Modeling Interference for Treatment Effect Estimation in Network Dynamic Environment
Authors: Qiang Huang
Jin Tian
Venue: ICLR 2026 Poster (2026)
Keywords: Dynamic Network
Interference
Causality
Primary area: causal reasoning

Abstract: In recent years, estimating causal effects of treatment on the outcome variable in network environments has attracted growing interest. The intrinsic interconnectedness of network and the attendant violation of the SUTVA assumption have prompted a wave of treatment effect estimation methods tailored to network settings, yielding considerable progress such as capturing hidden confounders by leveraging auxiliary network structure. Nevertheless, despite these advances, the existing methods: (i) mainly focus on the static network, overlooking the dynamic nature of many real-world networks and confounders that evolve over time; (ii) assume the absence of dynamic network interference where one unit’s treatment can affect its neighbors’ outcomes. To address these two limitations, we first define a new estimand of treatment effects accounting for interference in a dynamic network environment, i.e., CATE-ID, and establish its identifiability under such an environment. Then we accordingly propose DSPNET, a framework tailored specifically for treatment effect estimation in dynamic network environment, that leverages historical information and network structure to capture time-varying confounders and model dynamic interference. Extensive experiments demonstrate the superiority of our proposed method compared to state-of-the-art approaches.

Published as a conference paper at ICLR 2026
MODELING INTERFERENCE FOR TREATMENT EFFECT ESTIMATION IN NETWORK DYNAMIC ENVIRONMENT
Qiang Huang,
Jin Tian,
Department of Machine Learning Mohamed bin Zayed University of Artificial Intelligence
Department of Machine Learning Mohamed bin Zayed University of Artificial Intelligence Abu Dhabi, UAE jin. t tiw.tiiaammaai... acc.ae
Abu Dhabi, UAE
qi giang. www.gg/mbruuiiac.c.oom
ABSTRACT
In recent years, estimating causal effects of treatment on the outcome variable in network environments has attracted growing interest. The intrinsic intercon- nectedness of network and the attendant violation of the SUTVA assumption have prompted a wave of treatment effect estimation methods tailored to network set- tings, yielding considerable progress such capturing hidden confounders by leveraging auxiliary network structure, Nevertheless, despite these advances, the existing methods: (i) mainly focus on the static network, overlooking the dynamic nature of many real-world networks and confounders that evolve over time; (ii) assume the absence of dynamic network interference where one unit's treatment can affect its neighbors' outcomes. To address these two limitations, we first define a new estimand of treatment effects accounting for interference in dynamic network environment, i.e., CATE-ID, and establish its identifiability under such an environment. Then we accordingly propose DSPNET, a framework tailored specifically for treatment effect estimation in dynamic network environment, that leverages historical information and network structure to capture time-varying confounders and model dynamic interference. Extensive experiments demonstrate the superiority of our proposed method compared to state-of-the-arr approaches.
INTRODUCTION
Treatment effect estimation (Winship & Morgan 1999) plays a fundamental role in understanding the relationship between treatment (a.k.a intervention) and outcome, serving as a cornerstone for decision-making across wide range of domains, such as healthcare (Hernán & Robins 2006), social networks (Barabas Jerit 2009). and economies (Lechner et al., (201)). The gold standard for estimating treatment effects is randomized controlled trials (RCTs) (Stanley 2007 Stolberg et al., 2004), which involve randomly assigning units different treatment arms (e.g., administering or withholding medication) and comparing their observed outcomes (e.g.. recovery rates). This design enables reliable estimation of treatment effects by eliminating confounding through randomization. However, RCTs often costly and time-consuming (Bondemark & Ruf 2015 Zabor et al. 2020). and may raise ethical concerns in certain contexts (Edwards et al.) 1999).
Given the limitations of RCTs, researchers have increasingly turned to rich and readily available observational data to estimate the conditional average treatment effect (CATE) Many observational
studies (Ganicoolo al. 2020 Hernán & Robins 2006) Rubin 2007] WWinship & Morgan 1999)
rely on the Stable Unit Treatment Value Assumption (SUTVA) (Green & Gerber] (2010), which assumes that units are independent and subject to interference from one another. Furthermore, one of the critical problems in estimating treatment effects is to eliminate confounding bias caused by confounders (Greenland et al. 1999). the variables that causally affect both treatment and outcome. To facilitate unbiased estimation, these studies also commonly adopt the assumption of ignorability (Greenland & Mansournia, 2015), which assumes the absence of unobserved confounders.
While much of the literature equates CATE with Individual Treatment Effect (ITE), in this work we strictly CATE, as ITE is not identical to CATE theoretically (Vegetabile 202T).

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However, the assumptions of no unmeasured confounding and interference often fail in practice (Guo et al.; 2020at| Yao et al.] (021). In a community- infectious disease study, socioeconomic status (SES) may affect both treatment (c.g.. compliance with mobility restriction) and outcome (e.g.. infection risk). For instance, lower-SES individuals may have limited access to safe transportation and are more likely to live in high-density housing, where close contact increases infection risk. However, SES, acting as a confounder, is often difficult to observe or measure directly. To address this, recent work (Chu et al., 202T Jiang & Sun 2022; Sui et al.; Veitch et all 2019) leverages network structures to infer hidden confounders from relational context, such as inferring SES from the occupations or attributes of social connections. Moreover, individuals are embedded in networks where one unit's compliance with mobility restriction can affect the infection risk of its neighbors.
phenomenon known as interference or the spillover effect (Benjamin-Chung et 2018 0018 Ma & Tresp
202T). Several studies (Huang et al. 2023; Rakesh et al. explicitly model interference for treatment effect estimation.
et al. 2024 have been made to
However, most of these methods are designed for static networks, assuming that the network structure and covariates remain unchanged over time. In practice, many network environments are inherently dynamic, with both the network structure and the attributes of individual nodes evolving over time. For example, in the aforementioned infectious disease study, the community structure may shift as residents relocate, while individual-leve covariates such as health status may also vary over time. These dynamic characteristics pose substantial challenges for treatment effect estimation in networked settings. First, the interplay between complex temporal evolution and network interference makes the identifiability of treatment effects, i.c., determining whether treatment effects can be recovered from observational data, a highly non-trivial problem. Second, as both network structures and node covariates evolve, the distribution of confounders becomes lime-dependent; modeling the evolution of confounders and controlling for varying confounding bias require further exploration. Third, the evolution of network and attributes alters the pattern and magnitude of interference between nodes, necessitating dynamic modeling of spillover effects based on the changing network structure.
To address the aforementioned challenges, we first define a new target estimand, Conditional Average Treatment Effects with Interference under Dynamic networks (CATE-ID), for treatment effect estimation in dynamic network environments with interference, and formally prove its identifiability under a set of assumptions. Building on this theoretical foundation, we propose DSPNET, a novel framework designed to estimate the target causal estimand by explicitly modeling both hidden confounders and interference in dynamic networks. Specifically, DSPNET integrates GCNs and RNNs aggregate neighborhood and historical information to infer dynamic hidden confounders. Then it learns a dedicated interference representation to capture spillover effects by encoding the treatments and characteristics of unit's neighborhood. Finally, DSPNET employs an adversarial learning strategy, encouraging balanced confounder representations to mitigate confounding bias when estimating treatment effects from an observational dynamic network.
2 PROBLEM FORMULATION
In this work, we use bold letters to denote vectors or matrices, and unbold lowercase letters for scalars, Specifically, let unbold capital letters denote random variables (c.g., X²), lowercase letters (e.g., x)) for their realizations. Let A' (0, N denote the adjacency matrix that encodes the network structure among N units at time step f, where A = =16 (A = 0) indicates the presence (absence) of an edge between unit i and j. X = {zf, ...., x'y represents the covariates of the N units at time step / with a E R.m denoting the covariates for unit i, and < denotes the covariates before time t for all nodes. Let D = [di:-... ..... ddy) denote the set of treatment assignments for the N units where dj = indicates that unit is treated and d: = otherwise, and Y = .... y'x } denotes the set of observed outcomes for NV units at time step Let G represent the neighboring set of at time step t and g", represent unit i's non-neighbors, and the covariates and treatments of unit i's neighbors and non-neighbors at time step t are denoted by X Dj, and X/_,, D'_.. respectively.
For the treatment effect estimation in L.LD setting, the target estimand is typically the conditional average treatment effect (CATE): (2x;) = ElY, [ - E|Y, where Y.(D;) denote unit i's potential outcome under treatment D,. However, the above estimand is not applicable in a network environment where interference exists. To account for interference, prior works (Forastiere et al.) 2021 Ma & Tresp 202T) often aggregate the treatments of neighboring units into a single scalar variable (e.g., via mean pooling) and treat it as a regular covariate. However, such one-dimensional
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summary be inadequate in nigh-dimensional environments, where it may fail capture the rich heterogeneity neighbors' influences. Therefore, we define the following generalized factor that captures the influence of neighbors' covariates and treatment assignments:
Definition 2.1. Environment Exposure. We define summary function that aggregates the treatments and covariates of unit i's neighbors at time step i, (-): (IR")110) x {0, 10 + & where & E TR is the exposure space, then the environment exposure is formulated by E F D...
To ensure well-defined potential outcomes under exposure E,, we adopt the following assumption: Assumption 2.2. Given the summary function F/. V D/ D..,> X Xy_, and 4 D2, D X X G_. if ( D/)) ( e. Di the following equality holds:
(Di, D'_.) = Y' D'. D.
(1)
where (D D's, Dj .) is the general case of unit i's potential outcome. Dú. D'. are the alternative assignments to D.., D/_. X _ respectively.
X X
This assumption implies that once the response to the environment exposure function, i.c. EY. is determined, the potential outcome of unit under treatment D is fully specified. Then we extend the notation (i(D:) by incorporating the environment exposure E and let Y: EE) denote unit i's potential outcome under treatment DJ and exposure E time step L.
