Estimation of Treatment Effects in Extreme and Unobserved Data
Authors: Jiyuan Tan
Vasilis Syrgkanis
Jose Blanchet
Venue: NeurIPS 2025 poster ()
Keywords: Causal Inference
Extreme Value Theory
Treatment Effect
Primary area: theory
TL;DR: We estimate average treatment effects, when the effect is moderated by extreme events and we are interested in the average effect in the extreme, which is rarely occurring in the observed data.

Abstract: Causal effect estimation seeks to determine the impact of an intervention from observational data. However, the existing causal inference literature primarily addresses treatment effects on frequently occurring events. But what if we are interested in estimating the effects of a policy intervention whose benefits, while potentially important, can only be observed and measured in rare yet impactful events, such as extreme climate events? The standard causal inference methodology is not designed for this type of inference since the events of interest may be scarce in the observed data and some degree of extrapolation is necessary. Extreme Value Theory (EVT) provides methodologies for analyzing statistical phenomena in such extreme regimes. We introduce a novel framework for assessing treatment effects in extreme data to capture the causal effect at the occurrence of rare events of interest. In particular, we employ the theory of multivariate regular variation to model extremities. We develop a consistent estimator for extreme treatment effects and present a rigorous non-asymptotic analysis of its performance. We illustrate the performance of our estimator using both synthetic and semi-synthetic data.

Estimation of Treatment Effects in Extreme and Unobserved Data
Jiyuan Tan"
Department of Management Science and Engineering
Stanford University j jiyuantan@stannford edu
Jose Blanchet
Department of Management Science and Engineering
Stanford University
jose. blanchet@stanford edu
Vasilis Syrgkanis
Department of Management Science and Engineering Stanford University
vayrgk@sttaffrd.eed
Abstract
Causal effect estimation seeks determine the impact of an intervention from observational data. However, the existing causal inference literature primarily addresses treatment effects on frequently occurring events. But what if we are interested in estimating the effects of policy intervention whose benefits, while potentially important, can only observed and measured in rare yet impactful events, such as extreme climate events? The standard causal inference methodology is not designed for this type inference since the events interest may scarce in the observed data and some degree of extrapolation is necessary. Extreme Value Theory (EVT) provides methodologies for analyzing statistical phenomena in such extreme regimes. We introduce novel framework for assessing treatment effects in extreme data to capture the causal effect at the occurrence of rare events interest. In particular, model extremities. We develop a consistent estimator for extreme treatment effects and present rigorous non-asymptotie analysis of its performance. We illustrate the performance of our estimator using both synthetic and semi-synthetic data.
employ the theory of multivariate regular variation
Introduction
We are interested in studying the effect of treatment e.g., different policies and drugs, on rare yet impactful events such large wildfires, hurricanes, tsunamis and climate change. These kinds of events happen at an extremely low frequency, but they can cause considerable damage to properties and pose serious threats to people's lives. For instance, may want know the effect of more
"Jyuaan Tan was partially supported by NSF Award IIS-2337916.
Jose Blanchet gratefully acknowledges support from DoD through the grants Air Force Office of Scientific Research under award number FA9550-20-145 10-01-09977--0000000000000001111 and ONR 1398311, also support from NSF via grants 2229012, 2312204, 2403007 is gratefully acknowledged.
Vasilis Syrgkanis was supported by NSF Award IIS- US3223391...
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

infrastructure investment or other kinds of precautionary policies on earthquakes. In many applications from financial risk to environmental policy it isn't enough know how treatment changes the average outcome; eerisionmmmaerss care about whether it alters the extreme tail. More formally, we may want to estimate the effect of treatment 1) on outcome Y, conditioning on some extreme events. Estimating this kind of effect can help policymakers evaluate the impact of policy and choose the best policy to reduce economic loss and save more lives when disasters happen.
Despite its clear importance, existing methods fall into two largely disconnected strands, each of which cannot fully address this question. One approach comes from the causal inference literature. Causal inference provides a comprehensive framework for counterfactual reasoning. Causal effect estimation is an important problem in this area, which finds wide applications in healthcare, education, business decision- decision-making, and policy evaluation. Classic causal inference literature mainly focuses on estimating the average effects among certain groups. Little attention paid to the causal effect on rare events. The scareity of extreme data makes inference more challenging than in classic settings. As result, naively applying classic causal inference estimation methods will produce poor results with large statistical error. For example, when making policies about earthquakes, we are usually unable to see a strong signal from historical data, as large earthquakes rarely occur and there are fewer samples in the dataset.
On the other hand, the Extreme Value Theory (EVT) studies the tail behaviors for statistical distribu- tions, which provides the ideal tools for analyzing rare events. However, this approach does not take the data structure into consideration. In particular, it does not accommodate counterfactual treatments or adjust for covariates, so it cannot tell us what would happen under an intervention.
To bridge these gaps, combine causal inference theory with EVT to provide novel framework for extreme effect measurement. Following researches in EVT Coles et al. [200]]. we use a multivariate regularly varying variable U model extreme events. The rare event can be modeled by the event [|| > 1} for large t. Our proposed estimand can be viewed as the Average Treatment Effect (ATE) conditioning on {|[6] 1) with rescaling as increases to infinity. Detailed definition and explanation can be found in Section 3. Estimation is challenging because the limiting tail distribution unknown and must be inferred from finite samples. To improve data efficiency and inference accuracy, we combine tail observations with moderate-frequene data in an extrapolation scheme, leveraging EVT insights alongside causal-inference techniques to achieve efficient estimation.
To the best of our knowledge, we are not aware of any work in the literature that considers this problem. In this paper, we take the first step to measure the treatment effect extreme events. To be more specific, our contributions can be summarized as follows.
1. We propose a measure for the treatment effect rare events named Normalized Extreme Treatment Effect (NETE), which essentially measures the magnitude of treatment on tailed events.
2. We develop two consistent estimators for NETE-a verse propensity weighting (IPW) estimator- by combining recent advances in multivariate
a doubly robust (DR) estimator and an in-
tall-dependence estimation Zhang et al. [2023] with double machine learning methodology
Chernozhukov et al. [2018), and derive finite saatee non-asymptotic error bounds.
3. Synthetic and semi-synthed experiments demonstrate good practical performance of our proposed estimator as compared to baseline estimators adapted from standard causal inference literature.
We briefly review some relevant literature in EVT and causal inference. Coles et al. (200T) provides a comprehensive introduction to EVT. A large amount of work focuses on the univariate setting Davison and Smith [1990), Leadbetter [199]] Pickands III (1975). Smith 1989 Recently, there have been many recent works on the multivariate generalization of these results Avella-Medina et al. [2022]. Zhang al. [2023. Causal effect estimation is a classical problem in
Related Work
causal inference |Rubin| 1974). J. Common estimators include IPW [Rosenbaum and Rubin 1983 DR
methods (Bang and Robins, 2005| Kang and Schafer 2007] Chernozhukov et al. [016 2017 2018).
Targeted Maximum Likelihood Estimation (TMLE) |van der Laan and Rubin 2006]. There have been some efforts in the literature trying to combine the two research areas. Gissibl and Klüppelberg [2088) considers special kind of Structural Causal Model (SCM) and shows that the proposed SCM is a kind of max-linear model. They also analyze the asymptotic distribution of their model.
Chernozhukov and Du 2006). Zhang 2018 Deuber et al. [024] consider the task of estimating the

---

extreme Quantile Treatment Effect (QTE). Aloui et al. (2023), Bodik 2024] assume the outcome falls into the domain of attraction and define the extreme treatment effect as the difference between EVI. Huang et al. (2024) study the estimation of extreme quantile effect and extreme average treatment effect in the continuous treatment setting. The other line of work Gnecco al. 202T J. Mhalla et al. [2000].Bodik et al. [023] uses EVT to help causal discovery. However, we want to point out that the problems these works consider are quite different from our setting. The most similar setting would be extreme QTE estimation Chernozhukoy and Du 2006), Zhang [2018). Deuber et al. (0024), but the QTE still cannot capture on how the expectation of the outcome changes under intervention. While all the previous work models extreme events using univariate variables, we model it using multivariate regularly varying variables. Moreover, our work can also be placed in the broader context in the literature that studies causal effects of treatment beyond the mean, for example, distributional effect
Abadie 2002), Gautier and Hoderlein [201]] Hohberg et al. [2020), Ratio- and Log-Ratio-Bass
Effects Cole and Hernán [2002], WanderWeele 2013), CATH Shalit et al. [2077]. Wager and Athey
2018
Abrevaya et al. 2015].
2 Preliminary
Causal Inference. We use the potential outcome framework Rubin 1974 in this paper. Let W, D,Y Y be the covariate, binary treatment and outcome, respectively. We denote (d)) to be the potential outcome when the treatment is set to be d and assume consistency i.e., ((D) Y throughout the paper. The Average Treatment Effect (ATE) is defined as
ATE (1) (O)).
The ATE measures the effect of a treatment on the outcome Y. In the policy-making making example, D is an indicator of whether to use the policy or not. W is a covariate that may influence D. like the geographic features of place, which will influence the local government's 's decision on policies, and Y can be the economic loss. The ATE in this case provides information about how much loss can be saved a policy is enforced. Under the following exogeneity and overlap assumptions, the ATE can be identified using the g- g-formula [ IW, D 1] E[Y[W, D = OJ].
Assumption 2.1 (Exogeneity). The data generation process satisfies (L), (0)) T D W.
Besides, the following overlap assumption is also often needed for non-asymptotic analysis. Assumption 2.2 (Overlap). There exists constant Cp E 1/2) such that the propensity score p(w)= = P(D = 1 W = w) [cp. 1 opl, Ve W.
This assumption ensures that there no extremely high or low propensity, which can make estimators unstable.
The study of extremity mainly concerned with the tail behaviors of heavy-tailed distributions, which are often modeled by the regularly varying distributions. In this paper, we modeled extremity by multivariate regularly varying distributions.
Extreme Value Theory.
Definition 2.3. A random variable U R is called regularly varying with index 8 oo) if for any norm ||- || in IRd and positive unit sphere S+ {ar R4. ||ж||| 1}. there exists probability measure 5.) on S+ and a sequence bn -> no such that n (([[[ (l),,, U/([U])) E) " cU U3 x S for some constant cy > 0, where x . is the product measure and (rr((, oo)) = r for all r > 0.
The parameter = 1/3 is called the Extreme Value Index (EVI), which characterizes the decay rate of the tail. Notice that this definition implies that as b, + co, the norm of and ||U|]| and its angle U/|[U]] become asymptotically independent. We will leverage this fact for estimation in later sections. A typical example of regularly varying distributions is the Pareto distribution.
Definition 2.4. The density of Pareto (type II) distribution with index B (0, 00) is f(x) 3(1 ()1+z)-(8++) Va 0.
Definition 2.3 implies that the rescaled norm of regularly varying variable is asymptotically a Pareto distribution.
Notations. In the rest of the paper, we use || || and || || as a shorthand for normm. We use the asymptotic order notation o(-), and (-)). We use E[:] to represent expectation. For matrix
3

