation works, we apply the procedure to two examples. First, we show the trivial case for (T = --step--ahead predictions and, then, for (T 2) --step-ahe predictions. Recall that the following only holds under our standard assumptions (i) consistency, (ii) positivity, and (iii) sequential ignorability.
(T = 1) steep-aaed prediction:
This is the trivial case, as there is no time-varying confounding. Instead, all confounders are observed in the history. Therefore, we can simply condition on the observed history and resemble the backdoor- adjustment from the static setting. Importantly, this is not the focus of our work, but we show it for illustrative purposes:
E YY+ [a:]
H1 -ha] Hy h4s A. = ar)
(60)
E[ [ar]
(61)
Ass. (ii)i
E He = hi, At arl
(62)
Ass.
B[G4
H, = h. A, = oz)
(63)
Def. G2+1
lt (he).
(64)
Det. of
(T = 2)-step-a prediction:
Importantly, (T 2)stepp-ahead predictions already incorporate all the difficulties that are present for multi-step ahead predictions. Here, we need to account for future time- tmeevaryyngg confounders such as (X++1, Yz-1) 1) as in Figure
E Y242(0nc41] H1, = he] ( [0
(65)
Hy Te, = or]
(66)
Ass. (i)))li))
E B Y (e22
Hi44
Ar ael
He, = he, At =at]
(67)
probs
E [(
H Hig A = A
H. -he, Ar at
(68)
Ass. (i)ttii
E
B (Y+2
Hit A = 0m0+1]
HI, = A; = ai]
(69)
Ass.
E E A4141 = =0
He = he, A: = at
(70)
Def. 6242
1 H, hu, A. =aa]
(71)
Def. #2+1
E G
H. = he, A. a.]
(72)
Def. G9
(he).
(73)
Def. of
25

---

Published as a conference paper at ICLR 2026
F ADDITIONAL RESULTS
In the following, we report additional results:
1. We first compare our ablations from Section [ to the baselines and report additional prediction windows for semi-synthetic data in Supplement E1
2. We perform sensitivity analysis w.r.t our generated pseudo-outcomes in Supplement F2 and, thereby, confirm that our IGC-Net generates meaningful pseudo-outcomes in the iterative learning algorithm.
3. We finally report the coefficient of variation of our IGC-Net and the baselines in Supple- ment F.4 which further supports the stability of our IGC-Net.
F.1 ADDITIONAL RESULTS AND ABLATIONS
In the following, report the performance of two ablations: the (A) IGC-LSTM and the (B) biased transformer (BT). For this, we show (C) additional results of our IGC-Net, the baselines, and the two ablations in Figure 5 and Figure 6
IGC-LSTM: Our first ablation is the IGC-LSTM. For this, we replaced the transformer backbone (-) of our IGC-Net by simple LSTM network. We find that IGC-LSTM is highly effective: outperforms all baselines from the literature while our proposed IGC- CeCCsraanformer is still superior. This demonstrates that novel method for iterative regression- based G-computation is both effective and general.
BT: We implement biased transformer (BT). Here, leverage the same transformer backbone
(-) as our IGC-Net, but we directly train the output heads g (-) on the factual data. Thereby, the BT refrains from performing G-computation. We can thus isolate the contribution of the iterative G-computation the overall performance. Our results show that the BT suffers from significant bias and, therefore, demonstrate that our proper adjustments for time-varying confounders are required for accurate estimates of the counterfactual outcomes.
We report additional results on
1. tumor growth data, where we report the performance of all methods for lower levels of confounding in Figure
2. MIMIC-II semi-synthetic data, where report additional prediction windows up to
T = 12 for N = 1000 F
26

---

Published as a conference paper at ICLR 2026
IGC-Net (ours)
6.0
IGC LSTM ablation
Biased transformer ablation
5.5
CT
CRN
TECDE
Average RMSE
5.0
RMSN
G-Net
4.5
4.0
3.5
3.0
2.5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Confounding strength (v)
Figure 5: Tumor growth data: We report previous results of the baselines with the ablations: IGC-LSTM and BT. + Notably, our IGC-LSTM has competitive performance, while BT suffers from significant bias. Our IGC-transformer remains the strongest method.
IGC-Net (ours)
1.4
IGC ablation
Biased transformer ablation
1.2
CT
CRN
TECDE
Average RMSE
1.0
RMSN
G-Net
0.8
0.6
0.4
0.2
2
3
4
5
6
7
8
9
10
11
12
Prediction horizon (1)
Figure 6: Semi-synthetic data: We increase the prediction horizon up to 12 for N 1000 training samples. We further implement two ablations: our IGC-LSTM and the biased transformer (BT). + As in Figure 5 our IGC-LSTM almost consistently outperforms the baselines. while the BT has large errors. Our /GC-transformer remains the best for all prediction windows. This shows that our novel approach for G-computation leads to accurate predictions, irrespective of the neural backbone. Further, it shows that proper adjustments are important for counterfactual outcome estimation.
27

---

Published as a conference paper at ICLR 2026
F.2 SENSITIVITY NOISE IN PSEUDO-OUTCOMES
Finally, we provide more insights into the quality of the generated pseudo-outcomes G7+5 in Figure Here, added increasing levels of constant bias the pseudo-outeomes during training. Our results show that these artificial corruptions indeed lead to a significant decrease in the overall performance of our IGC-Net. We therefore conclude that, without artificial corruption, our generated pseudo-outcomes are good estimates of the true nested expectations. Further, this shows that correct estimates of the pseudo-outeomes are indeed necessary for high-quality, unbiased estimates. Of note, the quality of the predicted pseudo-outcome, is also directly validated by the strong empirical performance Section
1.6
1.4
Average increage RMSE
1.2
1.0
0.6
0.2
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Artificial noise on first pseudo-outcome
Figure 7: During training, we add artificial levels of noise the pseudo-outcomes of our IGC-Net (prediction window confounding strength performance quickly deteriorates. This is expected, as it implies that the pseudo-outcomes generated by our IGC-Net meaningful and important for accurate, unbiased predictions.
10 synthetic data). We see that
28