Formally, we define our target estimand, the Conditional Average Treatment Effect with Interference under Dynamic networks (CATE-ID), as an extension of the standard CATE dynamic network settings with interference. Specifically, CATE-ID measures the expected difference in outcomes under alternative treatment assignments conditioning on the unit's covariates, historical information, and neighbors' covariates at time step
T = (1, F. e))lat
(V, F e H. Xg.).
where 71¹ = (X DEt A ct DSt and network structures for time step t. CATE-ID incorporates environment exposure, enabling the assessment of an intervention's s intrinsic causal effect on an individual while excluding interference. For instance, in the aforementioned study, we can capture the true effect of mobility restriction itself on infection risk. climinating the bias from the indirect effects transmitted through social contacts (c.g., unit's 's infection risk may increase due to its neighbors' non-compliance with the mobility restriction, then the effect of the intervention may be underestimated).
Dis is the historical information that encodes past covariates, treatments,
X
D'
CAUSAL IDENTIFIABILITY
D'
Building on the theoretical frameworks proposed in (Forastiere et al., 2021, Ma & Tresp (021). we introduce the assumptions adopted in our setting and formally establish the identifiability of CATE-ID de-
H
X
E
fined in Eq. (2 for dynamic network environments with interference.
Figure 1: Causal Graph.
Previous literature (Shalit et al. 2017 Schwab et al. 2018 Ma et al.
2022) typically relies on the ignorability assumption, which presumes the absence of hidden con- founders. In this work, we extend this assumption to allow for the presence of hidden confounders:
Assumption 3.1. Extended Ignorability Assumption. There exists function 4= (-):: 2 (x s. H") that encodes the information of unit i's covariates, historical factor, and its neigh- bors' covariates into full confounders Z such that, given Zí, the treatment D and environment exposure E are independent of the potential outcomes, i.e., (1, E,), (1 E.) 1 E
Assumption 3.1 implies that all confounders have been captured by Z Noting that this assumption is conceptually aligned with the standard ignorability assumption which assumes that all confounders
FFoloowig prior works in dynamic causality (Lim 2018 Bica et al. 2020 Ma et al. 2021) past outcomes Y are often excluded, as their influence is assumed to be captured by past covariates and treatments. with the goal of estimating marginal treatment effects each time step rather than modeling outcome trajectories. Nonetheless, our framework can readily incorporate < if required by specific applications.
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measured in the observed covariates, extended ignorability assumes that all confounders absorbed into the learned latent factor Zí. Furthermore, to guarantee correspondence between poten- tial outcomes and observations, generalize the standard consistency assumption (VanderWeele & Hernan 2013) to the setting with environment exposure:
Assumption 3.2. Consistency Assumption. An individual's potential outcome under particular treatment and environment exposure is exactly the outcome we would observe if the individual actually received that treatment and exposure, i.c., (D E = Y, with observed D, and E,
Based the above definitions and assumptions, the causal graph for single time step in the dynamic network setting is depicted in Figure [ where the subscript denoting unit index is omitted for generality and simplicity. Formally, we establish the following theorem on the identifiability of CATE-ID in the presence of hidden confounders and interference:
Theorem 3.3. If we can recover the distribution p(Y;) (2 Et, Df) and p(Z)) H', X.)). the estimand CATE-ID presented in Eq. (2 can be identified from the observational dynamic network.
Proof. The identified form of CATE-ID under interference is derived by:
/ [y, - e Y E e H', X
By [1, e/) (7 = H', X3. 21 H' X
Ez By [Y, e/) (, e H4, X3, Z E 10 Ht, X3.1
(3)
Ez B (1, e (/ e0) E Di He x
Ez By | E = Dj 1] Ey E =
0) | Ht, X
where equation (1) is the straightforward expectation over full confounders Z equation (2) is derived by Assumption 3.1 equation (3) can be inferred from condition independence such that
Y H', X1, X 144 E from the causal graph, and equation (4) is based Assumption 3.2
METHODOLOGY
Time Step
H
Treateret
In this section, we introduce Dynamic SPillover modeling NETwork (DSPNET), a novel framework for estimating the tar- get treatment effect estimand that explic- itly addresses interference in dynamic net- work environments. The overall workflow of DSPNET in a single time step is illus- trated in Figure 2 and its key components are detailed in the following subsections.
1
Outcome Prediction
A'
D'=0 Outcome Prediction
+++1
Figure 2: The workflow illustration of DSPNET.
4.1 REPRESENTATION LEARNING OF FULL CONFOUNDERS
As previously presented in Assumption 3.1 the full confounders Z can be inferred via the function 4, (-) by incorporating historical information, neighbor's 's covariates, and unit's own covariates. Here, we approximate the function & (-).) using multi-layer graph convolutional networks (GCNs) combined with multilayer perceptrons (MLPs) to learn the representation of the full confounders Z7:
fll A'),, H.)).
where (-) and f:(:) represent the function parameterized by multiple GCN and MLP layers. H is the encoded historical state for unit at time step f. To model the historical state H we employ a recurrent neural unit, such as Gated Recurrent Unit (GRU) (Cho et al., 2014) or a Long Short- Term Memory (LSTM) (Hochreiter & Schmidhuber) 1997), to encode full confounders, treatment assignment, and the historical state the previous step:
H ( "1,," ", Hi-)
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where RNN(-) can be instantiated as either GRU an LSTM cell, depending on the implementation choice. The initial historical state, i.e., H,, is set zero vector.
4.2 INTERFERENCE MODELING
In many networks, interference depends not only on neighbors' treatment assignments, but also on how these treatments interact with intrinsic behavioral patterns of individuals. For example, a health intervention (c.g., jog) may affect a user only if its treated neighbors actively engage in and share health-related behaviors. However, previous works (Forastiere et al. 2021 Ma & Tresp 2021 often model interference by simple aggregations (e.g., mean pooling), which oversimplify these patterns.
To more effectively model interference affected by neighbors' behavioral patterns, we propose inferring an interference representation ei for each unit as a proxy for the environment exposure variable E, incorporating both the treatments and attributes of its neighbors for capturing the heterogeneous influences. Specifically, we first project each unit's observed covariates into latent space via a function gr(-), parameterized by a stack of GCN layers, to obtain the hidden state r of each unit i. Then aggregate the hidden states of unit i's neighbors by incorporating their treatment assignments to formulate the interference representation ej for unit at time step t:
r =
d
JE
The resulting et can therefore be interpreted as a data-driven embedding of the influence with behaviors exerted by treated neighbors.
4.3 OUTCOME PREDICTION
Given the representation 2 of full confounders and the interference representation e/, our goal is to estimate the potential outcomes under alternative treatment assignments. To this end, we construct two separate MLP networks corresponding to treatment treatment d and d = 0, respectively. Formally, the potential outcome of unit i w.r.t treatment assignment df at time step t is given by:
y -0) (1)=
0 =
f(z), ei,
(7)
if 11
where the functions (.) and [-) are both parameterized by stacking multiple MLP layers, (0) and g (1) represent the predicted potential outcomes under treatment di = 0 and d' = 1, respectively. Then the predicted factual outcome is computed of (1 d;) ()) + dj (1).
Given the predicted factual outcome of and observed outcome yt for each unit and time step, we employ the Mean Square Error (MSE) loss to minimize the discrepancy between them:
T
N
Cy = T
v/)2.
(8)
4.4 BALANCING CONFOUNDER REPRESENTATIONS VIA GRADIENT REVERSAL
Estimating treatment effects requires addressing confounding bias, which arises from the differences in confounder distributions between treatment and control groups, and (Shalit et al. 2017) theoretically shows that learning representations that minimize distributional discrepancies between different groups can effectively reduce the upper bound of the estimation error. Motivated by this, we adopt an adversarial learning strategy with a Gradient Reversal Layer (GRL) (Ganin et al. 2016 Ma et al.. 2021), which encourages confounder representations to be balanced across treatment groups, thus mitigating confounding bias while preserving predictive information.
First, we model treatment assignment with prediction function fa(:), parameterized by an MIP, which takes the full confounder representation z as input and outputs the probability of receiving treatment, i.c., p p(D;
1|x{)= fa(z)), and trained by the cross-entropy loss:
T
N
La = T
Σ
[d = 1|2/)) + (1 dd)oog(111111 p(D) = 1|21))]
(9)
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Then, the Gradient Reversal Layer operates as follows: let L denote the final loss function of the proposed DSPNET framework, which can be formulated as follows:
L = Ly + aLa + w||@||;;
(10)
where è denotes the set of learnable model parameters, and w are hyperparameters that control the contributions of the treatment prediction loss and the regularization term, respectively. Let + represent the parameters associated with the full confounder representation learning module. Then, during backpropagation with GRL,, the update for O modified as follows:
QLy 80, 20
JaLd 01101
+ - - - n
(11)
002
where 7) is the learning rate. That is, when updating the parameters of e., we multiply the gradient from treatment prediction module by negative constant -3 during backpropagation, and all other parameters @ O' are updated by standard gradient descent. Intuitively, the GRL discourages the confounder representation from carrying predictive information to treatment, thereby aligning the representation distributions across treatment groups while preserving outcome-relevant information.
4.5
TIME AND SPACE COMPLEXITY ANALYSIS
At each time step t. DSPNET consists of four main components: (i) an Lg-layer GCN backbone. (ti) the interference module, (iii) a GRU-based temporal encoder, and (iv) an Lm -m-layer MLP for potential-outcome and treatment prediction.