---

A, we denote A to be its i-th column. Unii[[a, b]) is the uniform distribution on interval [a, bj and Ber(p) is the Bernoulli distribution with expectation p. represents the independence relationship between two random variables.
3 Treatment Effect on Extreme Events
3.1 Extreme Semi-parametric Inference
While standard causal estimands capture average effects of D on Y, they obscure what happens in the tails-iic when rare, high-impact events occur. To address this, we model rare events with an explicit extreme factor U. The data we consider is of the form {(X,, D.. Y,, U where D, and Y are as defined in Section 2 W = (X, U) is the covariate, is the extreme part of the covariate. We use || to model the severity of rare events-larg norms indicate more extreme realizations. For example, in a hurricane-loss application, U might the vector of maximum wind speed, rainfall, and storm surge; X the region's location; D the level of infrastructure investment; and Y the resulting economic loss.
In what follows, we introduce novel estimand that quantifies the causal effect of D on Y specifically in the tail region defined by large ||U|] We then establish conditions for its identification under multivariate regular variation and propose two consistent estimators. We will make the following i.dd assumption.
Assumption 3.1. The random variables {(X,, Dr, Y,, U2) are i...d. Furthermore, U is regularly varying.
We are interested in the effect of treatment on the tail events of U. Similar to ATE, a naive definition of the extreme treatment effect would be
FTTE_ lim B[ - (() || > t], <
(3.1)
which is simply ATE conditioning on large ||U|| However, in the case of extreme effects, the outcome may be unbounded due to the presence of extreme noise. As t increases to infinity, this effect may increase to infinity, making this quantity meaningless. Considering the climate change example, is possible that dramatic climate change will damage even destroy human societies, causing the effects of some policies to explode even though the policy can effectively reduce losses and slow down the process. Fortunately, regularly varying distributions have the nice property that as t increases to infinity, ||/t ||U|| > t converges weakly to the Pareto distribution (See Definition (..3) Inspired by this property, characterize the growth of this quantity, we introduce the following polynomial growth assumption.
normalize the quantity (1) Y()) || > by its growth rate. To
Assumption 3.2 (Asymptotic Homogeneous Property). We assume that the covariate X is bounded, i.e. ||X|| < R. Let f(X, D, U) = E|y X, K,D.U. U]. There exists L-Lipschitz continuous function g(x, d, u) and a function e(t) F R$ that satisfies lim e(t) and
[xx, d, tu) g( d, w)l < e(t), Va E BR, u E Sd-11 ta
This assumption characterizes the growth of the outcome with respect to the extreme noise. In many real-world examples, this assumption is satisfied. For instance, research show that landslide volume often follows power-law relationship with rainfall intensity Tuganishuri al. [2024]: the economic loss caused by hurricanes scales polynomially with the maximum wind speed Zhai and Jiang (004)).
In these cases, f grows polynomially with respect to ||O'] and e(l) 0 exactly. We define the Normalized Extreme Treatment Effect (NETE) as
Y1) - (())
NETE
lim E
|0
(3.2)
ta
where a is known index in Assumption 3.2
from prior knowledge. Note that the previous definition
(.I. is special case of (3.2) when = 0. The intuition for the scaling factor t" is that under
Assumption 3.2 E is of the order ([( and (3.2) is of the order ((E((UU]) /11) |U >
t)). which is finite if a < B. (3.2) implies that for a large threshold 4, we have ( Y ~
NETEETE Therefore, NNETE measures the influence of treatment on the susceptibility of outcome
with respect to extreme noise U.

---

We want to remark that NETE naturally sits at the nexus of two well-studied strands of work, tail- conditional expectations in EVT, and average effects or distributional shifts extreme quantiles. e.g., ATE and QTE. NETE can be understood as a causal analogue of EVT quantity R[Z/t] Z > 1]. where Z is regularly varying variable. It generalizes ATE to the setting of extreme events and aligns with the growth rate given by EVT.
3.2 Extreme Effect Identification and Estimation
The estimand (.2 designed to measure the treatment effect under extreme events, i.e., extremely large ||/|]| In practice, there may only be small fraction of extreme samples in the dataset, which creates difficulties for statistical inference. To efficiently estimate the NETE, we leverage the asymptotic independence property of regularly varying variables (See Definition 2.3 to derive novel identification formula. In particular, we have the following decomposition.
(1) (O) |00|
1(X,1,0) - [(X,0,U)
lim E
1
lim E t-000
|| 1
(3.3)
1-000
1a
S(X, 1,U) /XX,0,0)
(|
lim E t-000
||
|
||U||]
= lim
E
- 9(X,0,
||0l|
>
1000
(3.4)
where we use Assumption 3.2 in the third equality. We can prove that the above quantity equals to
lim 1-00
oxx,,, ||l|| t] lim B|| /t" ||U|| > tl.
The first factor measures the average effect of treatment across different directions, while the second factor only depends the norm of the extreme noise, which can be estimated via standard techniques in extreme value theory. We summarize the identification formula in the following proposition.
Proposition 3.3 (Identification). Suppose that U multivariate regularly varying and Assumption 2.1
2.2 3.1
3.2 hold, we have
NETE
lim 20
ox | ||'l|| > f) Jim B[I 1-50
| > t].
Proposition 3.3 separates the estimation of NETE into parts, the expectation of the spectral measure and the index estimation, which facilitates the estimation. While in theory naive identification (3.3) works as well, we found that in practice (3.3) performs poorly (See Section for empirical experiments). One reason is that without properly scaling, the (3.3) suffers from exploding ||U|] [|. causing larger estimation errors.
Inspired by this decomposition, we estimate the two factors separately. To make our framework more flexible, allow approximate scaling exponential a, as input in Algorithm I 0n can be obtained from some prior knowledge or via other heuristics. For the first factor, we design two estimators, the Inverse Propensity Weighting (IPW) and the Doubly Robust (DR) estimators. To derive the estimators, we first randomly split the data into equal halves and use the first half for nuisance estimation, i.e., propensity and outcome. Note that the domain of the propensity function is unbounded due to the presence of U. Generally, it is difficult to estimate such a function given scarce data in the tail. To bypass this barrier, we make the following independence assumption.
Assumption 3.4. (Independence) The extreme variable U is independent of D, X, i.e., U L.
Under Assumption 3.4 only X affects treatment assignment. We use the first half of data to regress (X, D, estimation of the propensity function P. Then, we use the second half for estimation. The IPW and DR estimators are defined in (3.5) and (3.6p, respectively.
D,U, U/ [D] on U/I a to get (normalized) pscudo-outcome and regress X on D to get an
Notice that the second factor is the a-moment of the random variable ||]]/ ||]] > (, which converges weakly to a Pareto distribution as / increases to infinity. Therefore, this quantity equals to the a moment of standard Pareto 1/(1- - a7) and the problem can be reduced to estimating the EVI of an asymptotic Pareto distribution. Here, we use the adaptive Hill estimator in (37 from
5

---

Algorithm Algorithm for NETE Estimation
Require: Dataset D {Xx, Di, Y, Ut) threshold 6, exponent estimation on, estimator
1: Randomly split D into two equal parts D1 and D2
2: Using D1, estimate:
a. Propensity function ((z) via regression D on X and clip the output of p(z) to the interval (c, 1 cl.
b. Pseudo-outcome regression ((z, d, by regressing Y/1|Uj on (X, D. U/
3: Define index set I {i: || i, (X,, De, Y1, U;) E D2) and set S. Ut/[[U for E
4: if estimator IPW then
5: Compute
Dj
1-D;)
JPW
S
1 1 p(X,))
(3.5)
I
p(X,)
AE
6: else if estimator = DR then
7: Compute
D; - ((X)) ((x,) p(X:))
DD Tntt
(Ys/11,,1 aT nn -Xx, D,, S.)
(3.6)
8: end if
9: Compute adaptive Hill estimator on {||U:|| i Z}:
1 h j=1
W [U
An 1
io 7kk)
log
(3.7)
where [|U 2 ... (1)( and & is chosen by
k max kE tIa n) and Vi E (la,... ,n), 7(k) 2(0m()))
Vi
10: return Festimator restimator
Tn.
n,
Boucheron and Thomas 2015), which provides a data-driven method for choosing the threshold.
Putting the two estimations together, we get our estimator of the NETE 0; n. superscript can be DR IPW. We summarize
Tn Paa where the
estimators in Algorithm [
Remark 3.5. Assumption 3.4 may not always hold in practice. The identification formula (??) still holds regardless of Assumption 3.4 When the assumption violated, the propensity score based method cannot be applied here. In this case, better estimators may be simple plug-in in estimator or the DR estimator since they do not require accurate propensity estimation.
Remark 3.6. The identification formula Proposition 3.3 and estimation methods can be easily extended for CATE estimation. We will discuss the extension in the appendix.
3.3 Non-asymptotic Analysis
Up to now, we have worked under very mild regular variation and asymptotic homogeneity conditions, which suffice to prove the consistency of our two-step estimator in the limit n, - 30. However, to obtain non coo--on-aan non--nnn-nnnnnnn non-asymptotic, finite-sample deviation bounds for both the spectral-measune term and the tail-index term. we must invoke more structured tail model. particular, existing results such as those in Zhang et al. 2023 rely on the fact that, beyond regular variation, the noise vector behaves exactly like (possibly linearly transformed) Pareto distribution. Although this is admittedly stronger than mere second-orde regular variation, it is at present the only framework in which we can directly apply sharp concentration incqualities and Wasserstein-distance bounds for spectral-meaaure estimation. We therefore make the following Pareto-type assumption.
Assumption 3.7. We assume that the distribution of U comes from the following class of models
M U My:

---

where M4 { the components Z is
: U = AZ, for A E A and ((2) E Mc). The set of possible distributions for
Z admits (Lebesgue) density h
(2))in B+
((Z): h(=)-8" I1 (1+2,)
<
E V2
8th II= (1+z.)
1(2) 0c II + (0-1)1911111 if |
> çk #
and the set of possible matrices A is
A= { A :1 min AAila & max |A S and JA20 g
Throughout, assume the constants satisfy m 2 2, 0 0 < < 1, and Ç >> 0.
u < 1/2,0 0.
This assumption states that the extreme variable is linear transformation of an approximate Pareto distribution. The parameter s measures how close Z is to a standard multivariate Pareto distribution. A small means the distribution is far from Pareto.
With these assumptions, we are ready to state our main theorem, which gives a non-asymptotic rate to our estimand.
Theorem 3.8. Suppose that Assumption 2.1 2.2
3.2 3.4 3.7 hold, a B, where a and / defined in Assumption 3.2 and Assumption 3.7 respectively. Furthermore, for any fixed t, with probability at least 1 5,
lp(X) p(X) & (n, 8), ann -a & RR(n, | X, X. |U > - D,, < (n;,,
where ni+ -!-//1 I[ > 1) and Ryp Rg: R. are estimation emrors that are monotonically decreasing with respect to sample size. Then, n > @(log(1/0)t)), with probability at least 1 8,8 E (0, 1/2), we have
OUR NNETE < <Olv ()
8/2 1/2 log(1/0)) 10/ 11((++)))
+t min(1.0) 90/ (n) ec())
(3.8)
and
@IPW
GNETE
((RR(n/226)
8/2n 1/2 log 1og 11(2+0)
+ + mim + B5/(1111120 + log (n, 8) e()).
(3.9)
variance f3/2n 1/2 The error bound (3.6) consist of the nuisance error (n EVI estimation error (1))) 1))2+()) error Ra (n. 8) and bias terms t- min (1,9) +t 8s/(1 (1x))- e(t). Similar pattern holds for 3.9 Given this general result, we choose the threshold in data- driven way to obtain better rate. The idea is to use the estimated index to balance the bias and variance terms in 3.8) and (3.9. The following corollary gives the convergence rate in different regimes.
Corollary 3.9. Under the assumptions of Theorem 3.8 further suppose that [n, (log(1/6)n -1/3), R2,,, 8) @(log(1/0)n 1/2), Ra (n, ((log(1/6)) )0)),))))))))..)
some Co > 0, the following conclusions hold.
1. If s (0. 1/(2 maxx(1,8)), takes t, e(n with probability at least 8, we have
ODR
DEET =((e(t..) + n. (aggloog11/) log(n) log(1/5)).
2. If 8 E [1/(2 + max (mxxx1111 1,8,),1/2), takes f ((nn with probability at
least we have
@DR NETE O(e(t,)) + 111(2mmmxx log(1/8) log(n)) log((/)))
7