---

Published as a conference paper at ICLR 2026
F.3 UNCERTAINTY QUANTIFICATION
We can additionally equip our IGC-Net with uncertainty quantification, e.g., with dropout Gal & Ghahramani 2016), standard and lightweight approach for predictive uncertainty estimation in neural networks. Because our model is fully differentiable and regression-based. MC dropout and similar approaches (Deng al. 2025) can be applied without modifying the our IGC-Net, which makes uncertainty quantification straightforward to incorporate.
Posterior preciclive approximation
0.10
True target
0.08
0.04
0.00
-10
20
30
Figure Our IGC-Net is easily compatible with any standard standard-proceduuee for uncertainty quantification. Reported is the posterior predictive using dropout and kernel smoothing.
29

---

Published as a conference paper at ICLR 2026
F.4 COEFFICIENT OF VARIATION
In the following, we additionally report the coefficient of variation of our main study on synthetic data in Section 5 Lower values in the coefficient of variation indicate more stable predictions. Table shows the results. Clearly, our IGC-Net is superior to the baselines and has significantly more robust estimates of the CAPO.
7=
11
7=
12
7
13
7=
14
7
=
15
7.
16
7=
17
7=
19
7
20
CRN Bica 2020
0.11
0.31
0.21
0.30
0.06
0.20
0.15
0.17
0.19
0.15
TE-CDE Scedat et
2022
0.13
0.10
0.03
0.10
0.09
0.14
0.10
0.09
0.12
0.09
0.10
CT Melnychuk
2023
0.21
0.21
0.17
0.18
0.19
0.17
0.32
0.18
0.22
0.17
0.21
RMSNs Lim et al
2018
0.06
0.05
0.07
0.07
0.07
0.09
0.12
0.13
0.10
0.12
0.11
G-Net
(L) ct
2021
0.11
0.09
0.08
0.07
0.07
0.07
0.09
0.10
0.13
0.13
0.11
IGC-Net (ours)
0.07
0.04
0.06
0.04
0.03
0.09
0.07
0.07
0.09
0.06
0.07
Table 8: Coefficient of variation synthetic data based the tumor growth model with
Lower values indicate more stable predictions. Our IGC-Net clearly outperforms the baselines.
30

---

Published as a conference paper at ICLR 2026
G DETAILS ON THE DATA GENERATING PROCESSES
G.1 SYNTHETIC DATA
We use data based on the Tharmasokineti--paarmeee pharmacodynamie tumor growth model (Geng al. 2017), which is a standard dataset for benchmarking causal inference methods in the time-varying setting (Bica al. 2020 Li al. 2021] Lim et al. [2018] Meinychuk et al. [2022). Here, the outcome
Y, is the volume of tumor that evolves according to the stochastic process
Y++1 = (1 + plog
K Y.
-aa,d + (,,d)) +
Y
(74)
Chemaherapy
Radiotherapy
Noise
Tumar growth
where aes Oy,, and 3, control the strength of chemo- and radiotherapy. respectively, and where K corresponds to the carrying capacity, and where p is the growth parameter. The radiation dosage de and chemotherapy drug concentration et are applied with probabilities
A,, A7 Ber (o (Di.. (Di.,(DissY- -
(75)
where max the maximum tumor volume, D15 the average tumor diameter of the last 15 time steps, and y controls the confounding strength. We use the same parameterization as Melnychuk et al.) (2022), and refer to their work for more details. For training, validation, and testing, we sample N 1000 trajectories of lengths T S 30 each.
We are interested in the performance of our IGC-Net for increasing levels of confounding. We thus increase the confounding from 10 to y 20. For each level of confounding, we fix an arbitrary intervention sequence and simulate the outcomes under this intervention for testing.
G.2 SEMI-SYNTHETIC DATA
We build upon the MIMIC-extract (Wang al. 2020), which is based on the MIMIC-III dataset (Johnson et al. 2016). Here, we use de = 25 different vital signs as time-varying covariates and as well as gender, ethnicity, and age as static covariates. Then, we simulate observational outcomes for training and validation, and interventional outcomes for testing, respectively. Again, our data- generating process is taken from (Meinychuk et al. (2022), which we refer to for more details. In summary, the data generation consists of three steps: (1) dg. = untreated outcomes YJ.j = 1,2, simulated according to
Y B-splinee + + (X))) ECo
(76)
where ag of and a² are weight parameters, B-spline(t) is sampled from mixture of three different
cubic splines, and (-) is random Fourier features approximation of a Gaussian process. (2) A total of d, = 3 synthetic treatments A,, / = 1, 2,3, are applied with probability
A ~ Ber(p)). p¹ (?t + + (X))
(77)
where of and 7 are fixed parameters that control the confounding strength for treatment A', Y: an averaged subset of the previous treated outcomes, b' is bias term, and f(-(-) is random function that is sampled from an RFF (random Fourier features) approximation of a Gaussian process. (3) The treatments are applied to the untreated outcomes via
min:-1..... 11 1A (wr 1)2
Yi
(78)
i=t-w!
where w/ is the effect window for treatment A' and زاا controls the maximum effect of treatment A'.
We run different experiments for training, testing, and validation sizes of N = 1000, N = 20000 and N 3000, respectively, and set the time window 30 < T < 50. As the covariate space is high-dimensional, we thereby study how robust our IGC-Net is with respect to estimation variance. We further increase the prediction windows from 7 2 up to 7 6.
31