For graph with N nodes, M, edges, and hidden dimension d,, the per-layer GCN cost is O(Nd M,da), ), leading (Nd, + M, for the full backbone. The interference module performs sparse, edge-win wise aggregation with cost O(M,d,)). The GRU encoder updates node-level hidden states with matrix multiplications of size d,, x dh, giving ((Nd)) per step. The MLP heads require N[L,Nd across all nodes. Aggregating these components over a sequence of length T and assuming Mr- = M, the overall per-epoch time complexity is as follows:
( + Md, + (T.g + + Nd,)) = (T, Md, + (Ig + N.m))
which linear in the number of edges M and nodes N. The space complexity of DSPNET is dominated by storing the sparse adjacency structure and node embeddings at each time step, i.c. O(M, + Nd,), which is also linear in M and N.
5 EXPERIMENTS
5.1 DATASETS
Flickr (Tag & Liu 2011 is popular image and video-based social network, where users connect and share multimedia content. In this dataset, each node corresponds to a user, and edges represent friendships between users. The features of node are constructed using bag-of-words representations of user's interest tag.
Flickr:
BlogCatalog (Zafarani & Liu 2009) is social networking platform where bloggers share their blogs and interact with each other. In the BlogCatalog dataset, each node represents blogger, and edges indicate social relationships between bloggers. The features are also constructed using bag-of- -orddddsssd representations of the bloggers' posts.
BlogCatalog:
To construct dynamic network, we introduce temporal variations by randomly adding or removing p% of edges in the underlying network structure and apply Gaussian noise perturbations to the same proportion of covariates in each time step (25 time steps in total) to simulate real-world fluctuations. Using the generated dynamic network, we simulate confounders, treatment assignments, and interference-nnt aware potential outcomes via an auto-regressive process at each time step, the detailed data generation procedure can be found in Appendix
5.2 BASELINES
Here we briefly introduce the baseline methods for estimating treatment effects in our evaluation, which can be categorized into two categories:

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Table 1: CATE-ID performance comparison by varying degrees of network dynamies. Bold: the best results. Underline: the 2nd best results. Lower is better. indicates statistically significant improvement over the strongest baseline (t-test, p-value < 0.05).
p% 0.1%
p% 0.5%
p%
1.0%
Datasets
Methods
VEPEμE
EATE
VEPEHE
6ATE
VEPERE
CATE
DESCN
17.982 23.872
16.996 43.82
29.551
=9.891
28.273
29,05
30.396 #6.052
29.058 25,873
DFITE
17.404 22,93
3.083 #0:466
20.527
=3.544
3,306 20.41
22,459
26,097
3.545 20.722
DERCER
21.704 23.786
17.246 43.825
31.406
=5.804
23.916
=5.023
31.847
26.221
25.925 =5.90
CFR
24.218 $3.929
2.754 20.599
26.716
#3,995
2.841
a0.444
29.372
3.185 40632
Flickr
NetEST
6,822 +1.107
1.405 +0.219
10.708
2.575
11,000 +1.806
2.418 +0421
Deconfounder
8,338 +1.230
4.738 =0,844
11.724 =3,344
6.854 #2.175
12,249 #1.912
7.13221.399
SPNET
8,693 #1.110
1.204 #0.216
11.320 =2.789
1.397 20.340
11.797 #1.679
1.542 #01.38
DNDC
2.589 #0,999
1.618 #0.781
3.062 +0,379
1.915
3.291 +0.502
2. 194 40.578
DSPNET
1.497 s0.145
0.890 s0.0mn
2.062 =0.408
1.144 10.128
2.189 =0.205
1.351 =0.209
DESCN
23,430 x3.422
22.348
26.393 #4.581
25.198
+4.429
s4.222 28.458
27.229 e4.654
DFITE
11.841 +3.243
3.446
=0/427
14.028 =4.200
3.618
20.766
14:483
23.05
3.559 a51599
DERCFR
35.321 +8.804
24.921 +3.208
39.149 +5.008
29.219 +4.523
39.286 +7.888
30.360 +8.270
CFR
11,547
1.295 =0.249
13.935 =4.166
1.171
14.546 #3.352
1,279 +0.246
BlogCatalog
NetEST
8,539 s1.074
1.586 =0,218
9.871 #1.161
1.847 20.214
9.533 a1.255
1.835 401225
Deconfounder
13.067 $1,963
8.884 17.
14.870 #2.515
9.709 a1.711
15.037 #2.336
9,910 a14491
SPNET
9.569 +1.240
2.298
w0.859
10.681 +1.771
2.597 +0.705
10.288 +1.756
2.149 #0.522
DNDC
2.475 40.462
1.454 20,400
2.419 40.332
1,319 +0.329
3.367 #0.75?
1.723 40:300
DSPNET
1.464 20.119
0.845 20.105
1.506 =0.237
0.913 20.204
2.227 #0.376
1.183 20.290
Non-Networked: (1) CFR (Shalit et al. 2017 a deep learning-basse approach which mitigates distributional imbalance between treatment and control groups by incorporating the Wasserstein distance regularizer; (2) DESCN (Zhong et al., 2022) is a model for estimating treatment effects by capturing integrated information treatment propensity. response, and hidden treatment effeets through a cross-network in a multi-task learning framework; (3) DFITE (Wang et al.) leverages diffusion models capture the latent space of these unobserved confounders by modeling the reverse diffusion process as a Markov chain to estimate treatment effects; (4) DERCFR (Wu et al. (0022) is framework which identifies and separates confounders from non-confounders for reducing bias of treatment effect estimation.
Networked: (5) NetEST (Jiang & Sun 2022) formulates the treatment effect estimation problem as multi-task learning task, employing representation learning techniques to align the distributions of treated and control groups for networked environment; (6) Deconfounder (Guo et al.. (020cc) utilize graph neural network to capture the hidden confounders by leveraging the network structure for treatment effect estimation; (7) DNDC (Ma et al.) (02T) is designed to leverage current and historical networked observational data to learn representations of hidden confounders over time for
the treatment effect estimation in dynamic network environment; (8) SPNet (Huang et al. (022)) aims
to model the interference by developing a attention mechanism for treatment effect estimation in static networked environment.
5.3 EXPERIMENTAL SETUP
For each dataset, we run each experiment ten times and report the average performance. In each run, the dataset is randomly split into training-609s validation-20%% and test-20% set. As described in data generation process in Appendix A we set the degree of dynamic p% = 0.1%, and the strength of interference C 50 unless otherwise specified. We adopt the grid search strategy based on the validation performance to identify the optimal hyperparameter configuration. For hyperparameters of DSPNET, the learning rate r) is set to 4 x 10 a and range in ( (1,2,3,4), and w ranges in {10-1, 10-2 10-3 10-4). We use Adam (Kingma & Ba 2014) the model optimizer and GRU cell to model the historical state. For baselines designed for static data, we train a separate model at each time step and report the averaged performance across all steps. More detailed experiments such as using LSTM cell, different strength of historical influence, different influence of network structure and different balancing strategies can be found in Appendix C

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30.2
25-0
SPNET
20.0
17.5
12.0
10.0
103
10.0
25
40
Streagth
Strogia
Streegth
strewgia
VEPEHE on Flickr
(b) EATE Flickr
(c) VEPEHE on BC
(d) GATE BC
Figure 3: Performance under varying strengths of network interference, "BC" denotes BlogCatalog.
5.4 DIRECT EVALUATION CATE-ID ESTIMATION
In this section, we directly evaluate the performance of CATE-ID estimation using the following two commonly used metrics: rooted precision in estimation of heterogeneous effect EEEEEE and mean absolute eπrоr on average treatment effect СATE, where VEPEHE and ATT aim to measure the accuracy of unit-level and population-level treatment effect estimation across T time steps:
T
N Σ im
T
N
N
VEPEHE T
+), T
CATE T
T
7
(12)
N
N
where of w1(1) (0) and म
(1) (0) are the ground-truth and predicted CATE-ID, respectively. We take the average of the two metrics over T time steps for the final results.
5.4.1 COMPARISON UNDER VARYING DEGREES OF NETWORK DYNAMICS
First, we evaluate the performance of different models in estimating treatment effects under varying degrees of network dynamics. Specifically, we set p% {0.1%, 0.5%, 1.0% to control the level of structural and feature perturbations, and compare the CATE-ID estimation performance of all models across these settings. The experimental results reported in Table [
As shown in the results, the proposed DSPNET consistently achieves the best performance across all dynamic settings. Notably, DSPNET maintains stable performance the proportion of dynamic edge and feature perturbations increases, demonstrating its robustness to network dynamics. The poor performance of non-network baselines (i.e., CFR, DERCER, DESCN, DFITE) highlights that ignoring network dependencies leads to biased treatment effect estimation in networked environments. Although NetEST, Deconfounder, and SPNET incorporate network structures. they assume a static network setting, resulting in performance degradation under dynamic conditions. DNDC, which tailored for dynamic networks, achieves relatively strong results but does not explicitly model interference. Consequently, its performance remains consistently inferior to DSPNET, underscoring the importance of capturing spillover effects for accurate treatment effect estimation.
5.4.2 COMPARISON UNDER VARYING STRENGTHS OF NETWORK INTERFERENCE
Then, we investigate how model performance varies under different strengths of network interference. Specifically, we keep all other parameters as default during the data generation process and control the strength of network interference using {10, 20, 30, 40, 50). ) The performance of different models under different interference strength is illustrated in Figure
The results show that the proposed DSPNET consistently outperforms all other models across all levels of network interference, and its performance remains relatively stable even under high interference strengths (c.g.. = 40 or 50), demonstrating its effectiveness in handling complex spillover effects and its suitability for real-world applications. While SPNET is designed to model spillover effects, does not account for temporal dynamics, resulting in inferior performance compared to dynamic models such DNDC and DSPNET. Moreover, C increases, the performance gap between DNDC and DSPNET becomes more pronounced, further highlighting the importance explicitly modeling network interference in treatment effect estimation.