---

Similar results hold for the IPW estimator. Due to limited space, we leave the result for IPW in the appendix. Many common machine learning algorithms, e.g., Lasso. logistic regression, neural networks, can achieve On rate in the assumption of Corollary 3.9 We want to highlight that if e(t) decays fast enough and become negligible compared to the other term and we know the correct scaling exponential a, Corollary 3.9 matches the rate of [Zhang al. 2023 Theorem 3.1] without prior knowledge on the index / in the Assumption 3.7 Besides, if we have additional prior knowledge on e(t) and Ca. we can adjust the choice of threshold
achieve better rate.
Remark 3.10. When the extreme noise is I-dimensional, the spectral measure is trivially 8(1) and there is no need to estimate the spectral measure. Following a similar argument Theorem 3.8 and Corollary 3.9 we can obtain a convergence rate of (ee(t,) + log(1/ -//(2=(((+++)))) + (log(1/))m) Cw).
Remark 3.11. Assumption 3.7 may seem restricted at first glance. This assumption is used here because the non-asymptotic result for regularly varying extreme distributions is rare in the literature and the goal of this paper is not to develop a new estimator for the spectral measure. To the best of our knowledge, Zhang et al. [023] is the only paper that gives such a result under Assumption 3.7 In fact, Assumption 3.7 proof. (1) The extreme noise U is regularly varying and its norm ||(']] satisfics the von Mises condition in BBuuchron and Thomas (2015). (2) There exists upper bound for the bias term [[[[(U[||[]
be easily replaced by the following two assumptions in
| > - lim,- E[/(U/|(U]) | > t] & O(t*)), for some constant Co for fixed Lipschitz function We leave this generalization to future work.
4 Experiments
Having established in Section 3 that under our regularity and overlap assumptions the DR- and IPW-based extreme treatment estimators enjoy provable non-asymptotic error bound, we next evaluate their finite-sample behavior and compare with our estimators with naive estimators that does not consider the regularly varying structure. In what follows, Section 4.1 presents purely synthetic simulations with known NETE. Section 4.2 then moves to a semi-synthetic setting-using real noise from wavesurge datasets- assess practical performance under realistic complexities.
4.1 Synthetic Dataset
The data generation process we use in this subsection is
X Unif([O, 1)9), D Ber(p(X)), where p(x) = 1/(1 + +xp((=x())
Y = | (D + U/||0|| + E) + ||U]]|// (/0/)/////.--- Unif(-u,
where > constant and b N A Unif([1, 2(dx).))) We consider two ways of generating the extreme noise. The first one follows Assumption 3.7
Z (Z1, Za.): 2, ~ Pareto(3), U AZ, A Rd.
We also consider a Pareto mixture, i.c., U = (U1, -.. .U,,,, U, ~ 0.5Parcto (3) + 0.5Pareto + 1). Note that Assumption 3.2 is satisfied with e(t) = t-a/2 By Proposition 3.3 we can calculate the ground-trun -ruth effect. The graph below shows the Mean Square Error (MSE) with our estimator using different sample sizes. We take different values for a, 8 in the experiments. In this case, by Proposition
3.3 we know that the ground-trute -ruth NETE is 11(1 aB)) We use Mean-Sop Saaun--qure--iiie Error (MSE). B[(e f ( to measure the error. As a baseline, we compare our estimator with naive IPW and DR estimators. Naive-IPW simply applies the standard IPW estimator the U; that has norm larger than threshold I, ignoring any tail-index modeling. Similarly, Naïve-DR augments it with the usual doubly-robust correction term but likewise ignores the Pareto structure. We leave the detailed math formulation of the baseline estimators to the appendix. The thresholds rule in Corollary 3.9 is used in the experiments and we use the same threshold selection rules for all estimators. We estimate the scaling exponential a by doing linear regression log() Y|) ~ log([[(: []) and use the coefficient of log([[U[]) as á, We leave the experiment details to the appendix. Fig. I and Fig. 2 show the experiment results. In the following, we use EVT-IPW and EVT-DR to represent @1PW and @DR in Algorithm
n,t
Figure and Fig. show that under different configurations of a, B, duy dz. our estimators generally perform better than the baseline estimators. The reason is that our estimators can make better
8

---

241 9-13 1.0R0.00
241, p-15 0,0033 4
C/00
180
180
780
3500
198
200
400
5-2.5.
5,245
447
180
1303
2003
2000
2000 2500
1006 12:00
20.00
2000
2003 3509
4003
Figure Experiment results of four different configurations when the extreme noise is linear transformation of Pareto variables. The configures of upper left, upper right, lower left and lower right a, B, dz, du (1, 1.5, 50, 10), (1, 1.5, 30, 5), (1,2.5, 30, and (2, 2.5, 30, 5) respectively. The results are averages of 50 repeated experiments. We use EVT-IPW and EVT-DR to represent @IPW and 0DR in Algorithm n,t
use of the regularly varying structure. In general, EVT-DR achieves the smallest MSE in most experiments and robust under different configurations. Note that the Pareto mixture does not satisfy Assumption 3.7 Fig. shows that our method still maintain good performance even if Assumption 3.7 is violated. We also observe that sometimes the MSE increases with more samples in Fig. 2 An explanation for this is that violation of Assumption 3.7 causes the threshold selection rule Corollary 3.9 not to applicable and the variance term dominates the error.
4.2
Semi-synthetic Dataset
Now, we use the wavesurge dataset Coles et al. 2001 to create a semi-synthetic dataset for our experiments. The wavesurge dataset has 2894 data points, which contain wave and surge heights at single location off south-west England. Since wave and surge heights are not in the same scale and may not be positive, we shift the data and normalize each dimension by its 10% quantile. Given the wavesurget dataset, we generate our semi-synthetic dataset in the following way.
X ~ Unif(0. 1), Ber(p(X)), where p(z) 1/(1 exp(-=Tb)), (1 D)Wa gaz (O, 1),
(4.1)
where W and S are the height of the wave and surge, respectively. In this experiment, we evaluate how well our proposed EVT-based estimators recover the Normalized Extreme Treatment Effect (NETE) when only limited "short-term" data available. We split the dataset into training set (1,000 observations) and test set (1,894 observations). First, we estimate the NETE on the training set using four estimators. Next, apply the identification formula from Proposition 3.3 together with ( to obtain a high-fidelity estimate of the NETE on the test set. Because the test-set estimate leverages additional data and the correct tail model, treat it surrogate "ground truth" for comparison. The woal-world implications of this experiment is that we can use some short-term data (the training set) predict long-term and unobserved behavior (the test set).
Table shows the results we get using different estimators. The results show that our EVT-IPW and EVT-DR give estimations that are closer to the test-set estimate than the naive estimators. In particular,

---

Bel: Bad FandO)
Ex Jel Pendh 54
MIC CoMMERE
1200
2403
20.0
2000
21.0
4000
2700
EV-00
EXTOR
Rave
Loneereee OPhen
1300 1200
2000
2003
2003
2000 40.00
30.8
4.000 2000
Figure 2: Experiment results of four different configurations when the extreme noise is Pareto mixture. The configurations of upper left, upper right, lower left and lower right are a, B3 du (1, 1.5, 10), (1, 1.5, 5), (1, 2.5, 5) and (2, 2.5,5 respectively. The results averages of 50 repeated experiments.
the naive estimators consistently overshoot the true NETE by an order magnitude. In addition, while more extreme tail configurations (e.g. (1,3)) slightly increase variance, the EVT-based methods remain stable, with EVT-DR deviating by at most 0.3 from the test-set estimate. These findings demonstrate that incorporating multivariate extreme value structure via our EVT-IPW and EVT-DR estimators substantially improves finite-sample estimation of treatment effects on rare, tail events, compared both naive methods.
Table 1: Causal Effect Estimates
(2)
EVT-DR
EVT-IPW
Naive-DR
Naive- IPW
Test-set Estimate
(2, 2)
0.18
0.25
41.93
27.34
0.13
(1, 3)
0.43
0.44
17.04
15.68
0.13
(2.5, 1)
0.13
0.18
31.64
26.06
0.20
(1.5, 1.5)
0.26
0.23
7.91
9.46
0.20
5
Conclusion
In this paper, tackled the challenge of estimating treatment effects on rare, high-impact events by combining causal inference with extreme value theory. We introduced a new estimand capturing how interventions shift the tail average of outcome distributions and derived simple identification formula using the spectral-maan magnitude decomposition of multivariate regular variation. Based on this, we proposed IPW and DR estimators with non-asymptotic error bounds under Pareto-type tails. Simulations and real-data experiments confirmed their advantages over naive estimators when targeting extreme outcomes. This work opens the door to more refined causal analyses in domains such as disaster risk and finance, where tail behavior matters most. A current limitation is our heuristic estimation of the tail index at future work will focus on theoretically grounded estimation of a and adaptive threshold selection.
10

---

References
Alberto Abadie. Bootstrap tests for distributional treatment effects instrumental variable models. Journal of the American statistical Association, 97(457):284 292, 2002.
Jason Abrevaya, Yu-Chin Hsu, and Robert Lieli. Estimating conditional average treatment effects. Journal of Business & Economic Statistics, 33(4))485-500, 2015.
Ahmed Aloui, Ali Hasan, Yuting Ng. Miroslav Pajic, and Vahid Tarokh. Treatment effects in extreme regimes, arXiv preprint arXiv:2306. 2023.
Marco Avella-Medina, Richard A Davis, and Gennady Samorodnitsky. Kernel pea for multivariate extremes. arXiv preprint arXiv:2211.13172. 2022.
Heejung Bang and James M. Robins. Doubly robust estimation in missing data and causal inference models. Biometries, 61(4):962-97) 9933, 2005, doi: 10.111 -4400.0422200000000
Nicholas Bingham, Charles M Goldie, and Jef Teugels. Regular variation, volume 27. Cambridge university press, 1989.
Juraj Bodik. Extreme treatment effect: Extrapolating causal effects into extreme treatment domain. arXiv preprint arXiv:2403. 10003, 2024.
Juraj Bodik, Zbyněk Pawlas, and Milan Paluš. Causality in extremes of time series, August 2023.
Stéphane Boucheron and Maud Thomas. Tail index estimation, concentration and adaptivity. 2015.
Victor Chernozhukov and Songzi Du. Extremal Quantiles and Value-at-Rine Riskk, May 2006.
Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo, Christian Hansen, Whitney Newey, and James Robins. Double/debiased machine learning for treatment and causal parameters. arXiv preprint ar arXiv: 1o0::::68000000 2016.
Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo, Christian Hansen, Whit- ney Newey, and James Robins. Double/debiased machine learning for treatment and structural parameters. Technical Report 23564, National Bureau of Economic Research, 2017.
Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo, Christian Hansen, Whit- ney Newey, and James Robins. Double/debiased machine learning for treatment and structural parameters. Econometrics Journal, 21(1):C1-C68, 2018.
Stephen R Cole and Miguel A Heránn. Fallibility in estimating direct effects. International journal of epidemiology, 31(1):163-163 2002.
Stuart Coles, Joanna Bawa, Lesley Trenner, and Pat Dorazio. An introduction to statistical modeling of extreme values, volume 208. Springer, 2001.
Anthony C. Davison and Richard I.. Smith. Models for exceedances over high thresholds. Journal of the Royal Statistical Society Series B: Statistical Methodology, 52(3):393 425- 1990.
David Deuber, Jinzhou Li, Sebastian Engelke, and Marloes Maathuis. Estimation and Inference of Extremal Quantile Treatment Effects for Heavy-Taile Tailed Distributions. Journal of the American Statistical Association, 119(547):206-22116 July 2024, ISSN 0162-1459, doi: 155001 0023.2252141
Dylan Foster and Vasilis Syrgkanis. Orthogonal statistical learning. The Annals of Statistics, 51(3): 879-908, 2023.
Eric Gautier and Stefan Hoderlein. A triangular treatment effect model with random coefficients in the selection equation. arXiv preprint arXiv: 109.0362, 2011.
Nadine Gissibl and Claudia Klüppelberg. Max-linear models on directed acyelic graphs. Bernoulli, 2464 2720, 2018. doi: 10.3155/11-BBF9411 URI. httpp:://oot http::::///ooo./////// wwwg/0.g.0000 3150/
17- J941