---

Published as a conference paper at ICLR 2026
H ARCHITECTURE OF ITERATIVE G-COMPUTATION NETWORK
In the following, we provide details on the architecture of our IGC-Net.
Multi-input transformer: The multi- transformer as the backbone of our IGC-Net is motivated by (Melnychuk et al. 2022), which develops an architecture that is tailored for the types of data that typically available in medical scenarios: (i) outcomes Y, Rd,xt, covariates X E RR,xxt and treatments A, E {0, } já=xt, In particular, their proposed transformer model consists of three separate tub-transformers, where each uub-transformer performs multi-headed self-attention mechanisms on one particular data input. Further, these sub-tras uub-transformers are connected with each other through in-between cross-attention mechanisms, ensuring that information is exchanged. Therefore, we build on this idea as the backbone of our IGC-Net, as we detail below.
Our multi-inpur transformer 2-(-) consists of three sub- transformer models 2 (.), k: 1,2,3, where 2dh (.) focuses on one data input U E {Y,, X,, A.- 1.. k E (13 respectively.
(1) Input transformations: First, the data U. E TRdxxtt is linearly transformed through
z. (Uf) W + 8 E txd
(79)
where Wkk00 E Rdaxda and fA.00 E RRdh are the weight matrix and the bias, respectively, and d, is the number of transformer units.
Next, we stack j J transformer blocks, where each transformer block j receives the outputs Z of the previous transformer block j - 1. For this, we combine (i) multi-headed self- and coss-attentions, and (ii) feed-forward networks.
(2) Transformer blocks:
() Multi- self- and cross attentattnnn The output of block j for sub-transformer l is given by the multi-headed cross-attention
2 = Q. + 5MHAC RD, V(.),
(80)
where 0% -Kha V.d are the outputs of the multi-headed self-attention
+ - +MHA(Q ,K.... V.
(81)
Here, (-A(-) denotes the multi-headed attention mechanism as in (Vaswani et al. 2017) given by MHA(g, k v) = 30 (Attention(g' k², u"),..., "...nntoio MM a )²))).
(82)
where
(1Tm Vdgker
Attention(q" km vm)) softmax
(83)
is the attention mechanism for m = I...,,M attention heads. The queries, keys, and values
qTh km n' E xxdde have dimension dypkr which is equal to the hidden size d, divided by the
number of attention heads M, that is, dgke= = d,/M. For this, we compute the queries, keys, and
values for the cross- pross-attentions as
Q = 2. Wk.m + Jk.m. E Rixdekv
(84)
Kk.ma Ri W w.mss jkmm E gixdoke
(85)
VRmm kw w.m. + Jkima e Bixdoky
(86)
and for the selftattentions
- Wkim. + b.mmm E Btxdake k.m.m. zk. Z. + hams E gtx
(87)
(88)
V. k.m_ (.. + boms e gixdyt.
(89)
where Wikmm, Wkkma E Rd xdyto and Jh.mi Jammi E Rd,ke are the trainable weights and biases for sub-transformers k 1,2,3, transformer blocks 1,...,J, and attention heads
32

---

Published as a conference paper at ICLR 2026
I...., M. Of note, each self- and cross attention uses relative positional encodings (Shaw et al. 2018 to preserve the order the imput sequence as in (Melnychuk et al. (022).
(ii) Feed-forward networks: After the multi heati- cross cross-attention mechanism, IGC-Net applies feed-forward neural network on each Z respectively. Further, apply dropout and layer normalizations (Ba et al. 2016) as in (Melnychuk et al. 2022 Vaswani et al. 2017). That is, our
IGC-Net transforms the output kJ for transformer block of sub-transformer k through sequence of transformations
FP (2 LayerNorm Dropout Linear Dropout o ReLU Linear (Z
(90)
(3) Output transformation: Finally, after transformer block J, we apply final transformation with dropout and average the outputs as
3
Z ELU Linear o Dropout
Σ 2, )
(91)
k=1
such that Zi E Rdd
G-computation heads: The G-computation heads {9g (-))0) receive the corresponding hidden state
Z and the current treatment ALts and transform it with another feed-forward network through
98 (7 Ac+s) = Linear o ELU Linear (7 Act6).
(92)
33

---

Published as a conference paper at ICLR 2026
I IMPLEMENTATION DETAILS
In Supplements 1.2 and 1.3 we report details on the hyperparameter tuning. Here, we ensure that the total number of weights comparable for each method and choose the grids accordingly, All methods are tuned on the validation datasets. As the validation sets only consist of observational data instead of interventional data, we tune all methods for r 1-step ahead predictions as in (Melnychuk) et al. 2022). All methods were optimized with Adam (Kingma & Ba 2015). Further, we perform random grid search as in (Melnychuk al. 2022).
On average, training our IGC-Net fully synthetic data took 13.7 minutes. Further, training on semi-synthetic data with to the baselines. All methods were trained on 1 NVIDIA A A100-PCIE-40GB Overall, running our experiments took approximately days (including hyperparameter tuning).
10000/200/
samples took 1.1/2.1/3 /3.0 hours. This is comparable
I.1 COMPUTATIONAL COMPLEXITY
Let N be the number of units, t the observed window and the prediction horizon, d the covariate dimension, H/ the hidden size of the backbone. L the number of backbone layers, and K the number of Monte-Carlo samples used by G-Net (Li al. 202T) and G-transformer (Xiong al. 2024). We denote by Cbackbone (t, 7) the cost of a single forward- barrdd--bwwrddddd pass of the sequence backbone over prediction horizon 5. For example, for an transformer or LSTM (for simplicity, assuming the same constant) this scales as
Cbackbono (t, O(FL(HH
+ H²)),
(93)
(e.g., for transformer would include the usual I-dependent attention term). both cases, dependence on is contained inside Cbackbone
Our method performs exactly one such backbone pass per unit, with a lightweight regression head on top. Thus, the total per-epoch cost is
Ciac = O(N Obackbono (t, T)),
(94)
with no additional simulation or sampling loop.
G-Net and G-transformer share this backbone cost but add Monte-Carlo simulation stage: for each unit and each time step they generate K synthetic covariate updates using hold-out residuals. Each such update is (d)); repeated for all time steps and all samples, this contributes
CMc O(NrKd)
(95)
This term is additive because the Monte-Carlo simulation is an extra phase on top of the backbone training. Within this term, is multiplicative with N, r, and for every unit N and every time step T. they perform K residual draws, each touching all d covariates. The total G-Net and G-transformer cost therefore
CG-NeeG-tmansfooer ONN Chackbone (t, 7) NrKd),
(96)
which is strictly heavier than our regression-only IGC-Net whenever K >> 1.
RMSNs have similar O(rL(dH + H²) order per network but must train both an outcome and propensity model, effectively doubling the backbone term.
34