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5.4.3 ABLATION STUDY
To investigate the contribution of each component in our proposed DSPNET model, we conduct an ablation study by evaluating the following model variants:
(i) w/o GRL: This variant removes the Gradient Reversal Layer which is responsible for balancing the confounder representation across treatment groups and mitigating the confounding bias.
(ii) w/o IM: This variant eliminates the In- terference Modeling component, thereby ex- cluding the learning interference represen- tation for outcome estimation.
Table 2: Ablation Study.
Flickr
Blogcatalog
Variants
v VEPEHE
EATR
VEPERE
EATR
Original
1.497 29.45
0.890 #0050
1,464
0.845
(ii)) w/o GRU: This variant excludes the Gated Recurrent Unit (GRU), disabling the model's ability to capture temporal depen- dencies and historical information.
we GRL
2.179 20.266
0.986 s0
1.886 20.227
1,089 s0.247
w/o IM
1.938 50,242
1.245 20.200
1.822 18
1,118 60.164
w/o GRU
10.235 a1.768
6.854 #1.014
10.652
3.547 20.912
The results are shown in Table 2 Specifically, removing the GRL component results in a moderate drop, underscoring its role in mitigating confounding bias. Excluding interference modeling leads to further degradation, highlighting the importance of capturing spillover effects in networked environments. The most substantial performance loss is observed when removing GRU component, demonstrating the critical role of capturing historical information in dynamic settings. Overall, these findings validate the necessity of each component ensuring the effectiveness of DSPNET.
5.4.4 HYPERPARAMETER ANALYSIS
0.0
To analyze the impact of hyperparameters (which controls the contribution of treatment prediction) and (which regulates the gradient reversal layer), we con- duct a sensitivity analysis by varying both parameters within the set {1,2,3, 3, 43. We visualize the performance trends across different combinations of and 3 using a histogram to facilitate comparison. As shown in Fig- 4 the proposed DSPNET exhibits stable performance across different hyperparameter configurations, indicat- ing that it is not highly sensitive specific choices of and B. Notably, when a, 3 E {1, DSPNET attains relatively better performance, suggesting that balanced and moderate contributions from treatment prediction and gradient reversal yield better results.
0.4
(a) VEPEHE on Flickr
(b) EATE on Flickr
(c) VEPEHE BC
(d) CATE on BC
Figure 4: Hyperparameter Analysis.
5.5 EVALUATING TREATMENT PRIORITIZATION RULES
Beyond directly measuring the CATE-ID esti- mation accuracy by / /ÉPEHE and CATE with ground-truth CATE-ID, we further evaluate the quality of treatment prioritization rules induced by the estimated CATE-ID of different esti- mators by adopting Rank-weighted Average Treatment Effect (RATE) Yadlowsky et al.] 2025). RATE provides a principled approach to assess how good the estimated CATE-ID is with- out requiring access to the ground -tunt CATE- ID values, focusing on its treatment prioritization ability, i.c., the extent to which individuals with higher estimated CATE-ID truly benefit more from treatment, it provides complementary perspec- tive on the quality of estimated CATE-ID beyond error-based metrics. The formal definition and more details about RATE metric can be found in the Appendix B
Table 3: RATE results, higher is better.
Flickr
BlogCatalog
Methods
RAUTOC
RaINT
RAUTOc:
ROINI
Deconfounder
0.03
2.01
0.19 2014 0.07 2.06
SPNET
0.26-024
0.10
0.05 +0.17 0.02 +0.06
NetEST
0.51
0.15aa12
0.35 20.15 0.15 10.0
DNDC
2.72an.99
1.04x027
3.03
1.09
DSPNET
2.98
1.13
3.91 a0.66 1.52
We report the R AUTOC and ROINT Table 3 comparing the proposed DSPNET with beasork-based baselines (Deconfounder, SPNET,
two variants of RATE averaged over all time steps in

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NetEst, and DNDC) BlogCatalog and Flickr with default generation. Results for those non- network baselines are omitted, as their performance was consistently poor in our earlier evaluations. As shown, DSPNET achieves higher and more stable RATE scores across datasets, demonstrating superior treatment prioritization capability over the other network- -based baseline methods.
Table 4: Time and Space Overhead
5.6 TIME AND SPACE OVERHEAD
Datasel
Scale
#Nodes
Eddes
Time
GPU Mem
1x
7.5K
239K
0.24s
2.8GB
To further evaluate the time and space over- head of DSPNET under large-scale dynamic networks, we scale the number of nodes and edges to roughly 1x, 2x, 4x, 8x and 10x of the original size on Flickr and BlogCatalog. DSP- NET was trained on each scaled dataset under the same hardware configuration, and we report the wall-clock time per epoch and peak GPU memory usage as shown in T
2x
15K
478K
0.3
5.6GB
Flickr
4x
30K
956K
0.5
11.3GB
8x
60K
1.91M
0.94s
22.5GB
10x
75K
2.39M
1.14s
IGB
1x
5K
171K
0.24s
1.7GB
2x
10K
342K
0.29%
3.4GB
BlogCatalog
4x
20K
684K
0.39%
6.8GB
8x
40K
1.36M
0.65s
13.2GB
10x
50K
1.71M
0.81s
16.5GB
Overall, the results show that both runtime and memory scale approximately linearly with graph size, consistent with our theoretical complexity analysis. Moreover, DSPNET continues to train and infer reliably even on graphs with 75k nodes and 2.39 million edges, suggesting that the framework is capable of handling substantially larger dynamic networks in practice.
6 RELATED WORKS
treatment effect estimation from observational data has received considerable attention in recent years, leading the development of numerous methodological approaches. Unlike traditional methods (Shalit et al.] 2017; Zhong et al., 2022; Wang et al.; Wu et al. [022] Yao et al. 2018) that assume independent and identically distributed (Li.d.) samples, networked data violate this assumption, as an individual's 's outcome can be influenced by their neighbors. To address confounding in such settings, several approaches- such as Deconfounder (Guo al. 2020c), NetEST (Jiang Sun 2022). CONE (Guo et al. (020b), and IGNITE (Guo et al.) 2021 have been proposed. These methods leverage network structures to capture hidden confounders and adopt various balancing strategies to mitigate confounding bias for reliable treatment effect estimation. However, they do not explicitly model network interference. To address interference, LCVA (Rakesh et al. (018)) utilizes a variational autoencoder capture spillover effects between units. SPNET (Huang et al.) 2023) further refines this by modeling heterogeneous spillover magnitudes across neighbor pairs. Additionally, (Ma & Tresp 202T) explores interference modeling via simple aggregation of neighbors' treatments, while HyperSCI (Ma et al., 2022) extends this idea to hypergraphs using attention mechanisms based on neighbors' representations. However, these methods are designed for static networks and cannot be directly applied to dynamic environments. Although DNDC (Ma et al. 2021) aims to estimate treatment effects in dynamic graphs, does not account for interference.
contrast, our work targets dynamic network environments, while simultancously modeling hidden confounders and interference, thereby addressing both time-evolving confounders and spillover effects.
7 CONCLUSION
In this paper, we study the problem of treatment effect estimation in dynamic network environments, explicitly accounting for time-varying hidden confounders and network interference. We begin by introducing new treatment effect estimand CATE-ID tailored for dynamic settings with interference and formally prove its identifiability. Building on this theoretical foundation, we propose DSPNET, novel framework that leverages both the evolving network structure and historical information to model dynamic hidden confounders and interference, and then learns the representations of confounders and environment exposure to enable accurate treatment effect estimation over time. Extensive experiments demonstrate the superiority of our framework over existing methods for estimating treatment effects from dynamic networked observational data.
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8 REPRODUCIBILITY STATEMENT
We have made significant efforts to ensure the reproducibility of our work. For the proposed algorithm. we provide an anonymous link the full source code. The assumptions required for Theorem 3.3 as well as its complete proof are clearly presented in Section [3] For experimental evaluation, we detail the entire dataset generation and processing procedure in Appendix [A and provide additional experimental results and analysis in Appendix C Together, these resources allow researchers to fully reproduce our theoretical results and empirical findings.
9 ACKNOWLEDGEMENTS
The authors thank the anonymous reviewers for their time and thoughtful comments.
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APPENDIX
A DATA GENERATION
In this section, we introduce how to generate the treatment, confounders, interference, and potential outcomes for dataset BlogCatalog and Flickr:
Step 1: Simulate the full confounders z we first introduce how to leverage the historical information and network structure to simulate the full confounders. The full confounders =f for unit at time step t could be simulated as follows:
1
A 42 (A1
M +2
Σ fz(W)) + (afz((z)) + +c"), DEg
(13)
where function (-) maps the features in terms of -foddds-words to topic distribution by training LDA topic model with 50 topics (Pritchard et al. 2000) such that the dimension of the output of f is 50, thus z E 50 V E 5R500 represents the historical information, G denotes the neighbor set of unit at time step I. λ1 A2 and X3 are to control the influence of historical information, network structure and current unit's covariates to the hidden confounders, respectively. Å1, A2, A3 are set to 1,,3,3 by default; e² E 1:50 is the noise vector and each element is sampled from the normal distribution of ~ (0, 0.001); Each element Vi, can be obtained using q-order autoregressive Miils 1990) as follows:
erd
(14)
b.
where 2/ denotes the j-th element of confounders 24 2-77 at time step t r, di represents the treatment assignment of unit i time step r, Pr.j ~ N(1 r/g, 1/4) and er ~ ((, 0.02) are to control the impact of historical confounders and treatment assignments from previous time steps, here we follow (Ma et al. 2021) and set the order q = 3. Noting that & at initial time step f = is set to zero vector.
Step 2:
Simulate observed treatment assignment d'. First we randomly select two vectors r rf from the current hidden confounders Z' in the LDA topic space the centroids for treatment and control group. The similarity between a unit's 's confounder representation z and each centroid is mcasured by their inner product:
$ -
2/3 8,1 =rr"
(15)
which indicates how close unit to the control or treatment centroid in the topic space, rh" represents the transpose of r/- Then we can simulate the treatment assignment de for unit i at time step & as follows:
exp(s(,1)
d B exp(s exp(s(,,)
(16)
where B denotes the Bernoulli distribution.