---

Nicola Gnecco, Nicolai Meinshausen, Jonas Peters, and Sebastian Engelke. Causal discovery in heavy-tailed models. The Annals of Statisties, 49(3) 2021.
Maike Hohberg, Peter Pütz, and Thomas Kneib. Treatment effects beyond the mean using distribu- tional regression: Methods and guidance. PloS one, 15())e0226514, 2020.
Wei Huang, Shuo Li, and Liuhua Peng. Estimation and inference for extreme continuous treatment effects. Journal of Business Economic Statistics, pages 1-26, 2024.
Joseph D.Y. Kang and Joseph L. Schafer. Demystifying double robustness: A comparison of alternative strategies for estimating population mean from incomplete data. Statistical Science, 22(4):523-539 2007. doi: 10. 00.121407--SS2211
M. R. Leadbetter. On a basis for 'Peaks over Threshold' modeling. Statistics & Probability Letters, 12(4):357-362, October 1991. ISSN 0167-7152. doi: 10.1016601667--1122119900077
Linda Mhalla, Valérie Chavez-Demoulie and Debbie Dupuis. Causal mechanism of extreme river discharges in the upper danube basin network. Journal of the Royal Statistical Society Series C: Applied Statistics, 69(4):741-764, 2020.
Quang Huy Nguyen. Tail distribution of the sums of regularly varying random variables, computations and simulations. PhD thesis, Lyon 1, 2014.
James Pickands III. Statistical inference using extreme order statistics. the Annals of Statistics, pages 119-131, 1975.
Paul Rosenbaum and Donald B. Rubin, The central role of the propensity score in observational studies for causal effects. Biometrika, 70(1):411535 1983. doi: 10. 10.1093/biomet/70.1. 1.44.
Donald B. Rubin. Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66(5):688 701, 1974. doi: 10.1037/h0037350.
Uri Shalit, Fredrik D Johansson, and David Sontag. Estimating individual treatment effect: general- ization bounds and algorithms. In International conference on machine learning, pages 3076-3085. PMLR, 2017.
Richard L.. Smith. Extreme value analysis of environmental time series: An application to trend detection in ground-level ozone. Statistical Science, pages 367-377, 1989.
Fangzhou Su, Wenlong Mou, Peng Ding, and Martin J Wainwright. When is the estimated propensity score better? high- nigh-dimensional analysis and bias correction. arXiv preprint arXiv:2303.17103 2023.
Jérémie Tuganishuri, Chan- Young Yune, Manik Das Adhikari, Seung Woo Lee, Gihong Kim, and Sang-Guk Yum. Prediction of volume of shallow landslides due to rainfall using data-driven models. Natural Hazards and Earth System Sciences Discussions, 2024:1-26, 2024.
Mark J. van der Laan and Daniel Rubin. Targeted maximum likelihood learning. International Journal of Biostatistics, 2(1), 2006. doi: 10.2202/1557-4479.000
Tyler Vander Policy-relevant proportions for direct effects. Epidemiology, 24(1):17--176 2013.
Stefan Wager and Susan Athey. Estimation and inference of heterogeneous treatment effects using random forests. Journal of the American Statistical Association, 113(52)):128-1142) 2018.
Alice R Zhai and Jonathan H Jiang. Dependence of us hurricane economic loss on maximum wind speed and storm size. Environmental Research Letters, 96))064419, 2014.
Xuhui Zhang, Jose Blanchet, Youssef Marzouk, Viet Anh Nguyen, and Sven Wang. Wasserstein- based minimax estimation of dependence in multivariate regularly varying extremes. arXiv preprint arXiv:2312.0980 12.06622. 2023.
Yichong Zhang. Extremal quantile treatment effects. The Annals of Statistics, 46666):3707-3740 December 2018, ISSN 0090-5364, 2168-8966. doi: 10. 10.1214/17A0OS1673
12

---

1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification:
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.
2. Limitations
Question:
Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification: Limitation is discussed in the conclusion section in the appendix.
Guidelines:
The answer NA means that the paper has limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g.. independence assumptions, noiseless settings, model well-specification. asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what implications would be.
The authors should reflect the scope of the claims made, e.g., if the approach was only tested on a few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution low or images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and faimesss
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community. Reviewers will specifically instructed to not penalize honesty concerning limitations.
3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
Answer: [Yes]
Justification: Proofs given in the appendix.
Guidelines:
13

---

The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced the statement of any theorems.
The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged provide short proof sketch to provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should properly referenced.
4. Experimental result reproducibility
Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided not)?
Question:
Answer: Yes]
Justification:
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is a dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution
specific model and empirical evaluation, may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access the model. In general. releasing code and data often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
While NeurIPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) the contribution is primarily a new algorithm, the paper should make it clear how reproduce that algorithm. (b) If the contribution is primarily
model architecture, the paper should describe the architecture clearly and fully.
(c) If the contribution is a new model (e.g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome describe the particular way they provide for reproducibility, In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material?
Answer: [Yes]
Justification:
The code will be provided in the camera-ready version.
14

---

Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurIPS code and data submission guidelines (https://nips.co cc/
muuldes/CodeSummisee
for more details.
While encourage the release of code and data, we understand that this might not be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines (https: for more details.
/ //nips. wwtpcccppppcccccccccccc.ccccccle wttp://ccggiiee/eeeeeeeeeeeeeeee wwweeeomieesooooooooooooo
The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if' applicable).
Providing much information possible in supplemental material (appended to the paper) recommended, but including URLs to data and code permitted.
6. Experimental setting/details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification:
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented in the core of the paper to a level of detail that is necessary appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, as supplemental material.
7. Experiment statistical significance
Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Answer:[Yes)
Justification:
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by error bars, confi- dence intervals, statistical significance tests, least for the experiments that support the main claims of the paper.
The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, overall run with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call a library function, bootstrap, etc.)
The assumptions made should be given (e.g.. Normally distributed errors).
should be clear whether the error bar is the standard deviation or the standard error of the mean.
It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
15

---

For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out range (e.g. negative enror rates).
If error bars reported in tables plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables the text.
8. Experiments compute resources
For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
Question:
Answer: [Yes]
Justification: All experiments can be easily reproduced using laptop.
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.
The paper should provide the amount compute required for each of the individual experimental runs well estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make into the paper).
9. Code of ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurlPS Code of Ethics
Answer: [Yes]
Justification:
Guidelines:
The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special cireumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g.. if there is special consid- cration due to laws or regulations in their jurisdiction..
10. Broader impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [NA]
Justification:
This is mainly theory work.
Guidelines:
The answer NA means that there is no societal impact of the work performed.
If the authors answer NA or No. they should explain why their work has no socictal impact why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious unintended uses (e.g.. disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deploymentt of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinfornation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
16

---

The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional unintentional) misuse of the technology.
there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML).
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification:
Guidelines:
The answer NA means that the paper poses no such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper. properly credited and are the license and terms of use explicitly mentioned and properly respected?
Answer: [NA]
Justification:
Guidelines:
The answer NA means that the paper does not use existing assets.
The authors should cite the original paper that produced the code package dataset.
The authors should state which version of the asset is used and, if possible, include URL.
The name of the license (c.g., CC-BY 4.0) should be included for each asset.
For scraped data from a particular source (e.g., website). the copyright and terms of service of that source should provided.
assets are released, the license, copyright information, and terms use in the package should be provided. For popular datasets, haperswwthcode cwm/ datasets has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided. If this information is not available online, the authors are encouraged to reach out to the asset's 's creators.
13. New assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [NA]
Justification:
17

---

Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/moddl as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent obtained from people whose asset is used.
At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsourcing and research with human subjects
For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well details about compensation (if any)?
Question:
Answer: [NA]
Justification:
Guidelines:
The answer NA means that the paper does not involve crowdsoureing nor research with human subjects.
Including this information the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then much detail as possible should be included the main paper.
According to the NeurIPS Code of Ethics, workers involved in data collection, curation,
or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional review board (IRB) approvals or equivalent for research with human subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or equivalent approval/review based the requirements of your country institution) were obtained?
Answer: [NA]
Justification:
Guidelines:
The answer NA means that the paper does not involve crowdsourcing research with human subjects.
Depending the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurlPS Code of Ethics and the guidelines for their institution.
For initial submissions, not include any information that would break anonymity (if applicable), such the institution conducting the review.
16. Declaration of LLM usage
Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods this research? Note that if the LLM used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, or originality the research, declaration is not required.
Answer: [NA]
Justification:
Guidelines:
18

---

The answer NA means that the core method development in this research does not involve LLMs as any important. original, non non-standard components.
Please refer to our LLM policy /https://neurig: /ttp://pp.ccc//offfeeeee///////s for what should or should not be described.
19

---

A Proofs
A.1 Identification Formula
In this subsection, we derive the identification formula in Proposition 3.3
Proof. We first prove 3.4b. By Assumption 3.2
(1)) (())
T(X,1,U) - 1(X,0,0)
lim E 1000
|00 > t
lim E f-00
||0|
ta
ta
f(X, 1) - -) f(XX000)
|
lim E
||0||
>|
||/||a
(1411 a
lim E
(,(X,,,,
g(X, 0, U/I + 20(1))
|1|0
>
We next argue that lim,- B(([U]])()) ||0| > 11 =a/(8- - ax). We have
1] 1+ j, P((UUI)/)) > r |1 > 1) dr
E(((U))))) ||
+1+ P(IUII/>> > 1110) dr
PQIU >()
S aP([UI -rl)r=-dd dr
P[ > t)
Note that ||U||| is also regularly varying. By Potter's theorem Bingham et 1989
Theorem 1.56].
for any c > 0 and sufficiently large t, we have
P([IUII rt) P([UT) > t)
< 2r -++c
Take <> 0 such that - - 1, have for sufficiently large
S aP([UU|) > rt)r dr P([ > t)
$ 2 Sr or an dr < co.
Therefore, by the dominance convergence theorem,
B((|U(]//))* | |ll|| > f| +1+ / ar 0 ,0-1 dr = 3/(B - a),
which implies
lim (())((()))))))) ||U|| > t] 00 100
and 3.4 holds. We then verify the uniform integrability of function
h(U) Ex 1,, 1,U/((U g(X, O, U/ 1/I/0))))
Note that by Assumption 3.2 g is a continuous function on a compact set and thus is bounded by
some constant C > 0. We have
E(((U)) || > 4 < 2C | > 1].
We have proven that the Right Hand Side (RHS) converges constant as ( - co, which implies that El[A(U)] | [']]| > 1] is uniformly bounded. We conclude that A(U') is uniformly integrable. By the uniforr-integraabiiity convergence theorem,
(I1!1)
lim E. ( - (x,00 U/10,I
||U|| 1
Be (lgl (X, -
Ee Ee-el(g -
where is the limiting distribution of (|UII/, |0| independent property of regularly varying distributions (Definition 2.3
and we use the asymptotic
20

---

A.2 Non-asymptotic Analysis
To obtain a convergence rate for the estimator 0g we first analyze the rate of the two factors To and DR
Lemma A.1. Under Assumption 3.1 3.7 with probability at least - 6, for sufficiently large we have
((
[og((/00) 11
1/(2+-8)
h - 7m &
where 7 = 1/3 is the EVI U.
Proof.
We adopt the non-asymptotic analysis of the adaptive Hill estimator for EVI in [Boucheron
and Thomas 2015]. the paper, the author adopts an adaptive estimator, choosing &s to be
k = max k (In ... .nnand Vi . ... n). 17(() - < (0)
Well and (0) scales like (2o0((2/6) log(n)). First, we verify the where 7(1) = Σド log [aa
von Mises conditions Boucheron and Thomas 2015 under Assumption 3.7 Let F be the CDF of ||]] By Assumption 3.7
we know that
g(2) ca m
(1 + 23) --- 1|=111 > (211--0)/o
Note that
[() Cx m0
+ 23)
a-1
1c 11
& gk= & &.
a. [1:
21) -a-1
Let ...... 7m ~ am + -a-1, 3 c.((ma) - 1. Then, we verify the upper bound for the
von Mises function, i.e., suP&?t [n)] < x(P)) for some O, where 7) is the von Mises function.
(tt) = (1)
(A.1)
U(t) 8
1 ((()((())) 3'
(A.2)
where S(t) is the density function of Σ 0; By Nguyen 2014 Theorem 2.1], have that
when |0]] max;(a; (()((()))))
f(t) = C 8- (1 + D(1 - 1/3)6-1 +)(())). -
(A.3)
Then.
F(I) 1 1-) Ct 8 DI o 1)
and
U(t) = // ( DC- -(
(A.4)
Plug
A.3 and
A.4
into A.2)
we get
(t))
1/8
8(1 DC- ((113)) +
Therefore, the growth rate of the von Mises function bounded. By Boucheron and Thomas 2015)
with probability at least 8, we have
<0((
(118((28)) 1/(2+0) n
h 7al $0
21