---

Published as a conference paper at ICLR 2026
1.2 HYPERPARAMETER TUNING: SYNTHETIC DATA
Coepert
Heperprneeee
Theegiig
1S734
Leaning
Facede
1.5734 budee allr)d))
Biuancod icpooration
0.56 Myse Mure Mapa Myy
0.5 16 Ma Mi
01.02
speck
Leaning
225,
Depader
LSTT4 balee wil
0.5 Muse 3 Mulu Mase
01.87
Nuntior spedk (sc)
Leaning
GUAS,
Eacadet
Bo and poonine aiee wiro
Slare Mane Mure Mape Myye ILS.. 1e., Mi.
Sege M Mala Myn
Peoo--oematt Soeward duden uaae tivec
are dirpeaa
Scoon mal
255
Dovides
hadden
Ra stced ewcce
Mure Sepaa Myys
Fiod Summard lublon aade Dive)
0LSC. 14., 25
Nicara dispica
Asscstoo
prosenaa aalee (A.))
0.Shamm Moses Mure Mure Mace
Food Samurd Jullnn aade Diee)
D.SC 16., M
speck
Leartigg
(L00 5.000
Poppraate swired
1.5Th4 bnlde wiiv
Saae Man Saea Myy
wive
1.5TM4 dinpuea
01.03
Stec prodice come
LUS 1.3.2
Nommtor specks
30
Poqueaity
enweik
bikee
baldes (A
1.Seum Mu..
dingrea
I1.82
Von lome
Stutibor of spicka
50
lreets
boldew (ii
LSTT
Ubex
(US,
Skadleer epeckie
50
LSTM lapax (2)
(LL-22
LA
Fead
Sequratal Vin peodined Naadiw apeci (og)
Table 9: Hyperparameter tuning for all methods fully synthetic tumor growth data. Here.
dyza = dy dg + d, is the overall input size. Further, de denotes the hidden representation size of IGC-Net, the balanced representation size of CRN (Bica et al. 2020 TE-CDE (Seedat al. 2022) and CT (Melnychuk et al. 2022), and the LSTM (Hochreiter & Schmidhuber, 1997) output size of G-Net (Li et 2001). The hyperparameter grid follows (Melnychuk al. (022). Importantly, the tuning ranges for the different methods are comparable. Hence, the comparison of the methods in Section 5 is fair.
35

---

Published as a conference paper at ICLR 2026
1.3
HYPERPARAMETER TUNING: SEMI-YYNTHETIC DATA
Mathed
Compenent
Hoperpaander
Vaning
LSTM
1,2
Mindsach
Esoaka
Balanoed eppesenaatien stoe 66.1
1..6
11.6
34ye
FF bidde unio (ne)
0,56 Jal, 20l
0.1.02
Minieach size
250, 512, 1024
Decodar
Batanoed repeneetatio
LSTM vaitwidks
1.76 26pm
Be Belance rxpeccstation sice caunier
Cikkkk (tta)
0.56, Stl.
doguot
0.1,02
Nucthe expocls (nc)
Nearal CDE feidic lapas
Learning mawet
0.00, comi, ro01
Mtatbarhh
liicke caiterol
0.5 Mape
Serd-toaaae hidden Owey
0.54, 74,
Drspect cae
0.1.22
TE-CDE Senta
Nuzzher
Nearal CDE lnidiin lapas
Learsing
6001 poet
Botunced repouantatoon enoodar
Balanied rscettctaio of.
0.5%
Fiod sew and hidddo (wwr)
0.54, Idl, Sel
LSTT depport
spochs
Learning (c)
Minibach aizz
S2, 64
Amerion heads (og)
Malggeskkral pioz
Transherrr
Food-Reowad liddon
0.5d
Seganmia drop rate ge
0.1.0.2
Mas pooaional encociig Vene
3M
Ntanbe qpacka (n.)
100
LSTM
1,2
Pupenily
momrrr
1. Man
setwork
LSTM despout sate (p)
0.1.02
Mas gralkan
0.5,
Noether spochs
LSTM cowig)
Busandy
Line
LSTM feidoe oall
0.54 Mure Din
LSTM deggorr mas
0.1.0
spochs
Lounnng maeii)
Misibarih
Decader
LSTM untrecii)
Mifor Ad Myg..
LSTM clopout
0.1.02
grallor
Leariing (c)
eusil, 1000
Minttach uae
66. 126 250
GN6 Lotdl MI
lead (ead-s--nd)
LSTM bnadie sante(dk))
LSTT ofu)
0.5% Lifure, 2elow
deopoca rate
Nurbo of spoddaa (n-)
(00
Tranaienze Mocket 2)
Leussigg rake
0,001, 000001
Muntbach
64
Traalienes (d4))
Idur... 20h
Ieano
Raienoal ageccsenttiinn vise offe
0.56 Eifeer Dige 0.54, Md., 24.
Feod new and hiddow Owey)
Soqezzia dispont
0.1
proilional
copochs
Table 10: Hyperparameter tuning for all methods on semi semi- synni-sytthetic data. Here, dyza dyy d2 + de is the overall input size. Further, d, is the hidden representation size of our IGC-Net, the balanced representation size of CRN (Bica et al. | 2020), TE EDE (Seedat al., (2022) and CT (Melnychuk et al.) 2022). and the LSTM (Hochreiter & Schmidhuber, (997) output size of G-Net (Li et al. 2021). The hyperparameter grid follows (Melnychuk al. 2022). importantly, the tuning ranges for the different methods are comparable. Hence, the comparison of the methods in Section 5 is fair.
36