Step 3: Simulate interference (spillover effect) It The interference I9 of unit i's neighbors on it can be computed as follows:
=- f((y) dz.
(17)
jES!
where C' is the scaling value to control the strength of interference in the network, w is the weight vector sampled from uniform distribution /V 50) where Iso is the identity matrix, the inner product w fo (az,) quantifies neighbor j's influence strength on unit which contributes to the interference if the neighbor receives treatment.
Step Simulate potential outcomes. Given the aforementioned steps, the potential outcomes could be formulated as follows:
(1) x(sŞ,0 + + I c
(18)
(0) = ks + I + E
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Table 5: Statistical Summaries on Flickr and BlogCatalog
Dataset
Flickr
BlogCatalog
Time Steps
25
25
Units
7575
5196
# Averaged Edges
239623
171661
Features
12047
8189
% Treated Ratio
49,48 +: 2.07
49.53 + 2.00
Average ATE
16.19 + 12.87
22.00 + 17.10
where & is the scaling factor and set to 100 by default, e ~ (0, 1) is the sampled Gaussian noise. Then the observed outcome for unit i at time step could be obtained by:
of == of (1) + d) (0).
(19)
Then, based on the above data generation process and default parameter settings, we randomly run the simulations 10 times on the Flickr and BlogCatalog datasets. The statistical summaries of the generated data are presented in Table
B RANK- WEIGHTED AVERAGE TREATMENT EFFECT (RATE)
In practical applications of treatment effect estimation, the primary goal often lies only in estimating the conditional average treatment effect (CATE) for each individual, but also in constructing treatment prioritization rules that rank individuals according to their estimated treatment effects. To evaluate the quality of such prioritization rules, (Yadlowsky et al. (025) proposed the Rank-weighted Average Treatment Effect (RATE), a general evaluation framework that quantifies how well an estimated prioritization rule identifies those who truly benefit most from treatment. At high level, the RATE captures the extent which individuals who are highly ranked by the prioritization rule are more responsive to treatment than randomly selected individuals, which is another perspective to evaluate the quality of the estimated CATE.
Unlike error-based metrics such as VEPEHE and CATE, RATE does not require access to the true CATE values for each individual. Instead, it leverages the ranking induced by estimated CATEs, thereby providing more practical evaluation criterion in real-world settings where the true individual treatment effect unobservable.
B. FORMAL DEFINITION OF RATE
Let S(X.) denote treatment prioritization score assigned to the individual X,, where S(.) is priority scoring function that could be a learned priority rule, a learned CATE estimate, a hardcoded heuristic, something else. In this work, our goal is to estimate the quality of the estimated CATE-ID, we take the estimated CATE-ID for each individual as the prioritization score:
5(X,) = FXx)),
(20)
a larger value of (XX)) implies that the individual should be treated first. For given quantile level 0 < g S 1, we define the Targeting Operator Characteristic (TOC) as:
TOC S) = (1) - Y (0) F(S(X,) 2 1 - ql - E[ (O),
(21)
where F(S(X)) the cumulative distribution function of the prioritization score S(X;). Intuitively, TOC(g; S) measures the incremental gain in treatment effect when prioritizing the top-q fraction of individuals based on the priority scoring function 5(-), compared to the overall population. Noting that if q 1, the first term in Eq. 21 is the average treatment effect, and so TOC(g; S) 0.
After defining the TOC(g; S), we can involve evaluating prioritization rules (based on the estimated CATE-ID) in terms of weighted averages of the TOC. Formally, Rank-weighte Average Treatment Effect (RATE) is defined as the a weighted integral of the TOC curve:
[' TOC(G; S) w(g)d4,
RATE(W:; S)
(22)
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where w(q) is nonnegative weight function that emphasizes different regions of the ranking. Different choices w(q) yield different variants of RATE. Here we introduce two variants of RATE based on different weight function as follows
(I) Area Under the Targeting Operator Characteristic (AUTOC). When the weight function is chosen uniform, i.e., w(q)= 1, RATE reduces to the the area under the TOC curve (AUTOC):
RaUTOC = J. TOC S)dq.
(23)
RAUTOC provides overall summary of how much benefit the prioritization rule delivers across the entire population distribution. A higher RACTOC indicates that the ranking consistently selects individuals with higher treatment benefit, demonstrating higher quality of the treatment prioritization rule induced by the estimated CATE-ID.
(2) Qini coefficient. The Qini coefficient is widely used variant of RATE that emphasizes the ability of treatment prioritization rule to correctly identify individuals with the largest treatment effects. Its definition can be written
ROINT= - ff (OC((;
ROINT-
(24)
we can see that it uses the quantile level q as the weight function. Compared to AUTOC, which applies uniform weighting over the entire population, the Qini coefficient assigns more weight to the upper quantiles of the prioritization rule, thereby stressing the importance of ranking performance among the top-scoring individuals.
C ADDITIONAL EXPERIMENTS
C.I MODEL ARCHITECTURE DETAILS
To enhance the transparency and reproducibility of our method, we provide a detailed description of the default model architecture used in the experiments. summaiiss the configuration of the backbone components, including the number of GCN and MLP layers, the hidden dimensions of GCN, MLP and recurrent layers, activation functions, and other relevant hyperparameters about training details.
Table 6: Model architecture specifications and training details.
Component
Layers Hidden Dimensions Activation
Remarks
GCN Backhone
70
ReI.U
MLP Backbone
70
ReLU
Recurrent Backbone
70
Gated Recurrent Unit
Treatment-Me
2
100
Sigmoid
MLP for treatment
Dimension Confounders
70
Final represcntation confounders
Dimension of Interference
70
Final representation of exposure
Optimizer
Adam, learning rate de 3, weight decay 1c 2
Other eeperraaasetes
epochs= 1000, 1, 1, le
C.2 PERFORMANCE COMPARISON UNDER VARYING INFLUENCE OF HISTORY
In this section, we investigate the impact of different intensities of historical information on the model's performance in estimating treatment effects. Specifically, we keep all other parameters in the data generation process as default and vary the value of X (5,10.20) to examine how different levels of historical influence affect the model's performance. The results presented in Table 7
We can see that our proposed DSPNET model consistently outperforms all baselines across different levels of historical influence. Most baseline methods exhibit significant deteriorating performance as Aj increases, which suggests that stronger historical dependencies make it more challenging for these models to accurately estimate treatment effects. However, our proposed model DSPNET suffers the least, demonstrating its superiority on capturing time-varying hidden confounder and interference on dynamic network environment.
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Table 7: CATE-ID performance comparison by varying influence of historical information Flickr and BlogCatalog datasets. Bold: the best results. Underline: the 2nd best results. Lower is better. indicates statistically significant improvement over the strongest baseline (t-test, p- < 0.05).
A1
A
Datasets
Methods
v VEPENE
CATE
V VEPERE
EATE
V
VEPEНE
CATE
DESCN
10.637 +2.198
9.621
17.982 #3872
16.996
25.112 16.005
23.865
DFITE
19.177 #10962
2.828
17.404 22.33
3.083
23.042
3.787
DERCER
12.175 42673
10.017 #2.34
21.704 +3.786
17.246 +3,85
29,889
23.725 +4.582
CFR
27,010 #11.249
2.932 +0.548
24.218 +3,039
2.754
+0.509
32.181 #14.65
3.154 +0.404
Flickr
NetEST
4.342 al.642
0.875
6,822
1.405 #0.219
9.136 #1.748
2,052 211333
Deconfounder
6.275 +0,727
3.428 40.401
8,338 +1,230
4,738 +0.844
10,598 +1 903
6,282 +0.944
SPNET
7.208 +0.001
1,043 +0.173
8,693 =1.000
1,204 s0.216
10.167 +1 +1.622
1,482 s0.445
DNDC
1,892 #0.142
1,314 20.154
2.589 20.199
1.618 e0.781
3.154 20.9M
1,881 =1,090
DSPNET
1,346 20.173
at.111 0.788
1.497 20.148
0.890 an.000"
1.805 =0.2887
1,072 an.318
DESCN
13.812 42,00
12,934
=2.083
23,430
43.422
22.348
#3.128
32,849
26.206
31.539 a6.139
DFITE
8.224 +2,468
2.547
40.589
11.84
+3.243
3,446
60.427
14,949
x3.912
4,383 +1.077
DERCER
21.791 45.340
16.090
#2.407
35,321
18824
24.921
23.295
#11.642 47.289
34.239 47,866
8,156 42,369
0,984 40.158
11,547
13.164
20.219 1,295
14.781
13.744
1.631 20.428
BlogCatalog
NetEST
5.302 40.664
1,272 40.235
8.539
a1.074
1,586 s0.218
11,67 +1
2.021 s0,302
Deconfounder
7,811
5.226
13.067
8.884
18.247 43,522
12,451
SPNET
6.674
1,643
9.569
2.298 20.859
12,206
2.743
DNDC
1.961
1.314
2.475 46.46
1,454 +0,400
2.905
1.597 144
DSPNET
1.309 a0.125
0.853 aturss
1.464 20.119
0.845 20.105
1.773 =n.426
1.068 =0.488
C.3 PERFORMANCE COMPARISON UNDER VARYING INFLUENCE OF CURRENT COVARIATES
As shown in the data generation, X2 is set to control the influence of the current unit's 's covariates on its hidden confounders z/- Here we compare the treatment effect estimation performance between baselines and the proposed model DSPNET under varying values of 22 on Flickr and BlogCatalog. We set the value A2 to (3,5,8) and remain the other parameter as default.