---

Lemma A.2. Undet the assumption of Theorem 3.8 with probability at least - 6, we have
Mint - 1 & Oly (t 6) + 80 1/2 + + 1-min1,00) t (-Ba/(1-22) e(t) + (n, 6)).
Proof. Let
f(X,1,U)- - ((),00U)
nf E
|110
|1||0n
We have the following decomposition
7 <
n1'l 1n) 17..
The first term comes from the standard statistical error of DR estimator, while the second term is the bias term caused by the finite threshold. For the first term, by standard DML theory [Foster and Syrgkanis 2023 we have
DD
ni 1/2 1/2
where n4 En/² T(I > random variable. By Bernstein's inequality, with probability at least 1 - 8,
T4 nP([UU] t)/2 > O (log(L/0) + v /P[(|UU log(1/0)
Therefore, with the same probability, when n > ((log(1/0)t))
n > nnP([IUT] > 1) = O(ml-
and we have
1/' < ( ())( 11/2 -
(A.5)
where we use the monotonicity of Rp, Rg.
For the second term (the bias term),
f(X, 1, - f(X,0,U)
In nl
E
|||0| >t { $ E[g((X, 1, U/ o(X, O, -,
| ā.. S(X,1, U,) - -(X,0,,
E
1 90X.://000000X000/0/ | > $)
||/||0
+
|| > t]
((X,1,0) -0X,,,,) (1 (1-1070--.)) )]
+
E
|
< 2e( + [X 1, U/
-lg(X 1/ UI) 1001000000000//0000000000000/0/0 wtt.:////1100000000///0
9(x, 0(x,0,001000) |0l|| d]I.
+
E
f(X,1,0) - ((X,0,0)
(1-100106)) (1-
|1
|
where we use Assumption 3.2 in the last equality. By the error rate assumption in Theorem 3.8
B
f(X, 1,U) ((X,0,U) (11
| |10|>
< CE || |
||
|
= O(log(t) R, (n,
22

---

Since is L-Lipschitz continuous, the second term is upper bounded by Wasserstein distance L LL//jun) where Eyynon is the distribution of U/||0||| conditioning on |U| and Cuynun is its limiting distribution as f + oc. Therefore, we have
In vl < 2e(() + LW IWi Su/jjm) + ((lo(())Raa 6))
< (e( + (t min(1..) : 85/(112 + loa ()),
(A.6)
where we use [Zhang et al.
2023 Proposition 3. in the last inequality to upper bound the bias term A.S and A we get
Wi(Cu Lu/1o))) Combing
Ih 7/ < O 8) Pn, 8 1/2 + min(1.0) ---05/(1-20 + +e(t)
log(t) (n, 8)).
Lemma A.3. Under the assumption of Theorem 3.8 with probability at least we have
GPW 7 < ((R,(nn2.6)) 8 1/2 t- min(1,8) --- e(t).
Proof. Similar to Lemma A.2 we have the following decomposition.
77 & IPW
n + |n/ - 1//
Term Iny 1/ can be bounded in the same way as the proof of Lemma A.2 By [Su al. 2023
A.2
Theorem 1]. we have
M n & ((R,(n/2,0) n4 1/2) (RR((/22,8)
1 -1/2 Ro 6)).
The rest of the proof is similar.
Now are ready to prove Theorem 3.8
Proof of Theorem 3.8 Note that by the asymptotic independence property of regularly varying
distribution,
NETE
Thn 17 .1a] DDR Wh1t
|p||
7/ + 17 1in 14/.
(A.7)
By Lemma A.l and
A.2
with high probability, 7n and 1 bounded. Note that by Lemma A.1
PPn - 1l = an an
= =((ā, al 16 - > = 000og(11)) + R. 8))
1- ory
Therefore, by Lemma A.2 and (A.7).
@DR
NETE < Olv (p R, 8, +//2 - + log(118)) -1(24)) 1/(2+8)
1/2
+ t min(1,9)
+ B0/(122) log(t) R. (n, 8) + e(t)).
The bound for @IPW can be proven similarly.
Corollary A.4 (Convergence rate for IPW), Under the assumptions of Theorem 3.8 further suppose that
(n, 8) = (((og(1/0))~1)), R,,n, 8) ((log(1/0) Ro (n, 8) = ((lo(11/8) C0)),
for some
Ca 0, the following conclusions hold.
1. If 8 E (0, 1/(2 + max (mxx(1,,)))) takes b, (1((1-2)))), with probability at least 8,
we have
@Pw
NETE O(e(tn) +n (log(16)) + log(n) log (1/1))))
23

---

2. If s E [1/[2 max takes t = 6(nlfa//4+2mmnn with probability at least have
10 ONNTE = O(e((n) +
- 1 log(1/6) + n log(n) (og((/6)))
Proof of Corollar 3.9
By Theorem 3.8 and the enror rate assumption in Corollary 3.9 we have
0DR n,t
- ONETE
< (llog (Llog n Log(L/0)n=1//=-))
+1-min 35/(1 log(() (og(1/0)) -m e((()
O(log(1/6)) log
+ min + 3x/ + log(t) log 1og(1/0)n + c(t)).
I E (0,1/(2 + max(1, 3))), we have
oR - ONTTE
< 0(log(1/8))9mm 1og(110)) 11221)))
+ 11-0a/(1120)) + log(t) (og(16)) ((())
Takes in O(n(2-20)9a) we get
ntt... AN
(10og(10))(0220..m + 1/(2+3)
log(1/0)n
1/(2243
+ n 8.80 log(t) log(1/6) e(tn)).
(A.8)
By Lemma A.1 we have
17n 71 1r 1/31 O(log(1/0)n~112=-))
Therefore, 8 = + On 1/(2+))). Plug this bound into (.88 and we can get the results.
Similarly, if E [1/(2 + max ()), 1/2), have
ODR NEEE
< O (llog(1/66))2/ -1/2 1/2 log(1/0))
min(1.8) log(t) log(1/5) -a + =(()).
Take 4,
we get the results.
B Experiment
In this section, we introduce some details our experiments and provide additional experiments regarding the sensitivity of the algorithm with respect the scaling parameter
B.1 Implementation Details
The two baseline estimators we consider are naive-IPW:
D3
1 D
Naw nut
Σ
Y
((X.)
1 1- -((()))
12m/2:110:|12
and naive-DR:
D. - x(X,) - -(X)))-((X,,00 G(X,, ( (X- D;, D,, U:))
-aive-DR DR Nn.
Σ
12//2:|10: St
where Ei=
2n=11/2++1 U(I > 1) and ((X) and 7(-) are the estimated propensity function and the outcome function respectively. The nuisance estimation of g is obtained by running regression (X, D.U). We clip the propensity to [10-4, 10-4] to ensure overlap assumption (Assumption 2.2
Unif([-1, 1J) in the data generation in synthetic experiments. We use sample splitting our experiment, using the first half for nuisance estimation. In the experiment, we use the same threshold t for all estimators, which is given by Corollary 3.9 To choose the threshold,
24

---

first use the adaptive Hill estimator Boucheron and Thomas 2015 to get an estimation of EVI Pre and then set the threshold to be f 0.25m (2/(1+2 mmm[1,7.)) as in Theorem 3.8 The approximate exponential a. coefficient of log( [|]] in linear regression log( Y ( ). For the adaptive
Hill estimator |Buccheon and Thomas 2015), we follow authors' choice for hyperparameters and
choose L, = r()) = Vlog log(n) and
k k: = min k -...-.. m) and Die
- 7()) 7() (6)
1,
vi
where 7(1) = = log |0 [[0)]
We logistic regression estimate the propensity function and random forest model the outcome.
For the semi-synthetic experiment, apply the same hyperparameter as above to estimate NETE. We shift the data to make it positive and normalize each dimension by its 10 % quantile. The Fig. shows the rough distribution of the wavesurge data after these transformations.
Scatter
height
Figure 3: The scatter plot of wavesurge data.
We now describe how we calculate test-set estimation in our experiments. By the data generation process,
Wai S
gNTE
lim E
|| t]
tor tag a S
lim E
|
f] i- (al 02)
ta2
where Proposition 3.3 in the second equality. We know the ground-truth on 02 and can estimate the EVI 7 using the test set. Suppose the estimated EVI is 7. we set the threshold to i, (5/(122 min and get estimation
Woi S
NETE best
E.
|10
[n]
(an + (2)
B.2 Additional Experiments
conduct additional experiments under same setup as in Section 4 Fig. and Fig. show the comparison of EVT-IPW and EVT-DR with and without ground-truth We can see that in most cases, their performance similar, indicating that our heuristic method for estimating a effective. Indeed, the heuristic approach even gives slightly better MSE.
25

---

5-13 5,0000
2-13
20
0-1, p-25 6.0-3 4,
312.. 202.3.22..0 d.00000 2,A4
12
Figure 4: Experiment results four different configurations when the extreme noise a linear transformation of Pareto variables. The configures of upper left, upper right, lower left and lower right are a, B, d2, du (1, 1.5, 50, 10), (1, 1.5, 30, 5), (1, 2.5, 30, 5) and (2, 2.5, 30, 5) respectively. The results are averages of 50 repeated experiments.
e-). Bet ceNOOL
pel3 caedi
VCc Eeteeenn Jtot.
2003
Figure 5: Experiment results of four different configurations when the extreme noise Pareto mixture. The configures of upper left, upper right, lower left and lower right are a, B, dz, d, (1, 1.5, 50, 10), (1, 1.5. 30, (1, 2.5, 30, 5) and (2, 2.5,300 5) respectively. The results are averages of 50 repeated experiments.
26

---

C Extension: Extreme Normalized Heterogeneous Effect Estimation
Proposition C.1 (Identification). Suppose that U multivariate regularly varying and Assump- tion 2.1 2.2
3.1 3.2 hold, we have
gENETE
(z)
lim Blg(2, 1, 1 - g(z, 0, 0/U//1) || t) lim / |0 t). t-oc
7000
Proof.
The proof similar the proof Proposition 3.3
By Assumption 3.2
(11)-((0) Y())
f(x, 1,), f(x,f( 0,U)
lim E
X z, ||
lim
|||0||
1-200
t
ta
f(x, -,,,,, 0,U,
|0
lim
|| >t
1-00
11'|10
(1411
11 >1}
lim E (o(,,, (,U/(UI (0x 0, 0,0/ + 2e(())
I-000
By the proof of Proposition 3.3
we know
lim E [(IUUTT/))) |U > 4 - =a/(3 - aa). Thus,
k-000
(1 (Y
|
lim E 1-000
x x, |U
x
lim toc
(g(2, 1./\\UI) g(x, O. U/|(UI))
||
ta
Following the same argument, one can prove the RHS uniformly bounded. By the dominance convergence theorem,
Y(1) - (Y)))
lim
X = x, || > 1 = Er ((((,, 1, 0) g(x; 0, 0))ra) Ee<clo(x, 1, 0) g(x, 0, E (r
1-500
Similar to NETE estimation, we can separate the estimation of CNETE into two parts. The scaling factor |||lU/////* /t2 |U]| > f] is the same as the factor in (A.7). For the spectral part, one can use meta learners, e.g, X-learner, S-learner, T-leamer, DR-learner, for estimation.
27