Reviews:
[{"review_id": "jE7riFQmIX", "reviewer": "Reviewer_R3mf", "summary": "The paper proposes IGC-Net, a neural method for estimating CAPOs over time from observational data. It aims to properly adjust for time-varying confounding by operationalizing iterative G-computation as a sequence of regression problems trained end-to-end. Experiments on a pharmacokinetic tumor growth simulator and semi-synthetic MIMIC-III show lower RMSE than prior neural baselines", "questions": "- Robustness & diagnostics: add overlap diagnostics; test positivity violations by skewing treatment assignment; report how IGC-Net degrades vs. RMSNs/TMLE-like DR estimators.\n\n- There’s limited analysis of convergence, computational cost vs. G-Net/RMSNs, or memory footprint for large τ.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "- The authors identified the limitations of existing work and proposed a new framework to address them. \n\n- Experiments are thoroughly conducted on both synthetic and real-world datasets. \n\n- Code and data are available for review.", "weaknesses": "- Missing important baselines. The paper omits several recent and competitive methods for time-varying counterfactual prediction, such as CGM [1], State-Space Counterfactual Models [2], and G-Transformer [3], that would provide a fairer and more rigorous empirical comparison.\n\n- The experiments implicitly assume correctly specified models and strong sequential ignorability and positivity. There is no investigation into the method’s robustness under violations of overlap or unmeasured confounding, nor any diagnostics for near-zero treatment probabilities, which is an issue particularly relevant for real-world EHR data.\n\n- Both synthetic environments exhibit stylized and stationary dynamics. The claim that IGC-Net is robust “especially for longer horizons” remains weakly supported; validation on scenarios with τ > 6, irregular sampling, missingness, or time-varying action spaces would provide stronger evidence.\n\n[1] Wu, Shenghao, et al. \"Counterfactual generative models for time-varying treatments.\" Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2024.\n\n[2] Wang, Haotian, et al. \"Effective and Efficient Time-Varying Counterfactual Prediction with State-Space Models.\" The Thirteenth International Conference on Learning Representations. 2025.\n\n[3] Xiong, Hong, et al. \"G-transformer: Counterfactual outcome prediction under dynamic and time-varying treatment regimes.\" Proceedings of machine learning research 252 (2024): https-proceedings.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "TOf5TwZVoP", "reviewer": "Reviewer_K5dA", "summary": "The paper proposes a novel, regression-based iterative approach to integrate G-computation into neural networks to address time-varying confounding.", "questions": "- The method adjusts time-varying confounders. How does the model address unobserved confounders?\n- Please see weaknesses.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- The paper proposes a method for treatment effect estimation over time, adjusting time-varying confounders.\n- The paper provides a theoretical foundation for the model.\n- An implementation code is available for review.", "weaknesses": "- The core idea is more likely to be an engineering adaptation of the G-computation. The manuscript does not convincingly differentiate its contribution and demonstrate conceptual advances from that method. \n- The motivation behind the study problem (treatment effect estimation over time) needs to be further clarified, particularly in relation to its real-world applicability. It is not evident whether the problem is testable, whether the authors have empirically validated it in real applications, or whether the underlying assumptions commonly hold in practical settings.\n- Experiments are conducted on synthetic datasets.  Even the semi-synthetic MIMIC-III uses simulated treatments and outcomes, with no evidence of applicability to real observational data. The study does not evaluate whether estimating CATE over time provides practical benefits or is actually necessary or useful in real-world contexts. The study shows performance under a controlled scenario rather than demonstrating practical utility.\n- The baselines are outdated. The paper excludes recent baselines for CATE over time, e.g., G-Transformer [1].\n\n[1] Hess, Konstantin, Dennis Frauen, Valentyn Melnychuk, and Stefan Feuerriegel. \"G-Transformer for Conditional Average Potential Outcome Estimation over Time.\" CoRR (2024).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "xKTgN1AUOh", "reviewer": "Reviewer_drGZ", "summary": "The paper introduces IGC-Net (Iterative G-computation Network), a neural framework for estimating conditional average potential outcomes (CAPOs) over time from observational data. The method addresses the challenge of time-varying confounding by leveraging iterative regression-based G-computation, avoiding limitations of existing methods like inverse propensity weighting. The main contribution of the paper is around avoiding high-dimensional probability distribution estimation that were used in SOTA neural network based G-computation methods. From the presented results, IGC-Net demonstrates superior performance in experiments across synthetic, semi-synthetic, and real-world data compared to baseline methods.", "questions": "Some of the key questions for the authors are as follows:\n- How does the method scale with larger prediction windows (τ) while maintaining performance? Have the authors considered trade-offs in performance with respect to traditional G-computational methods as the prediction window changes? \n- Have the authors investigated the effect of availability of large scale datasets for G-computational methods? For example, is there an inflection point such that availability of data would allow the model to learn the join distribution instead of the first moments", "limitations": "", "rating": 2, "confidence": 5, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "Some of the key strengths of the paper are as follows:\n- While G-computation has already been adapted to deep learning models in literature, the authors aim to circumvent the problem of full distribution estimation, by proposing an iterative regression-based approach. Using this idea of iterated expectations the authors are able to avoid costly monte carlo sampling and problems of high-dimensional overfitting that arises in presented literature\n- Commendably, the authors provide a comprehensive evaluation across synthetic, semi-synthetic, and real-world data, showing consistent outperformance of baseline methods.