The experimental results are shown in Table g outperforms all the baselines under different levels of current covariates' influence. Moreover, can be observed that under varying levels of influence λ2 the proposed model DSPNET exhibits strong stability in estimating treatment effects, as it effectively captures confounders in the latent space and learns the factors that truly affect the outcome.
We can see that our proposed model DSPNET
C.4 PERFORMANCE COMPARISON UNDER VARYING INFLUENCE OF NETWORK STRUCTURE
In the data generation, Ag is to control the influence of network structure, i.e., unit's neighbors, on its hidden confounders. Similarly, here conduct the experiments compare the treatment effect estimation performance between the baselines and the proposed model DSPNET under varying Ag values. We the value of Ag to also range in (3,5,8) and remain the other parameters in data generation as default.
The experimental results are shown in Table 9 Still, our proposed model DSPNET outperforms the other baselines in all settings of A values and the performance of DSPNET remains stable when the influence network structure varies.
C.5 ROBUSTNESS STUDY OF UNOBSERVED CONFOUNDERS
We also conduct robustness analyses regarding the unobserved confounders that may not be fully captured. Specifically, we explicitly select 10%, 20%, 30% covariates that affects both treatment and outcome as the latent confounders, and these selected latent confounders not included in the construction of function (-), thereby simulating scenarios where the confounder modeling module fails to capture all confounders directly.
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Table 8: CATE-ID performance comparison by varying influence of current covariates on Flickr and BlogCatalog datasets. Bold: the best results. Underline: the 2nd best results. Lower is better. indicates statistically significant improvement over the strongest baseline (t-test, p-value < 0.05).
A 3
A =
A
Datasets
Methods
VEPEUE
EATE
VÉPEBE
EATE
VÊPENE
FATE
DESCN
17.982 23,572
16.996 43.821
14.089 =2.125
13.141 =2.122
11.797 =2.562
10.823 =2.582
DHITE
17.404 22.93
3.083 #0.466
14.872
=2.19
2.679
=0.700
16.166 23.933
2.634 40.70
DERCER
21.704 23.786
17.246
43.825
15.100 =2.852
11.958
#2.36
13,250 #2.015
10.515 #1.760
CFR
24.218 23.939
2.754 =0,599
23.425 =2.193
3.081 20.664
23.708 =2.499
3.048 20.788
Flickr
NetEST
6,822 #1.107
1.405 #0.219
5,437 20.615
1.074 20.179
4.750 20.311
0.904 40.15
Deconfounder
#1.210
4.738 #0,844
7.309 20,885
4. 4.154 20.789
11.017
3.759 40.708
SPNET
8.693 s1.030
1.204 60.216
8.006 60,600
1.173 20,20
7.541 20.839
1.068 20.206
DNDC
2.589
1.618
2.338
1.561
2.100
1.361
DSPNET
1.497 29.148
0.890 20,060
1.440 #0.137
0.825 #0.129
1.373 #0.151
0.784 =0.140
DESCN
23.430
22.348
19.826 =5.019
18.804 #4.852
18,436
17.393
DFITE
11.84 +3.243
3.446 +0.427
11.050 +4.279
3.222 +0.471
12.446 +4.225
2.866 +0437
DERCER
35.321 s8.524
24.921 +3.295
29.706 =6.265
22.365 25.321
31.197
21.824 #4.618
CFR
11.547 23.164
1.295
#0.249
10.574 +4,037
1,033 20.207
12.396 #4.525
1.021 40.144
BlogCatalog
NetEST
8.539 +1.074
1,586
+0.218
7,205 +1. 300
1,422 +0.188
6.675 +1.177
1,332 +0.176
Deconfounder
13.067 21,863
8.884 =1.170
11,527 =3.180
7.659 #2,212
10.195 23.03
6.600 =1.91
SPNET
9.569 a1.742
2.298 =0,829
8,290 #1.515
1.733 20.433
8.421 21.420
2.235 a0.551
DNDC
2.475 40.460
1.454 +0.400
2,180 18.182
1,260 18.
2,273 +0.348
1.517 +0416
DSPNET
1.464 20.119
0.845 s0.1es
1.549 =0.144
0.852 =0.083
1.573 #0.129
0.951 =0.147
Table 9: CATE-ID performance comparison by varying influence of network structure on Flickr and BltaCog datasets. Bold: the best results. Underline: the 2nd best results. Lower is better. indicates statistically significant improvement over the strongest baseline (t-test, p-value < 0.05).
As 3
A
As
Datasets
Methods
VEPEUE
EATE
VEPEHE
EATE
VEPERE
EAT
DESCN
17.982 23,872
16.996 43.821
16.726
=2.266
15.802
#2.203
10.468 21,00
9.648 41305
DFITE
17.404 42,933
3.083 20.46
20.351
58.152
3.076:0061 20611
16.333 45.05
2.649 20.393
DERCFR
21.704 43.786
17.246 43,805
17.721
+1.587
14.079
a1.777
12.066 +2.430
9,898 +2.171
CFR
24.218 +3,939
2.754 +0,509
28.309
+7.360
3. 10.
+0.649
27.616 90.904
3.171 +0.524
Flickr
NetEST
#1.107
1.405 =0.219
6,222 20,662
1.256 #0.277
40.501
0.842 20.144
Deconfounder
8.338 +1.230
4.738 20.844
8.082 77.770
4.607 60,00
6.273 40.665
49,590
SPNET
8.693
1.204 #0.216
8.432
1,238 +0251
7.031 +0.666
0.982
DNDC
2.589
1.618
2.273
1.485
1,946 19.317
1.322
DSPNET
1.497 40.145
0.890 s0.060
1.565 20.171
0.939 20.137f
1.305 #0.88*
0.770 20.092
DESCN
23.430
22.348
18.261
17.300
13641
12.651
11.815
DFTTE
11.841 x3.243
3,446 #0.427
10.308 =4,022
2.867
20.600
7.579 x1.930
2.311 40.500
DERCER
35.321 48.324
24.921 43.295
27.508
27.344
20.028
#4.403
18.786 #4.343
13.430 #2.645
CFR
11.547 43.164
1.295
20.249
10.060 23,000
1,079
20.225
7.198 42.081
0.865 40.159
BlogCatalog
NetEST
8.539 a1.174
1.586 s0,218
6.648 #1.136
1,563 20.132
4.815 40.683
1,219 a0.19
Deconfounder
13.067 21.863
8.884 =1.170
10.264 =1.967
6,707 21.373
7.156 +1.385
4,605 40:97
SPNET
9.569 a1.742
2.298 20,829
7.918 a1.529
1.796 20.475
6.575 +1.327
1.544 20.441
DNDC
2.475 s0.460
1.454 s0,400
2.057 107
1.250 129
1,800 a0.214
1.078 40.109
DSPNET
1.464 20.119
0.845 20.105
1.521 20.129
20.110
1.316 20.0%
0.790 20.102
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Table 10: DSPNET performance under different unobserved confounding levels.
Flickr
BlogCatalog
Level
VEPERE
CATE
VCPEEE
CATE
10%
1.535 + 0.133
0.911 + 0.102
1.613 + 0.188
0.949 + 0.206
20%
1.694 + 0.102
0.968 + 0.081
1.697 + 0.089
1.009 + 0.064
30%
1.712 +: 0.129
1.112 + 0.093
1.830 + 0.194
1.021 = 0.212
original (0%)
1.497 + 0.145 0.890 = 0.080
1.464 = 0.119
0,845 = 0.105
Table 11: Performance of DSPNET and network-based baselines under different unobserved con-
founding levels.
Level 10%
Level = 20%
Level
30%
Dataset
Model
VEPERE
CATE
V VEPERE
CATE
VEPERE
CATE
Deconfounder
8,350 + 1.324
4,807 + 0.942
8.578
1.375
4,950 + 1.003
8.810 0.998
5.216 = 0.667
NetEST
6.982-11.121
1484440.004
7.172:1.259
1.590:0.189
1.375
1.610=0.219
Flickr
SPNET
8.870=11.133
1.34410.26
9.045=1.260
0.355
9.233=1.453
0.390=0.210
DNDX:
2.637++0.888
1.7244+0.581
2.749-0.752
1.751 +0.585
2.878-0.604
1.768+0.592
DSPNET
1.53:10.133
0.911:10.12
1.694=0.102
0.968
1.712=0.129
1.112=0.093
Deconfounder
13.231 # 1,839
8.932 +: 1.212
13.773 + 1.792
8.978 #: 1,280
13.906 +: 2.092
9.126 = 1,483
NetEST
8.659:11.065
1.63244..199
8.859=1.095
1.752+0.319
9.132=11114
1.827=0.322
BlogCatalog
SPNET
9.725=1.546
2.227:100838
9.862=1.346
2.681
10.379:::.475
2.782=009455
DNDC
2.571-
1.527-40.488
2.748=00334
1.684-0.388
2.906=0.440
1.692=0.44
DSPNET
1.11310.188
0.949:10.206
1.697=0.089
1.009:0.064
1.830=0.194
1.021=0.212
The CATE-ID estimation performance of DSPNET for different levels of unobserved confounding shown in Table IO Besides, we also compare the CATE-ID estimation of DSPNET with those network-based baselines (NeEET,, Deconfounder, SPNET and DNDC) under different levels of unobserved confounding, as shown in Table TT We can see that DSPNET remains stable and continues to outperform baselines under different unobserved confounding levels. The above results indicate that our method is robust even when there are unobserved confounders, as the proposed model can infer the dynamic latent confounders by leveraging the network structure and neighbors' characteristics.
C.6 EMPIRICAL STUDY OF MODEL COMPLEXITY
We conduct an empirical study to examine how increasing the architectural depth and width affects the performance of DSPNET. Specifically, independently explored three key architectural hyper- parameters about model complexity: (I) the depth the GCN backbone, (2) the depth of the MLP backbone, (3) the size of the hidden dimensions.