Reviews:
[{"review_id": "qKtYXggMD7", "reviewer": "Reviewer_GEJF", "summary": "The work introduces Normalized Extreme Treatment Effect (NETE), a causal estimand that targets how an intervention shifts tail outcomes—e.g. damage during 100‑year storms—rather than means. Building on multivariate regular variation, the authors:\n\n- formalise NETE and prove identifiability under potential‑outcome exogeneity plus an “asymptotic homogeneity” growth condition\n\n- derive a decomposition that separates spectral‑measure and α‑moment terms, enabling plug‑in estimation\n\n- craft two estimators—IPW and doubly‑robust (DR)—combined with an adaptive Hill tail‑index estimator \n\n- provide non‑asymptotic error bounds under a structured Pareto‑mixture model \n\n- validate the approach on extensive synthetic grids and a wave‑surge semi‑synthetic dataset, where EVT‑DR consistently attains the lowest MSE versus naïve baselines", "questions": "Please see the section on strengths and weaknesses.", "limitations": "Limitations have not been discussed.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### Strengths\n- Novel Problem Framing. NETE fills a genuine gap by marrying EVT with causal inference to quantify tail counterfactuals—distinct from existing QTE work.\n\n- Methodological Rigor. Doubly‑robust construction and adaptive Hill estimation yield consistency plus finite‑sample rates.\n\n- Synthetic Thoroughness. Four‑way sweeps over tail index, dimension, and growth exponent highlight estimator robustness.\n\n- Clear Mathematical Exposition. Assumptions and steps are easy to trace; proofs provided.\n\n### Weaknesses & Questions for the Authors\n1. Observability of Extreme Noise U. Real‑world practitioners seldom measure the latent driving shock; instead Y alone reflects severity. How realistic is it to assume ∥U∥ is observed so that {∥U∥ > t} can be conditioned on? Could the method be adapted when only Y (or a proxy) identifies extremes?\n\n2. Independence Assumption. Assumption 2.1 treats U independent of treatment assignment after conditioning on X. In many policy settings the exposure and hazard covary (e.g. flood defences built where storms frequent). Please discuss robustness / sensitivity when this fails.\n\n3. Tail‑Model Specification. Non‑asymptotic bound (Thm 3.5) hinges on Pareto‑mixture Assumption 3.4; yet Fig. 2 shows violation degrades MSE. Can the authors provide a diagnostic or adaptive procedure to detect mis‑specification in practice?\n\n4. Scaling‑Exponent α. α is estimated by a log‑log regression; no theory is provided for its error propagation. Empirically, how sensitive is NETE to mis‑estimated α?\n\n5. Compute & Reproducibility. Please provide (i) code, (ii) random seeds, (iii) hardware spec, and (optionally) (iv) wall‑clock times so reviewers can replicate Tables 1–2.\n\n6. Real‑world Case Study. A genuine observational dataset—e.g., hurricane damage with/without building codes—would greatly strengthen practical relevance.\n\n7. Why are only averages shown in Fig 2 although the experiment was repeated 50 times. Please add CI.\n\n8. A paragraph on Limitations is missing.", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for the valuable feedback! Please see the following detailed response to your questions. We hope our responses can resolve your concern. \n\n1. Observability of Extreme Noise U. How realistic is it to assume ∥U∥ is observed so that {∥U∥ > t} can be conditioned on? Could the method be adapted when only Y (or a proxy) identifies extremes?\n\nThanks for the great question. We can think of U as some factors that model the extreme events, e.g, speed and radius of a hurricane, which are often observable. In many cases, we are interested in the influence of extreme events rather than the events themselves. For example, we care about how much economic loss would be caused by the extreme events. That’s why in our model, the outcome is a function of U, X (covariate) and D (treatment). We will make this point clear in our paper. When only Y identifies the extremes, the identification formula (Proposition 3.3) no longer holds and we need to develop new identification techniques and change our framework. Indeed, in the literature, [1,2,3] consider such settings and develop estimation methods for their proposed estimands. \n\n[1] Aloui, Ahmed, et al. \"Treatment Effects in Extreme Regimes.\" arXiv preprint arXiv:2306.11697 (2023).\n\n[2] Bodik, Juraj. \"Extreme treatment effect: Extrapolating dose-response function into extreme treatment domain.\" Mathematics 12.10 (2024): 1556.\n\n[3] Huang, Wei, Shuo Li, and Liuhua Peng. \"Extreme continuous treatment effects: Measures, estimation and inference.\" arXiv preprint arXiv:2209.00246 (2022).\n\n2. Independence Assumption. Please discuss robustness/sensitivity when this fails.\n\nThanks for the valuable feedback. We acknowledge that Assumption 2.1 may not always hold in practice, as policies are often influenced by the extreme event U. Regarding the situations where the independence assumption is violated, there are two cases. First, we have prior knowledge about which extreme variables influence the treatment assignment. In this case, we suggest including the extreme variables as covariates. Please see our response to the first question to Reviewer iYgk for detailed discussion. Second, we do not know which extreme variables will influence the treatment, but we treat U to be independent of treatment. In this case, the IPW estimator will be biased since the propensity estimation does not include (part of) U as inputs and the estimated propensity function will not converge to the ground-truth propensity. However, if all other assumptions in Theorem 3.5 still hold, the DR estimator is still consistent thanks to the double robust property.  \n\n3. Tail‑Model Specification. Can the authors provide a diagnostic or adaptive procedure to detect mis‑specification in practice?\n\nThanks for the important question. Unfortunately, in theory, we don’t have a good way to test whether Assumption 3.4 holds or not. In practice, we suggest plotting the spectral distribution $U/ \\|U\\| \\mid \\|U\\| > t$ for a large threshold t. If Assumption 3.4 holds, by Lemma 2.1 in [1], we should be able to see points concentrate on a few clusters. If points spread evenly on the sphere, Assumption 3.4 may be violated.\n\n[1] Zhang, Xuhui, et al. \"Wasserstein-based minimax estimation of dependence in multivariate regularly varying extremes.\" arXiv preprint arXiv:2312.09862 (2023).\n\n4. Scaling‑Exponent α. α is estimated by a log‑log regression; no theory is provided for its error propagation. Empirically, how sensitive is NETE to misestimated α?\n\nThis is a great question! We did an experiment to see the sensitivity of alpha. In particular, we compare the MSE of using the true $\\alpha$ versus using our heuristic to estimate the $\\alpha$ in the first synthetic experiment in our paper. Unfortunately, we did not find a place to show our figures here. The following table shows part of the results. We can see that actually the MSEs are closed and our heuristic for $\\alpha$ estimation works well. \n\n| Sample size | MSE (est α) | SE (est α) | MSE (true α) | SE (true α) |\n|-----------:|------------:|-----------:|-------------:|-----------:|\n|       1,000 |      1.4982 |    1.0741 |       1.2913 |    0.8634 |\n|       2,000 |      0.6739 |    0.6832 |       0.5383 |    0.5219 |\n|       3,000 |      0.3911 |    0.3724 |       0.5100 |    0.3942 |\n|       4,000 |      0.3333 |    0.3664 |       0.3625 |    0.3329 |\n|       5,000 |      0.2499 |    0.2726 |       0.3246 |    0.3023 |\n\n5. Compute & Reproducibility. Please provide (i) code, (ii) random seeds, (iii) hardware spec, and (optionally) (iv) wall‑clock times so reviewers can replicate Tables 1–2.\n\nThanks for asking. We will provide the code in the camera-ready version. Unfortunately, due to Neurips' policy, we cannot provide any link in the rebuttal stage. \n\n6. Real‑world Case Study. A genuine observational dataset—e.g., hurricane damage with/without building codes—would greatly strengthen practical relevance.\n\nThanks for the suggestion. We want to mention that it is difficult to find realistic datasets that include covariates, extreme events and outcomes. To conduct such a real-world study, we need to collect data from several different data sources and construct a new dataset, which requires a substantial amount of time and effort. Given that the goal of this paper is to propose a new framework for estimating extreme effects, we think that synthetic and semi-synthetic experiments are enough to verify our theoretical results. We will work on real-world problems in later studies. \n\n7. Why are only averages shown in Fig 2 although the experiment was repeated 50 times. Please add CI.\n\nThanks for pointing that out. We will add the error bar to all graphs. Unfortunately, we did not find a place to show our figures here. \n\n8.  A paragraph on Limitations is missing.\n\nThanks for the feedback. We briefly mention the limitation in the conclusion section in the appendix. We will add a more detailed explanation of the limitation."}, {"review_id": "3E6NnBjVEP", "reviewer": "Reviewer_jtyN", "summary": "This paper presents a thorough theoretical analysis of estimating average treatment effects under extreme noise conditions. It adapts tail estimators to the causal inference setting, generalizes identifiability theorems under commonly assumed conditions, and supports its results with experiments on synthetic (and semi-synthetic) data.", "questions": "I added the questions in the weaknesses above, please read above for further details. \nThree things that, in my opinion, would significantly increase the value of the paper:\n\n- A more thorough literature review  \n- Clearer mathematical statements (it was sometimes difficult to identify the definition of each symbol)  \n- Experiments: discussion of the effect of missing confounders on stability, explanation of stability with respect to the number of samples, and inclusion of error bars (especially as a function of the number of samples, to test the hypothesis mentioned by the authors)", "limitations": "Yes. I don't think any important limitation is missing as the authors state the assumptions under which their analysis hold.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### Strengths\n\n- I appreciate the motivation to estimate treatment effects under extreme scenarios which makes the scenario studied by the paper relevant and unique to the best of my knowledge.\n- The theoretical analysis is thorough. \n\n### Weaknesses\n\n- Since there is no widely agreed-upon definition of extreme treatment effects in the literature, and the authors appear to propose a new one, it would be helpful to state this more clearly in the abstract (e.g., \"introducing a new definition to model extremities in treatment effects\"). \n\n- The sentence *\"Classic causal inference literature mainly focuses on estimating the average effects among certain groups\"* gives the impression that no prior work has modeled quantities beyond the population average (ATE). However, there is a substantial body of work on estimating conditional average treatment effects (CATE) [1,2], modeling distributions [3,4], and on tail/extreme treatment effects [5,6,7].\n\n- As previously mentioned, a quick search reveals at least two papers available online that tackle the intersection of Extreme Value Theory (EVT) and causal inference in similar (though not identical) settings — namely, Huang et al. (2022) and Aloui et al. (2023). A more thorough literature review focusing on this intersection is necessary. Both papers cite additional related works. While the current paper focuses on the average treatment effect under heavy-tailed exogenous variables — a different setting — the use of EVT theory is highly relevant and similar. A discussion of these differences would strengthen the literature review.\n\n- The authors only study an average (aggregate) quantity, not one conditioned on covariates. I believe conditioning on covariates would make the contribution more complete and relevant. For example, in healthcare, we may care about the extreme response of a treatment for a specific individual, such as  \n\n $$\\theta^{\\text{NETE}}(X) = \\lim_{t \\rightarrow \\infty} \\mathbb{E}\\left[\\frac{Y(1) - Y(0)}{t^{\\alpha}} \\middle|\\ X, |U| > t\\right]$$\n\nDo the authors see a natural extension of their work to this conditional setting?\n\n- In Assumption 3.2, I find the statement is unclear. Should it state that there exists some $\\alpha$ ? Is $\\alpha$ unique for a fixed $g$? Also, is $e(t)$ a function of $g$? That is, should the statement read: `` $\\exists g, \\exists e$ such that …”? Clarification is needed for me to understand the statement better, and $\\alpha$ should be more explicitly defined. I recall seeing similar assumptions in EVT literature — could the authors point to any related work? Also, does the property hold only as $t \\to \\infty$, or for all $t$?\n\n- Regarding the statement *“E[Y(d)] is of the order $O(\\|U\\|^{\\alpha})$ and (3.2)”* — does this mean that $\\alpha$ is fixed for each $Y$? Please clarify.\n\n- The sentence *“In these cases, $f$ grows polynomially with respect to $\\|U\\|$ and $e(t) = 0$ exactly.”* refers to just one choice of \\(e\\). However, many functions \\(e(t)\\) could verify the required property, even if they are nonzero but converge to zero as $t \\to \\infty$. Is my understanding correct?\n\n- The claim that the definition *“generalizes ATE to the setting of extreme events and aligns with the growth rate given by EVT”* is somewhat misleading. It is not obvious how this is a generalization of ATE. Rather, it appears to be a separate definition. It may be more accurate to say it generalizes the *unnormalized* version (ETE), if anything. Or am I missing something? \n\n- Could the authors add error bars in Figure 2? The experiments are repeated over 50 different seeds, meaning the data changes each time, and reporting variance would be helpful.