\n- Finally, the authors have provided a detailed architecture and hyperparameter tuning, ensuring methodological rigor and reproducibility. The presentation is easy to follow and covers the most important aspects of the paper well", "weaknesses": "While the paper has made a commendable efforts, there are several key issues with the paper\n- First, the authors haven't considered some of the latest literature on this topic. For example, G-transformer [1] was already proposed by the authors of G-net as a signficant improvement by adapting the backbone from RNN to a transformer model. A similar effort has also been reported in [2]. Another paper that aims to capture the uncertainty in G-computation has been proposed in [3]\n- Second, while the authors have proposed a neat computational approach to estimating the dynamic treatment effect, it is not evident whether the estimation process is able to capture the predictive uncertainty as well as a full scale MCMC methods\n\n\n[1]: Xiong H, Wu F, Deng L, Su M, Shahn Z, Lehman LH. G-Transformer: Counterfactual Outcome Prediction under Dynamic and Time-varying Treatment Regimes. Proc Mach Learn Res. 2024 Aug;252:https://proceedings.mlr.press/v252/xiong24a.html. PMID: 40433313; PMCID: PMC12113242.  \n[2]: Hess, Konstantin, et al. \"G-transformer for conditional average potential outcome estimation over time.\" arXiv preprint arXiv:2405.21012 (2024)  \n[3]: Deng L, Xiong H, Wu F, Kapoor S, Ghosh S, Shahn Z, Lehman LH. Uncertainty Quantification for Conditional Treatment Effect Estimation under Dynamic Treatment Regimes. Proc Mach Learn Res. 2024 Dec;259:248-266. PMID: 40443560; PMCID: PMC12121963.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ubqa6ch0V3", "reviewer": "Reviewer_Kwm7", "summary": "The authors propose a new methods for estimating potential outcomes over time for treatment sequences. The authors argue that existing methods do not properly adjust for time-varying confounding and point out that existing methods that do control for this type of confounding have some limitations. To this end, they propose a new neural network method that leverages G-computation. The authors show both theoretically and empirically that their method effectively controls for time-varying confounding.", "questions": "In addition to the question in the Weaknesses section, I have some other questions:\n\n- In my understanding, $g^{0}_\\phi$ is the only component used at inference. However, I fail to see how it can make predictions for an arbitrary treatment sequence. From Figure 1, it appears that only $a_t$ is used as input. Is this correct? If so, could you explain the intuition as to why it should not take the whole treatment sequence as input?\n\n- In Figure 3, is the biased transformer the same as Causal Tranformer (CT) used in the previous experiments? \n\n- Is it correct that for each level of confounding $\\gamma$, the treatment sequence used for evaluation is always the same for all samples? If so, could you comment on whether sampling multiple different treatment sequences and calculating your error metric over these different sequences as well would be a better or worse way to evaluate the different methods?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- Good theoretical background and motivation as to why a new method is needed. \n\n- The authors make clear and significant contributions.\n\n- Extensive and strong experimental results that show that IGC-Net achieves state-of-the-art performance for the datasets used.", "weaknesses": "At some points, the notation is confusing to me, making it hard to understand all the different parts of the paper. Below, I give some examples.\n\n- $g$ can have two different meanings if I understand it correctly. $g^a_{t+\\delta}$ is used in the theory for iterative G-computation, while  $g^\\delta_{\\phi}$ is a block of the neural network architecture that uses different sub- and superscripts. It would be helpful to the reader if the notation were clarified in some way.\n\n- In Figure 1, it is not obvious to me how I should interpret $a$ and $A$ during training and inference. Is $A_t$ the treatment that is actually observed at time $t$, and $a_t$ the treatment for which you want to estimate the CAPO? Does this mean that during training, these are the same? \n\n- I find the notation $a= a_{t:t+\\tau-1}$ confusing, is this standard in the literature? If not, I would suggest a different notation that makes it clearer that $a$ is the whole treatment sequence. \n\nIf I understand correctly, you always need to decide on the forecasting horizon $\\tau$ beforehand. Does this mean that if you wanted to know the effect of a treatment sequence that is shorter than your horizon (e.g., $\\tau-2$}), you would have to train a whole new model? If so, how does this compare to the baselines? \n\nHow do the contributions of IGC-Net compare to [1]? I think the learners introduced in that paper should be discussed in the related work section. \n\n\n[1] Dennis Frauen, Konstantin Hess, and Stefan Feuerriegel. Model-agnostic meta-learners for estimating heterogeneous treatment effects over time. In International Conference on Representation Learning, 2025.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "3ahOXmurJm", "reviewer": "Reviewer_Wupz", "summary": "This paper proposes IGC-Net, a neural network approach for estimating conditional average potential outcomes (CAPO) over time in the presence of time-varying confounding. The key contribution is a fully regression-based iterative G-computation method that avoids the instabilities associated with inverse probability weighting when propensity scores are close to zero. The methodology uses a clever forward-generation approach with neural networks (LSTM or transformer) to approximate sequential conditional expectations through pseudo-outcomes. The paper includes both semi-synthetic experiments based on MIMIC-III data and real-world validation, demonstrating improved performance over existing methods, particularly under strong confounding.", "questions": "I have listed structured questions (with help of LLM) in the above weakness part. I am going to say here my honest thoughts when reading the paper as it presents, and hopefully this can help you understand how a new reader perceives your paper. These raw feelings are genuine and I hope they provide a more human-to-human communication and contexts for the structured question above.\n\n\n\n# Review of Paper 7297: IGC-Net for Conditional Average Potential Outcome Estimation\n\n## Initial Impressions on abstracts\n\nThis is a paper on IGC-Net for conditional average potential outcome estimation over time. The main problem addresses potential outcomes over time when confounding can be time-varying. The paper proposes a neural network for proper adjustment of time-varying confounding. I agree with the claim that not dividing by the propensity score creates limitations and instability when the propensity score is often close to 0. The estimation focuses on conditional average potential outcomes, which is fine.