For each hyperparameter, we varied one factor while fixing the remaining two to their default settings. Concretely, evaluated GCN depths of 1, 2, 3 layers. MLP depths of 3, layers, and hidden dimensions of 100, 150, 200. The performance of DSPNET for CATE-ID estimation on Flickr and BlogCatalog in different architectural settings is shown in Table 12
The results show that the performance of DSPNET under different MLP layers and hidden dimensions remains stable across all tested configurations. However, adding more GCN layers leads to clear performance drop due to the well-known over-smoothing effect, where deeper GCNs produce increasingly similar node representations and erase individual-level heterogeneity essential for accurate CATE estimation. Moreover, in many networks, 1-hop neighbors already provide sufficient information, while deeper propagation introduces irrelevant signals from distant nodes, further degrading performance.
C.7 PARAMETER ANALYSIS OF CONTROLLING OVER-FITTING TERM
In the hyperparameter analysis of the main body, we only investigate the impact of the hyperparameter (control the influcence of treatment prediction) and / (control the contribution of gradient reversal
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Table 12: Empirical study of model complexity.
Flickr
BlogCatalog
Setting
Value
VEPERE
CATE
VEPERE
CA7B
1,4974+0.145
0.890+0.080
1.464+0.119
0.845+0.105
of GCN Layers
2
5.299:14.407
2.543++2811
6,293:1:.441
3.09113..00
3
15.703-13.403 403
6.7141:2.826
16.868=7.206
8.75811.103
3
1.455:100.45
0.814 110
1.355:10,145
0.81411.110 110
# of MLP Layers
4
1.571=10.107
0.91810.116
1.77140.107
0.85810.116
5
1.416=0.115 0.850#0.116
1,486=0.149
0.850=0.116
100
1.43510.121
0.88710.087
141240.110
0.81210.1411
# of Hidden Dim
150
1.373+00103
0.836+0.089
1.119+0.221
0.772+0.130
200
1.436+0.159
0.844+0.084
1.577+00433
0.827+0.154
component), here we further conduct additional experiments on analyzing the impact of w controlling the over-fitting term in Eq. the proposed model DSPNET.
We set w to range in {10 10 2,, 1,001,,, } and plot the curve chart of CATE-ID estimation performance in terms of /EPENE and aTE on Flickr and BlogCatalog. The results are shown in Figure 5 we can see that the proposed DSPNET performs steadily under varying values of w in both VEPEHE E and EATE, which means that DSPNET not sensitive the hyperparameter controlling over-fitting term.
1.6
1.4
Metric Value
Metric
1.2
Eare
1.0
1.0
0.8
0.8
10
10
10
10-1
10
10
(a) w Analysis on Flickr
(b) w Analysis on BlogCatalog
Figure Hyperparameter Analysis of w.
C.8 COMPARISON FOR DIFFERENT BALANCING STRATEGIES
Apart from the gradient reversal method adopted in DSPNET, another common approach to mitigate confounding bias is to enforce distributional balance of confounder representations in the latent space. Two widely used balancing strategies include the Wasserstein-1 1 (Wass) distance and Maximum Mean Discrepancy (MMD). Both aim to minimize the distributional divergence between the treated and control groups with respect to the confounder representations, thereby ensuring that the learned confounders are not predictive of the treatment assignment.
To demonstrate the effectiveness of the gradient reversal strategy used in our model, we compare it against two widely used balancing strttggess-Wassersteie Wasserstein-1 (Wass) distance and Maximum Mean Discrepancy (MMD)-in in the task of treatment effect estimation Flickr and BlogCatalog. As shown in Figure 6, our gradient reversal consistently outperforms the alternatives in different metrics and datasets.
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Guzz
03
Drader
(a) Flickr
(b) BlogCatalog
Figure 6: Treatment effect estimation performance of DSPNET under different balance strategies.
Table 13: Performance comparison between unit GRU and LSTM.
p% = 0.1%
p% = 0.5%
p% = 1.0%
Datasets
Model
VEPEHE
6ATE
VEPERE
EATE
VEPEHE
EATE
DSPNET
1.49720145
0,000
2.062 20.498
1.144 20.12
n.28
1.35
Flickr
DSPNETISTM
1.498 20.119
0.871 20.099
2.181 20.419
1,227 20.332
2.023 20.137
1,276 20.15
DSPNETORC
1 1.464 10.119
0.845 20.108
1,506 20.237
0.913 20
2.227 20.378
1.183 20.290
BlogCutalog
DSPNET
1,517 40.171
0.906 +0.99
1.512 +0.118
0.938 17.
2.260 +0.502 0.948 -0.145
C.9 COMPARISON OF GRU AND LSTM UNITS FOR ENCODING HISTORICAL INFORMATION
In the experiments in main body, the proposed DSPNET employs Gated Recurrent Unit (GRU) (Cho et al. 2014) to encode historical information by capturing hidden confounders, treatment assignments, and past temporal states. While GRUs computationally efficient and effective for modeling sequential dependencies, another widely used recurrent architecture is the Long Short-Term Memory (LSTM) network (Hochreiter & Schmidhuber] T997). To assess whether the performance of DSPNET depends on the choice of recurrent unit, we conducted an ablation study comparing GRU and LSTM as alternative modules for encoding historical information.
We replaced the GRU cell in DSPNET with an LSTM cell while keeping all other components, hyperparameters, and training configurations unchanged. Here we report the comparison results between GRU and LSTM cell on Flickr and BlogCatalog by default generation for varying degress of network dynamics. As shown in Table 13 one can see that both GRU- and LSTM-based variants of DSPNET achieve comparable performance.
C.10 DIFFERENT EXPOSURE FUNCTIONS
In real-world networks, interference depends not only on neighbors' treatment assignments, but also how these treatments interact with intrinsic behavioral patterns of individuals. For example, health intervention (c.g., jog) may affect a user only if its treated neighbors actively engage in and share health-related behaviors. Hence, simple exposure summaries (e.g., averaging neighbor treatments) oversimplify these dynamics. Unlike prior work, DSPNET leverages treatment assignments as gating signals and builds learnable interference representation through an additional GCN module, which serves as the exposure summary function for modeling interference, as shown in Equation (6)
To examine how sensitive DSPNET the design of the summary function, we conducted experi- ments where we varied the aggregation rule of DSPNET, we derive the following three variants of exposure summary function to capture the interference from neighbors:
Sum-Pooling: directly of the treatment values of unit i's neighbors, thus the exposure
summary of unit is formulated as e Ejest dy.
Average-Pooling: average the treatment assignments of unit i's neighbors, then the exposure
summary of unit is formulated as ei Σ,eg! d;
[0
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Table 14: Comparison results for different variants of exposure summary function.
Flickr
BlogCatalog
Variants
VEPEHE
CATE
VEPEHE
EATE
Sum-Poote Sum-Pooling
1,570 #0.190
1.163 20.162
1.752 10.166
1.183 #0.182
Average-Pooling
1.695 =0.152
1.142 #0.135
1.543 #0.164
1.073 +0.1%
PS- WSeihiggg
1.598 #0.121
1.121 #0.135
1.502 +0.062
0.891 #0.091
Original
1.197:0.15
0.890 0.080
1.464 #0.119
0.845 =0.105
PS- "S-Weighting: use each unit's neighbors' propensity scores as weights to aggregate the GCN-based neighbor representations as the summary exposure: ei =jegg Tax)) rj.
where T ((x))) is the propensity score, here we use the MLP network with softmax function to predict the propensity scores.
Then we compare the variants of the above three summary functions with the original strategy of DSPNET on Flickr and BlogCatalog with default generation for the CATE-ID estimation task. The comparison results are shown in Table [4] We can see that the exposure function with representations (i.e., the PS-Weighting and Original) is relatively better, indicating that considering the heterogeneity of neighbor's interference is important, but the other variants are also competitive.
C.11 CONFOUNDER DISTRIBUTION VISUALIZATION
Additionally, we compared the distributions of confounder representations learned by the DSPNET model, both with and without the balancing strategy, i.e., the gradient reversal component. In particular, we randomly sampled representations of control and treated group samples at selected time step from models trained under conditions with and without the balancing strategy. These representations were then reduced to two dimensions using t-SNE, and visualized through scatter plots. As illustrated in the Figure 7 the confounder representations of the treated and control groups obtained using the balancing strategy more closely clustered compared to those without the balancing strategy, indicating a smaller distance between the two groups.
D LIMITATION
In this work, our proposed approach explicitly models local interference, assuming that only treat- ments assigned to immediate neighbors influence an individual's outcome. While this simplifies analysis and computational complexity. it inherently neglects global interference effects- soeetts--seerriosss where units beyond direct neighbors can impact the outcomes through indirect or cascading pathways within the network. Such global spillover effects are plausible in many real-world settings, particularly in dense or highly interconnected networks, and their omission could potentially lead to incomplete or biased causal estimates. Therefore, extending our approach to account for broader network influence remains an important direction for future research.
And work assumes that given unit's treatment status does not influence the treatment assignments of its neighbors, we only consider the interference which refers to the influence of one unit's neighbors' treatment on its outcome. However, in real-world networked settings, treatments may spread contagiously through social influence processes, violating this assumption. Ignoring such treatment dependence could limit the generalizability of our findings. Incorporating treatment contagion mechanisms into the modeling framework represents another valuable avenue for future research.
Furthermore, in observational social networks, covariates and structure are often entangled through homophily. And homophily and contagion (peer influence, interference) are fundamentally con- founded in observational settings, making it impossible to cleanly distinguish "similarity due to shared attributes" from "similarity due to peer influence". In this work, we does not aim to identify or separate homophily from contagion, but acknowledge that fully separating homophily-driven sim-
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treated group control group
group
(a) Balance BlogCatalog
(b) Non-balance on BlogCatalog
treated group
control group
group group
(c) Balance on Flickr
(d) Non-halance on Flickr
Figure 7: Confounder distribution visualization with and without balancing strategy BlogCatalog and Flickr.
ilarity from contagion-driven influence in dynamic observational networks is an open and important problem.