\n\n- The authors mention that as the number of samples increases, the assumption becomes violated and the estimator becomes dominated by error. This is quite counterintuitive: if the estimator is consistent, it should converge to the true estimand as the sample size grows. Could the authors elaborate on this phenomenon? Is there a way to filter out “bad samples” that lead to this behavior?\n\n- A final question: Could the authors expand on how they envision extending this work to the estimation of conditional average treatment effects? Also, what do they expect regarding the performance of their estimator when conditional unconfoundedness is violated? While this question likely deserves a dedicated study, if the authors have time during the rebuttal phase, it would be informative to include a synthetic experiment where $X \\sim \\text{Unif}[0,1]^d$ with $d$ ranging from 5 to 10, and only the first 5 dimensions used to adjust for bias (as is done now). How would the performance degrade as dimensionality increases (i.e., as more confounders are missing)? While not a formally defined sensitivity analysis, this could still help us understand the robustness of the method to unobserved confounding.\n\n\n#### References\n\n[1] Shalit, Uri, Fredrik D. Johansson, and David Sontag. \"Estimating individual treatment effect: generalization bounds and algorithms.\" International conference on machine learning. PMLR, 2017.\n\n[2] Abrevaya, Jason, Yu-Chin Hsu, and Robert P. Lieli. \"Estimating conditional average treatment effects.\" Journal of Business & Economic Statistics 33.4 (2015): 485-505.\n\n[3] Gautier, Eric, and S. T. E. F. A. N. Hoderlein. \"Estimating the distribution of treatment effects.\" arXiv preprint arXiv:1109.0362 (2013).\n\n[4] Hohberg, Maike, Peter Pütz, and Thomas Kneib. \"Treatment effects beyond the mean using distributional regression: Methods and guidance.\" PloS one 15.2 (2020): e0226514.\n\n[5] Huang, Wei, Shuo Li, and Liuhua Peng. \"Extreme continuous treatment effects: Measures, estimation and inference.\" arXiv preprint arXiv:2209.00246 (2022).\n\n[6] Aloui, Ahmed, et al. \"Treatment Effects in Extreme Regimes.\" arXiv preprint arXiv:2306.11697 (2023).\n\n[7] Bodik, Juraj. \"Extreme treatment effect: Extrapolating dose-response function into extreme treatment domain.\" Mathematics 12.10 (2024): 1556.", "was_revised": true, "final_justification": "The paper is technically solid and it studies a new interesting problem. If the authors add a more complete literature review and make the edits that are included in their response I think the paper is good shape. I will summarize the issues that are resolved (if they ll be added to the revised manuscript):\n\nSummary of issues resolved:\n- more complete literature review.\n- adding error bars.\n- clarification about some of the mathematical statements.", "rebuttal": "Thanks for the detailed feedback and valuable suggestions! Please see the following responses. \n\n1. It would be helpful to state clearly in the abstract that the authors appear to propose a new definition of extreme treatment effects.\n\nThanks for the advice. We will add a sentence in our abstract to make this clearer. \n\n2. The paper gives the impression that no prior work has modeled quantities beyond the population average (ATE). A discussion of these differences would strengthen the literature review.\n\nThanks for providing the related reference. We acknowledge that the expression of the sentence may be inappropriate. We will provide a more thorough literature review in later versions. Currently, there are two approaches in the literature to characterize the extreme treatment effect (ETE). The first approach is to use extreme Quantile Treatment Effect (QTE) [3, 4, 5, 6], which we discuss in detail in our paper. The other approach is to assume the outcome falls in the domain of attraction and use the change of Extreme Value Index (EVI) as a measure for ETE [1, 2]. In particular, [3] also considers using the ratio of tail expectation under different treatments as a measure. However, our setting is different from these works in that (1) We allow extreme exogenous variables and the outcome is a function of treatment, covariate and the extreme variables. (2) We model extreme events by a multivariate regularly varying variable, while all these works focus on univariate settings. Moreover, our work can also be placed in the broader context in the literature that studies causal effects of treatment beyond the mean, for example, distributional effect [7,8,9], Ratio‐ and Log‐Ratio‐Based Effects [10,11], CATE [12,13,14]. \n\n[1] Aloui, Ahmed, et al. \"Treatment Effects in Extreme Regimes.\" arXiv preprint arXiv:2306.11697 (2023).\n\n[2] Bodik, Juraj. \"Extreme treatment effect: Extrapolating dose-response function into extreme treatment domain.\" Mathematics 12.10 (2024): 1556.\n\n[3] Huang, Wei, Shuo Li, and Liuhua Peng. \"Extreme continuous treatment effects: Measures, estimation and inference.\" arXiv preprint arXiv:2209.00246 (2022).\n\n[4] Victor Chernozhukov and Songzi Du. Extremal Quantiles and Value-at-Risk, May 2006.\n\n[5] Yichong Zhang. Extremal quantile treatment effects. The Annals of Statistics, 46(6B):3707–3740,December 2018. \n\n[6] David Deuber, Jinzhou Li, Sebastian Engelke, and Marloes H. Maathuis. Estimation and Inference of Extremal Quantile Treatment Effects for Heavy-Tailed Distributions. Journal of the American Statistical Association, 119(547):2206–2216, July 2024.\n\n[7] Abadie, A. (2002). Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models. J. Amer. Statist. Assoc., 97(457): 284–292.\n\n[8] Gautier, Eric, and S. T. E. F. A. N. Hoderlein. \"Estimating the distribution of treatment effects.\" arXiv preprint arXiv:1109.0362 (2013).\n\n[9] Hohberg, Maike, Peter Pütz, and Thomas Kneib. \"Treatment effects beyond the mean using distributional regression: Methods and guidance.\" PloS one 15.2 (2020): e0226514.\n\n[10] Cole, S. & Hernán, M. (2002). Fallibility in Estimating Direct Effects. Epidemiology, 13(3): 297–306.\n\n[11] VanderWeele, T.J. (2014). Policy‐Relevant Proportions for Direct Effects. Epidemiology, 24(2): 175–176.\n\n[12] Shalit, U., Johansson, F. & Sontag, D. (2017). Estimating individual treatment effect: generalization bounds and algorithms. International Conference on Machine Learning (ICML).\n\n[13] Wager, S. & Athey, S. (2018). Estimation and inference of heterogeneous treatment effects using random forests. Journal of the American Statistical Association, 113(523), 1228–1242.\n\n[14] Abrevaya, Jason, Yu-Chin Hsu, and Robert P. Lieli. \"Estimating conditional average treatment effects.\" Journal of Business & Economic Statistics 33.4 (2015): 485-505.\n\n\n\n3. Do the authors see a natural extension of their work to this conditional setting?\n\nThanks for the great question. Indeed, our results can be extended to the conditional setting using a similar argument without much difficulty. The identification formula (Proposition 3.3) can be adapted to \n$$ \\theta^{{CNETE}}(x) = \\lim_{t \\rightarrow \\infty} \\mathbb{E}[g (X, 1, U/\\|U\\|) - g (X, 0, U /\\|U\\|) \\mid \\|U\\|> t, X = x] \\cdot \\lim_{t \\rightarrow \\infty} \\mathbb{E}[\\|U\\|^{\\alpha} / t^{\\alpha} \\mid \\|U\\|> t] . $$ \nSimilar to CATE estimation, one can design different estimators based on this identification formula, e.g., T learner, S learner, X learner, DR learner. \n\n4. Clarification of  Assumption 3.2.\n\nThanks for the question and sorry for the confusion. The correct statement should be that there exists some constant $\\alpha$, functions $g(x,d,u), e(t)$ such that the inequality holds for all x, t, u, d. It is easy to see that $ \\lim_{t\\rightarrow \\infty} f(x,d,tu)/t^\\alpha = g(x,d,u)$. Therefore, the constant $\\alpha$ is unique. Otherwise, if there exists $\\alpha’$ that satisfies the same relationship, we have $\\lim_{t\\rightarrow \\infty} t^{|\\alpha - \\alpha’|} <\\infty$. Since $\\alpha$ is unique, by this relationship, $g$ is unique too. The error term $e(t)$ is not a function of $g$ and only depends on t. This assumption can be viewed as an asymptotic version of homogeneous functions. \n\n5. Is $\\alpha$ fixed for each $Y$? Please clarify.\n\nThanks for the question. Yes. $\\alpha$ is fixed for each $Y(d)$. Furthermore, for different $d$, the alpha is the same. \n\n6. Many functions $e(t)$ could verify the required property, even if they are nonzero but converge to zero as $t\\rightarrow \\infty$. Is my understanding correct?\n\nYes! Your understanding is correct. Since $e(t)$ is only an upper bound, it can be satisfied by many functions as long as they converge to 0 as t grows to infinity.\n\n7. The claim that the definition “generalizes ATE to the setting of extreme events and aligns with the growth rate given by EVT” is somewhat misleading. It is not obvious how this is a generalization of ATE. Rather, it appears to be a separate definition. It may be more accurate to say it generalizes the unnormalized version (ETE), if anything. Or am I missing something?\n\nThanks for the suggestion! We intended to say that NETE provides a causal measure in the extreme setting just like ATE in the regular setting. Since this expression may cause confusion, we will change it in the later version.\n\n8. Could the authors add error bars in Figure 2? The experiments are repeated over 50 different seeds, meaning the data changes each time, and reporting variance would be helpful.\n\nThanks for pointing that out. We will include error bars in our figures in later versions.  Unfortunately, we did not find a place to show our figures here. \n\n9. The authors mention that as the number of samples increases, the assumption becomes violated and the estimator becomes dominated by error. \n\nThanks for the question. We want to clarify that in the second experiment (Fig 2 in the paper), we design the data generation process such that assumption 3.4 (Pareto mixture) is violated all the time. Since our non-asymptotic analysis is based on this assumption, violation of this assumption may cause the error bound in Theorem 3.5 to be invalid. We will make this point clearer in our experiments section. There is a way to detect whether assumption 3.4 is violated. Please see the third point of our response to Reviewer GEJF for explanation.  \n\n10. What do authors expect regarding the performance of their estimator when conditional unconfoundedness is violated? \n\nThanks for the questions. When the conditional unconfoundness assumption is violated, our identification formula no longer holds, and thus our estimator is non-consistent. There have been many works in the literature discussing this assumption. One approach is to completely drop this assumption and consider using partial identification methods to obtain a bound for the estimand [1,2]. The other approach is to conduct a sensitivity analysis [3]. Following the reviewer’s advice, we examine what would happen empirically if this assumption is violated. Our data generation process is \n\n\\begin{align*}\nX \\sim \\mathrm{Uniform}([0,1]^{10}),\\  p_i = \\frac{1}{1 + \\exp\\bigl(-\\beta^\\top (X \\circ X)\\bigr)}, \\quad D_i \\sim \\mathrm{Bernoulli}(p_i), \\quad  \n\\end{align*}\nand\n$$Y = \\|U\\|^2(D + \\gamma^T(X \\circ X) + U/\\|U\\| + \\epsilon) + \\|U\\|,$$\nwhere $U,\\epsilon$ are generated the same way as in the first synthetic experiment in the paper and $X \\circ X$ is the element-wise multiplication. The following table shows that the MSE decreases as the observable dimension increases. \n\n| # of Dimensions | EVT-DR MSE |\n|----------------:|-----------:|\n|               5 |      0.2016 |\n|               6 |      0.1145 |\n|               7 |      0.0652 |\n|               8 |      0.0419 |\n|               9 |      0.0204 |\n|              10 |      0.0133 |"}, {"review_id": "vjq17lymJq", "reviewer": "Reviewer_U7z2", "summary": "The authors propose a principled approach to estimate causal effects conditional on threshold exceedances in a heavy-tailed data-generating process. Their method is based on a model in which data is generated as a function of a Pareto-type intensity random variable. The causal effect is quantified as the rescaled difference in means between treatment groups. The authors introduce multiple estimators and analyze their non-asymptotic theoretical performance. These results are illustrated through extensive experiments comparing the performance of the proposed estimators for the so-called NETE.", "questions": "- Would it be possible to provide deeper insight into what the NETE represents and what type of causal relationship it captures?\n- Similarly, could a synthetic experiment be constructed where the NETE identifies a causal relationship that would not be detected by a classical causal inference method (again, assuming the mean exists)?\n- Where is the proof for Proposition 3.3? Not sure see why this holds.\n\nMore generally:\n- Line 13+: The term “extremities” is somewhat awkward, as it can imply an upper bound. Consider using “extremes” or “extreme events” instead.\n- Line 84: The term “consistency” is unclear in this context. Please clarify whether it refers to consistency of an estimator, or something else.\n- Lines 94 and 104: Is this the same constant c? If so, it should be explicitly stated; if not, the notation should be differentiated.\n- Lines 91 and 115: The mean is used before it is formally defined. Consider introducing the necessary definitions earlier for clarity.\n- Line 91: The orthogonality symbol is used without explanation. Please define this notation when it first appears.\n- Line 94: The term “estimated propensity” is vague—does it refer to an estimated propensity score? If so, please make this explicit.", "limitations": "Limitations were detailed in the weaknesses section.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### Strengths\nThe methodology is clear, the results are sound and mathematically well-founded. The contribution is both novel and timely.