\n\nThe paper claims to be the first to perform fully regression-based iterative G-computation for CAPO in a time-variant setting. I think this section can be improved—I don't understand why performing the full regression iterative G-computation method is significant. The evaluation is based on experiments, and while we have experiment-based evaluation, I need to look at the simulation setting more carefully. Also, for ICLR conferences, it would be good to have real-world data. Since this is treatment over time, I imagine MIMIC-III data would be a good fit.\n\n## Table 1 Analysis\n\nI'm not following the literature too closely on neural network-based estimation, but Table 1 is actually very good at showcasing the problem. One thing I'm curious about: why do CT and TE-CDE, which are more recent, lack proper adjustments, whereas RMSN and G-Net in Table 1 are further away in the past but have proper adjustments? This is a very interesting observation. I have not read the literature review of those papers (CT, TE-CDE), so I don't know the full context. The CT paper and the TE-CDE paper are from 2022, the RMSN paper is from 2018, and the G-Net paper is from 2021.\n\n## Introduction\n\nI have general knowledge about causal inference. For the last paragraph, it would be good if you could explain a little bit about what G-computation is so that I don't have to Google it again. I just happen to be more familiar with the terminology from Don Rubin rather than James Robins.\n\nThe introduction is really good. It paints a clear picture of the field and its limitations—a very concrete problem it's trying to address. One thought: there is actually good reason for there not being many developments related to neural networks for causal inference. First, on clean tabular data, tree-based models have higher popularity. Second is interpretability. If you're using a clinician observational study dataset from EHR, even logistic regression is better understood—it's explainable and more transparent. Even when logistic regression performs worse (say, within 10% compared to neural networks), a clinician would tend to use logistic regression. It's just the conservative nature of humans—nothing we can do about that. I think it's still worthwhile to pursue this type of research using neural networks because accuracy is important. I'm just curious whether the authors have any discussion on this later. (Hey I came back from future, and the authors don’t have discussion on interpretability)\n\n## Related Work\n\nIn the related work section, line 83 mentions a group of methods is not working, and I am convinced based on the narrative. I then flipped to the numerical example section and indeed saw that when the confounding strength is higher, the mentioned approach suffers higher bias. This is good validation. I also realized it's using MIMIC-III synthetic data, which answers my question from when I was reading the abstract. You should mention that in your abstract.\n\nThe related work is excellent—really well written. It tells me what's the problem with inverse probability weighting IPW and defers to a later proposition. But it's a known problem, so I would completely trust that.\n\n## Setup and Methodology\n\nIn the setup, only binary treatment is considered. As I recall, MIMIC-III probably doesn't have binary treatment data for emergency room interventions, but it's okay for now. I'm curious if there's a discussion later on treatment that is more than just binary.\n\nThe setup and estimation tasks are all excellent. Line 126 on identifiability is very good—it's standard and very thoughtful to include those assumptions. Line 137 is correct about future potential confounding, and the explanation placed here is really good.\n\nI really like Equation 2. Causal inference is all about mathematical framing, and Equation 2 makes the problem very clear. It would be good to explain how Equation 3 differs from Equation 2. After staring at it, I see it's basically adjusted by the probability of the “A” distribution. I understand that Supplement C has this formula. This looks intuitively right, so I wouldn't check it, but it would be helpful—I'm just being lazy—if you could still explain the intuition here.\n\nThis is a very good presentation. When I look at Equation 3, I would think a naive or straightforward approach is just through integration, and then it's pointed out that the integration has this distributional estimation problem. Very intriguing.\n\n## Pseudo Outcomes and Methodology\n\nIn line 173, you use \"low variance pseudo outcome.\" I'll need to read more, but one thing I was thinking when I read this was: in general, it is not great to look at the future Y variable when you're developing the causal method. I'm curious to see how you make that happen. In what sense is the outcome \"pseudo\"?\n\nThe iterative regression in line 180 is intuitively right. In causal inference, we use sequential, carefully constructed regression as an estimation vehicle. That is a very standard technique. Very nice opening to Section 4 at line 184.\n\nEquations 6 and 7 are smart. They're basically regression, looking at the conditional expectation, gradually projected down from the remote future into the present. Because of the conditional expectation property, of course, it's unbiased. The sequential recursive formula is basically a sequential projection.\n\nLine 222 is where I first became not crystal clear about how it is being done. How is your pseudo-data generated? Shouldn't it just be a natural projection down? Why does that generate predictions? So interesting. Rather than the true mathematical way of keep projecting from the future to present, the learning actually reverses that. Like data assimilation, you generate the future step, keep generating. And then after generating the tau steps, you produce the loss, matching this generated tau-step-ahead with the actual Y. And therefore, that's why you use neural networks as an approximator. Otherwise, before line 225, you don't really need neural networks yet. The math is tight for backward recursion, but computationally prohibitive. Line 225 introduces a neural network forward-generator to that true conditional expectation.\n\n## Training Questions\n\nThat brings me to a question about this training. If you are generating t+tau steps ahead and then doing the regression, what if I generate just delta steps ahead (delta smaller than tau), and then do the regression of y_{t+delta} directly, not using the pseudo outcome but using the actual outcome to match the generated pseudo outcome? Is it because it actually has the realization, so it fails to be a proper projection from step y_{t+tau}? Is that why you didn't do that?\n\nYou are using LSTM or transformer. I would say a transformer or using pre-trained generators from existing generative AI pre-trained networks, it feels like if you have a more powerful generator, it would help. In your case, there is actually a very good link between generative AI and conditional expectation, which is very interesting. But I agree that this neural backbone can be swapped. I like that you tested at least two: transformer and LSTM.