E LLM USAGE
We used large language models (LLMs) solely to aid in the writing process, including polishing grammar and improving clarity of exposition. No part of the research design, theoretical development, experiments, or analysis relied on LLMs.
23


Reviews:
[{"review_id": "U5sptiU5GD", "reviewer": "Reviewer_kQia", "summary": "This paper focuses on the treatment effect estimation in dynamic network environments where both time-varying hidden confounders and network interference exist. The authors propose a new treatment effect estimand designed for dynamic settings with interference and introduce a new causal inference framework that explicitly models both time-varying hidden confounders and network interference based on graph nerual networks. To mitigate confounding bias in observational data, the proposed framework uses adversarial learning to enforce balance in the learned confounder representations. The framework is designed to accurately estimate causal effects in settings where the network structure and confounding evolve over time.", "questions": "1. Can the proposed approach be extended to settings where the underlying network structure is partially or entirely unobserved? Exploring the applicability of the proposed framework in such scenarios may offer a valuable direction for future research.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. The paper highlights an important and underexplored perspective, estimating causal effects in dynamic network environments, which has received relatively little attention despite its relevance.\n2. The proposed framework, based on graph neural networks, is well defined and effectively demonstrates the advantages of learning representations of hidden confounders over time and estimating treatment effects in dynamic networks.\n3. This paper is very well-organized, easy to follow, and clearly presents its contributions.", "weaknesses": "1. The paper lacks clarity on how the proposed method addresses the entanglement between network structures and covariates. A more detailed explanation—whether through theoretical justification or intuitive examples—would help clarify how the model disentangles these dependencies and ensures valid causal estimation.", "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": "TnfsWnoVK9", "reviewer": "Reviewer_NsgB", "summary": "The paper works on the observation study problem where all network interference, network dynamics, and hidden confounders are present in a dynamic network causal model. The work targets the conditional treatment effect CATE-ID and estimates the conditional probability densities of treatments, confounders, and potential outcomes through an RNN coupled with a GNN. This is a methodological paper with performance validated by thorough real data simulation.", "questions": "1. (related to the weakness). How can the method be generalized to other causal estimands of interest? For example, the policy value (average treatment effects under a certain stationary distribution of networks/treatments..) \n2. Does the method require the network dynamics to be stationary?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "- **Originality**: the work is novel in considering (i) dynamic network in causal inference, (ii) set of confounders that depends on the full history. \n- **Quality**: the paper is well-written with clear explanation on the methodology and have solid empirical results. \n- **Clarity**: the writing is very clear and easy to follow. \n- **Significance** : the paper provides a general framework for causal effect estimation on dynamic networks. Although no contribution to the fundamental theory, the work provides a decent insights of deal with such complicated causal inference tasks", "weaknesses": "- The major estimand of the paper is to estimate the CATE-ID, which conditions on the realized treatments and exposures. It appears to be off-topic to most causal inference tasks as the usual goal is the **average** treatment effects under a given policy or a given stationary distribution.", "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": "qCgir2fTSI", "reviewer": "Reviewer_pbEV", "summary": "The authors propose an end-to-end framework, DSPNET, which integrates GCN and RNN to represent dynamic confounders while simultaneously modeling neighborhood interference. The method is evaluated on semi-synthetic Flickr and BlogCatalog datasets.", "questions": "1. The authors claim in the Reproducibility Statement that they have provided the source code to ensure reproducibility. However, the code link on the first page of the paper is invalid.\n\n2. The authors assume the existence of a function Φ𝑧(⋅) that can capture all latent confounders (Assumption 3.1). This assumption may be too strong in realistic scenarios. It is suggested to include robustness or sensitivity analyses in the appendix to evaluate the impact of unobserved confounders that may not be fully captured.\n\n3. The datasets used are static and semi-synthetic. It is unclear whether the equations used to generate treatment and outcome variables, as well as the way dynamics are manually introduced, are theoretically justified or empirically grounded. The authors should clarify how this data generation process may affect the validity of the results.\n\n4. The paper lacks architectural transparency. The number of GCN and MLP layers, hidden dimensions, and epoch are not reported, and there is no analysis of how network depth or model complexity affects performance. Including these details would strengthen both reproducibility and clarity.\n\n5. The scalability of the proposed model to large-scale dynamic networks (e.g., with millions of nodes) is unclear. The authors are encouraged to provide a quantitative time or space complexity analysis.\n\n6. There is a typographical error: “Abalation” should be corrected to “Ablation.”", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 1, "strengths": "The paper addresses an important problem of modeling causal effects under network interference in dynamic networks.", "weaknesses": "Weak novelty. The overall framework of this manuscript is highly similar to Ma, Jing et al., WSDM 2021 (DNDC: Deconfounding with Networked Observational Data in a Dynamic Environment), with only an additional “neighborhood interference” modeling component. However, the interference module itself is relatively simple, and the contribution is not substantial enough to meet the innovation standards expected at ICLR.", "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": "hMhnFDRjsy", "reviewer": "Reviewer_mUQv", "summary": "Overall, this paper offers a **technically sound and empirically thorough** approach to a timely and underexplored problem — causal inference in dynamic network environments with interference.\nKey strengths include the introduction of a formally identifiable estimand (Eq. 2; Sec. 3), a well-structured architecture combining temporal and graph components (Fig. 2; Sec. 4), and strong empirical results (Table 1, Fig. 3).\nHowever, the **proof of identifiability** relies on strong and untested assumptions (Assumptions 3.1–3.2), and the **causal interpretation** of learned embeddings (especially the interference term ( e_t^i )) remains opaque.\nThe **datasets are synthetic**, which limits the generalizability of findings.\nOverall, the work is **technically competent and innovative**, but it needs clearer causal justification and stronger empirical grounding.", "questions": "1. **Validity of the Identifiability Assumptions**\n   The identifiability proof of CATE-ID (Sec. 3.2, Theorem 3.3) hinges on the Extended Ignorability and Consistency assumptions (Assumptions 3.1–3.2).\n   Could you clarify **how these assumptions are justified or empirically supported** in your experimental setup?\n   For example, are all relevant confounders explicitly simulated and observed in the synthetic data, and how sensitive is DSPNET to violations of these assumptions?\n\n2. **Interpretability of the Interference Representation ( e_t^i )**\n   The model learns a dynamic exposure representation ( e_t^i ) through neighborhood aggregation (Eq. 6).\n   Could you provide **qualitative or quantitative analyses** showing what this embedding captures?\n   For instance, does it correlate with known structural properties (e.g., degree, clustering, influence centrality), or can it be interpreted as a measurable causal quantity such as “average neighbor treatment intensity”?\n\n3. **Comparison with Prior Dynamic Network Models**\n   DSPNET combines GCN, GRU, and adversarial balancing layers.\n   Could you **clarify the novelty over DNDC (Ma et al., 2021)** and **SPNET (Huang et al., 2023)** beyond architectural integration?\n   A detailed ablation or theoretical justification isolating what enables DSPNET to outperform these baselines would help clarify its unique contribution.\n\n4. **Realism and Generalizability of the Evaluation**\n   All experiments are conducted on synthetic data (Flickr and BlogCatalog dynamic variants).\n   Could you comment on **how realistic these synthetic dynamics are**, and whether DSPNET could be applied to real-world dynamic networks (e.g., temporal citation graphs, contact tracing, or recommendation systems)?\n   Are there any known limitations or scalability barriers when moving from synthetic to real data?", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "* **Novel causal estimand and theory** — The paper proposes CATE-ID (Eq. 2) to extend CATE to dynamic settings with interference and proves its identifiability under explicit assumptions (Theorem 3.3). This formalization fills a theoretical gap in existing literature (Sec. 3).\n* **Architectural integration of temporal and relational modeling** — DSPNET elegantly combines GCNs (Eq. 4) and GRUs (Eq. 5) to model time-varying confounders, capturing historical and neighborhood dependencies.\n* **Explicit interference modeling** — The environment exposure variable ( e_t^i = \\sum_{j \\in G_i^t} d_t^j r_t^j ) (Eq. 6) effectively parameterizes spillover effects rather than using static aggregation (Sec. 4.2).\n* **Adversarial confounder balancing** — The GRL mechanism (Eqs. 9–11) applies domain-adversarial learning to minimize bias across treatment groups, grounded in causal representation learning theory (Shalit et al., 2017).", "weaknesses": "* **Overly strong identifiability assumptions** — The Extended Ignorability (Assumption 3.1) and Consistency (Assumption 3.2) presuppose that all confounders are captured by Φ_z(·) learned via GCNs. No empirical verification or sensitivity analysis is given.\n* **Causal interpretation is weak** — The interference representation ( e_t^i ) is learned implicitly but lacks interpretability or causal diagnostics (e.g., no analysis of which neighbor interactions drive outcomes).\n* **Limited realism in evaluation** — All experiments are synthetic with simulated treatments, outcomes, and interference (Appendix A). No semi-synthetic or real-world dataset (e.g., citation, epidemiological, or economic network) is used.\n* **Scalability untested** — There is no complexity or runtime comparison (Sec. 5.3 omits computational benchmarks), and DSPNET’s feasibility on large-scale graphs is unclear.\n* **No uncertainty estimation** — The model reports point estimates without confidence intervals or statistical tests, which is critical in causal inference.\n* **Potential redundancy with prior works** — DSPNET’s components (GCN+GRU+GRL) resemble DNDC (Ma et al., 2021) and SPNET (Huang et al., 2023); the novelty mainly lies in combining them rather than introducing fundamentally new mechanisms.", "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)