\n\n## Results Section\n\nI'm going to skip ahead to look at the results to see if transformer and LSTM actually give you a substantial difference. My impression when it comes to causal inference and this type of analysis is that transformers are actually not that helpful on top of LSTM. They should provide similar levels of results.\n\nYour Figures 6 and 7 in supplement are too busy to read. Oh, the transformer is indeed giving you slightly better results than the LSTM. Is there a particular reason? Is it because transformers are just better at generative AI and LSTM is more for prediction? What does that ablation study tell you?\n\nFigure 2 gives a very good schematic of how the thing is cascading. It's pretty intuitive. The training couples the generation step and the learning step. It generates and contrasts what's generated with the actual observation tau periods later, constructs a loss, and does this iteratively.\n\n## Identifiability Concerns\n\nAnother question just popped into my mind: would there be an identifiability issue? That is, two trained networks will give you the same g_{t+tau} because they are labeled on y_tau. However, during the process from t to t+tau—you know, the t+delta part—the two networks could give you very different results. I know that earlier you have an identifiability section, but that is in line 126, more from a theoretical perspective of SUTVA-like assumptions. How will actual neural networks behave? We know that neural networks could achieve the same accuracy with two drastically different networks.\n\nI'll skip ahead to Algorithm 1. I think I have a fairly good intuition now. Indeed, the Y is used as G_{t+tau}. All the rest are pseudo-Y, pseudo observations. So how do you make sure that your pseudo observation is actually identifiable?\n\nOtherwise, I think the procedure is tight. Now skipping ahead to the experiment part, Section 5. By Section 4, I'm very convinced about what's going on, so I will accept that.\n\n## Experimental Results\n\nSkipping ahead to Section 5, which I previously briefly reviewed. The results are indeed good, and I have good intuition for why they are good. You have MIMIC-III data for semi-synthetic experiments, which is very good.\n\nIn Figure 3, my question is: why does Figure 3 show the LSTM is slightly worse than the transformer? It would be good to discuss why the transformer is better than the LSTM as a backbone.\n\nOh, you do have real-world data in Supplement E—the real-world MIMIC-III data. That's fairly strong. Let me look at the figures. You should add a sentence saying that the real-world data confirms the findings. Using real-world MIMIC-III data confirms the same findings.\n\n## Overall Assessment\n\nRight now, I think it's a very solid paper. The only question I have is on identifiability. If I initialize your IGC-Net with another random initialization and train another instance of your IGC-Net, will they give the same pseudo observations g_{t+tau}? Why or why not? If not, then the interpretation of conditional expectation becomes a little bit questionable. If it is the case, I'm kind of not seeing how the structure is preserved and why it's exactly identifiable from an intuitive perspective.\n\n**Overall: Excellent paper, well-written, very enjoyable to read.**", "limitations": "", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "## Strengths\n\n1. **Excellent presentation and writing**: The introduction and related work sections are very well written, providing clear context and concrete problem motivation. The mathematical framing, particularly Equation 2, makes the problem formulation clear and accessible.\n\n2. **Strong methodological foundation**: The sequential recursive formulation (Equations 6 and 7) is smart and theoretically sound, using conditional expectation projections from the remote future into the present. The approach is intuitive and properly grounded in causal inference principles.\n\n3. **Effective problem motivation**: Table 1 does an excellent job showcasing the limitations of existing methods and positioning the contribution. The paper clearly articulates why inverse probability weighting methods fail under strong confounding.\n\n4. **Comprehensive evaluation**: The paper includes both semi-synthetic and real-world MIMIC-III data (Supplement E), providing strong empirical validation. The results consistently demonstrate that the method works well, particularly when confounding strength is higher.\n\n5. **Good ablation studies**: Testing both transformer and LSTM backbones provides useful insights into model architecture choices.", "weaknesses": "1. **Identifiability concern**: The main weakness is the lack of discussion about empirical identifiability of pseudo-observations across different random initializations (not the theoretical identifiability or SUTVA). If two IGC-Net instances with different initializations give the same g_{t+tau} but very different intermediate pseudo-observations at t+delta (delta < tau), the interpretation of conditional expectations becomes questionable. The paper addresses theoretical identifiability (SUTVA-like assumptions) but not the practical identifiability of neural network approximations.\n\n2. **Limited treatment flexibility**: The setup only considers binary treatments, which may not align well with MIMIC-III data where emergency room interventions are typically not binary. The paper lacks discussion on extending to multi-valued or continuous treatments.\n\n3. **Missing interpretability discussion**: Given the conservative nature of clinical applications, there should be discussion about interpretability trade-offs. Even when neural networks provide better accuracy, clinicians often prefer logistic regression for its transparency and explainability.\n\n4. **Presentation issues**:\n   - Figures 6 and 7 in supplement are too busy and difficult to read\n   - Abstract should mention the use of synthetic MIMIC-III data\n   - Should add a sentence explicitly stating that real-world data confirms the findings (currently only in supplement)\n\n5. **Ablation analysis implication**: While the paper shows transformer performs slightly better than LSTM, there's insufficient discussion of why this is the case and what this tells us about the method. Is it because transformers are better at generative tasks while LSTMs are better at prediction?\n\n6. **Unexplored training alternatives**: The paper doesn't discuss why intermediate-step training (using y_{t+delta} for delta < tau with actual outcomes rather than pseudo-outcomes) wasn't considered or wouldn't work. \n\n## Minor Issues\n\n- The observation about CT and TE-CDE (2022) lacking proper adjustments while older methods like RMSN (2018) and G-Net (2021) have them is interesting but not discussed\n- No discussion on whether more powerful pre-trained generative models could improve results", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)