\n\n### Weaknesses\n\n- Existence of the mean: One key reason why existing approaches for estimating causal effects in the extremes avoid analyzing the Expected Treatment Effect (ETE) is that this quantity does not always exist-unlike quantiles, which are commonly used in such settings. This is why the authors focus on the NETE instead of the ETE. However, beyond the mathematical convenience, it remains unclear what kind of relationships the NETE can capture. In multivariate regular variation, similar standardization techniques are used to quantify dependence. No analogous interpretation is provided in the present work.\n- Relevance of the synthetic data experiment: It is not clear from the experiment what specific insights the NETE provides that could not be obtained through a classical causal analysis-assuming the mean exists. The added value of NETE over traditional estimands should be better illustrated or clarified. In partuclar, the claim on l.120-121 is unclear: in general when studying a mean effect, the average, if it exists, it highly impacted by rare events (and not obscured). This point would benefit from further explanations.", "was_revised": true, "final_justification": "I maintain my score as explained in the below comment and sincerly thank the authors once again for carefully considering my remarks.", "rebuttal": "Thank you for your detailed evaluation of our paper, which will definitely make our paper clearer and better!  Please see the following responses. \n\n1. Would it be possible to provide deeper insight into what the NETE represents and what type of causal relationship it captures?\n\nPlease see the second bullet point of our response to the Reviewer iYgk for a detailed answer.\n\n2. Similarly, could a synthetic experiment be constructed where the NETE identifies a causal relationship that would not be detected by a classical causal inference method (again, assuming the mean exists)?\n\nIn the example in the previous answer, the NETE captures how fast the expected outcome in the tail grows with respect to U. ATE can only capture the change in the overall expectation. While in theory one can estimate CATE and use CATE to capture similar properties, insufficient tailed samples will create a significant challenge for estimation. \n\n3. Where is the proof for Proposition 3.3? Not sure why this holds.\n\nThanks for asking. The proof can be found in the appendix, which is in the supplementary material. \n\n### Clarify questions:\n\n1. Line 13+: The term “extremities” is somewhat awkward, as it can imply an upper bound. Consider using “extremes” or “extreme events” instead.\n\nThanks for the suggestion. We will change the wording.\n\n2. Line 84: The term “consistency” is unclear in this context. Please clarify whether it refers to the consistency of an estimator, or something else.\n\nThanks for pointing this out. ‘Consistency’ here refers to the consistency assumption in casual inference, which states that an individual's observed outcome is equivalent to their potential outcome under the treatment they actually received.\t\n\n3. Lines 94 and 104: Is this the same constant c? If so, it should be explicitly stated; if not, the notation should be differentiated.\n\nThanks for pointing out the notation abuse. They are different constants. We will explicitly state this in the paper.\n\n4. Lines 91 and 115: The mean is used before it is formally defined. Consider introducing the necessary definitions earlier for clarity. The orthogonality symbol is used without explanation. Please define this notation when it first appears.\n\nThanks for pointing these out. We will move the definition of expectation earlier and add the definition of the orthogonality symbol. The orthogonality symbol represents an independent relationship. \n\n5. Line 94: The term “estimated propensity” is vague—does it refer to an estimated propensity score? If so, please make this explicit.\n\nThanks for asking. It refers to an estimated propensity score. We will make this explicit."}, {"review_id": "we1dGTYsY8", "reviewer": "Reviewer_jd2q", "summary": "The paper tackles the challenging problem of estimating the impact of an intervention on rare but extreme outcomes, like extreme hurricanes or other climate events. The authors do so by combining tools from both causal inference and extreme value theory (EVT). They make several contributions:\n\n* Define key estimands when there is extreme tail risk, as well as corresponding identification and assumptions\n\n* Propose an algorithm for estimating these effects, combining both causal ML methods and EVT tools\n\n* A non-asymptotic analysis of the proposed algorithm\n\n* Several experiments and a semi-synthetic application", "questions": "* I had a hard time following the discussion in Sec 2 and 3.1 that defines the key quantities of interest, and especially the relationship between U and the other variables. The most intuitive explanation is the sentence on line 124 “for example …”. But it would be useful to give more clarity on the relationships between U and Y especially. e.g., do you think of Y as having a structural component and U noise? The synthetic dataset in Sec 4.1 is a useful step. \n\n* For the semi-synthetic dataset, does $Y$ correspond to anything concrete? Is there any notion of uncertainty that can help calibrate whether these point estimates are “large” or “small”?", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths:\n* The paper rightly highlights the need for this type of approach. The paper then does an excellent job of bridging the otherwise distinct fields of causal inference and EVT, and gives a very thoughtful discussion of the benefits and drawbacks of each approach.\n\n* The proposed algorithm and corresponding technical analysis seem to be state-of-the-art, and seem to perform well in experiments. \n\n* The paper is up front about remaining challenges and suggests many useful directions for future work. \n\n\nWeaknesses:\n* The appendix appears to be missing, which makes review more challenging. \n\n* The relationship between $Y$ and $U$ needs further clarification (see below). \n\n* Recognizing that this is challenging, there is no discussion of uncertainty quantification, which would be particularly important in a setting like this.", "was_revised": true, "final_justification": "Keeping my positive score.", "rebuttal": "Thanks for your valuable review of our paper! We are sure your feedback will make our paper better! Please see the following paragraphs for our responses. \n\n1. The appendix appears to be missing, which makes the review more challenging.\n\t\nThanks for asking. The appendix is in the supplementary material.\n\n2. It would be useful to give more clarity on the relationships between U and Y, especially. e.g., do you think of Y as having a structural component and U noise? The synthetic dataset in Sec 4.1 is a useful step.\n\nThanks for asking! We agree that the name “extreme noise” can be confusing. We will make the discussion clearer in later versions. As in the example of line 124, we think U is also a structural component of the model, which represents extreme events. A more appropriate name for U may be “extreme factors”. \n\n3. For the semi-synthetic dataset, does it correspond to anything concrete? Is there any notion of uncertainty that can help calibrate whether these point estimates are “large” or “small”?\n\nThanks for the question. In the semi-synthetic dataset, we use real-world data as the extreme noise U and generate the rest of the variables by equations (4.1). (4.1) does not correspond to a real-world example. We use this example to conceptually verify our theoretical results. For uncertainty quantification, please see our response for the next question.\n\n4. Recognizing that this is challenging, there is no discussion of uncertainty quantification, which would be particularly important in a setting like this.\n\nWe thank the reviewer for highlighting the absence of uncertainty quantification. We agree that assessing the variability of our extreme‐treatment estimates is both important and nontrivial. A natural approach to estimating the sampling variability of our estimators is the bootstrap [1]. However, straightforward resampling of extreme observations can fail to reproduce tail dependence and may severely underestimate variance [2]. Recent work on adapting bootstrap methods to heavy‐tailed and extreme‐value settings [3] offers promising strategies—for instance, resampling only the exceedances above a high threshold or applying a parametric tail bootstrap based on the generalized Pareto approximation. While these approaches suggest viable adaptations, a full theoretical justification in our context would require substantial new analysis. We therefore view rigorous confidence‐interval construction for extreme‐treatment effects as a direction for future work and refrain from making formal claims about interval validity in the current manuscript.\n\n[1] Efron, B. (1979). Bootstrap methods: Another look at the jackknife. The Annals of Statistics, 7(1), 1–26.\n\n[2] Cornea‐Madeira & Davidson (2015). “A Parametric Bootstrap for Heavy-Tailed Distributions.” Econometric Theory 31(3): 449–470.\n\n[3] de Haan, Laurens, and Chen Zhou. \"Bootstrapping extreme value estimators.\" Journal of the American Statistical Association 119.545 (2024): 382-393."}, {"review_id": "2EQimAtZxA", "reviewer": "Reviewer_iYgk", "summary": "This paper introduced the Normalized Extreme Treatment Effect (NETE), and then studied its identification and estimation problems.", "questions": "Assumption 3.1 appears somewhat restrictive. It is reasonable to expect that the vector of maximum wind speed, rainfall, and storage would influence the level of infrastructure investment. The variable U could serve as a confounder. Can U be included in the covariate vector X to control for its confounding effects?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strength**\n\nThis paper is theoretically well-founded. The NETE represents a particularly interesting quantity in the context of causal inference. I have no concerns regarding the theoretical development presented in the paper.\n\n**Waekness**\n\n1. My main concern lies in the explanation of the NETE. While these quantities may represent interesting measures in causal inference, the current exposition is limited. To enhance clarity and interpretability, I suggest providing a more detailed explanation, ideally supported by visual illustrations. For instance, consider the joint distribution of (Y_1, Y_0, U) or (Y_1 - Y_0, U): under what conditions does the NETE attain large or small values? Plots or density functions illustrating these relationships would be highly informative.\n\n2. Furthermore, the explanation of the results for the semi-synthetic dataset is limited. In most parts of the semi-synthetic application, the focus is primarily on the statistical properties of the estimators. However, more detailed interpretation of the results is needed to enhance the reader’s understanding of their practical implications.\n\n\n3. From a statistical perspective, extreme value theory is well-established and well-motivated. However, researchers in the machine learning or causal inference community may be less familiar with this framework. Therefore, a more accessible explanation and stronger motivation would help broaden the impact and understanding of the work. In particular, the meaning of \\alpha may be important and warrants further clarification.\n\n4. Assumption 3.1 appears somewhat restrictive. (See question)", "was_revised": true, "final_justification": "I will keep my positive score.", "rebuttal": "Thanks for the valuable feedback! Please see below for our detailed responses. We hope our responses can resolve your concern. \n\n1. Assumption 3.1 appears somewhat restrictive. Can U be included in the covariate vector X to control for its confounding effects?\n\nThanks for the insightful question! The short answer is that we can include U in the covariate vector, but for estimation, we need to adapt our estimators. Following the same argument as Proposition 3.3, one can derive a similar identification formula. However, when we include U in the covariates, the domain of propensity is not compact. It is difficult to estimate the propensity function defined in the whole real space. If we don’t have access to the propensity function, which sometimes can be obtained from policy documents, we suggest using the DR estimator or the regression adjustment estimator for estimation in this setting. \n\n2. My main concern lies in the explanation of the NETE. Provide a more detailed explanation, ideally supported by visual illustrations. \n\n\nThanks for the valuable suggestion. We now include a more detailed, intuitive discussion of the NETE in a simple setting:\n\n **Data‐Generating Process**: Consider no covariates and let \\(U\\) be a univariate Pareto with extreme value index $1/\\beta $. We generate potential outcomes as\n   $$Y(d) = \\bigl(d\\theta_{1} + (1-d)\\theta_{0}\\bigr)\\,U^{2}+ 0.1\\,\\sqrt{U}+ \\varepsilon,\\quad\\varepsilon \\sim N(0,\\,0.1),$$\n   where \\(0 < \\theta_{0} < \\theta_{1}\\).  In this case, $\\alpha = 2$ so that\n   $$\n   E\\bigl[Y(d)/t^{2}\\mid U > t\\bigr]\\sim c_{d} t^{2}\n   $$\n   for constants $c_{d}$.  By definition, the NETE is \n   $$\n   \\mathrm{NETE} = c_{1} - c_{0}= (\\theta_{1} - \\theta_{0}) \\cdot \\frac{\\beta}{\\beta - 1}.\n   $$\n   Intuitively, NETE measures how much faster the treated outcome grows in the extreme tail compared to the control.\n\n **Interpretation** : \n   - A **large positive NETE** occurs when:\n     1. $\\theta_{1} - \\theta_{0}$ is large (treatment increases the leading coefficient), or  \n     2. $\\beta$ is close to 1 (Pareto tail is very heavy).  \n   - These two factors correspond to:\n     1. **Faster tail‐growth under treatment**, and  \n     2. **Longer tail of $U$**.  \n\n **Planned Illustration** :We will add a figure plotting 10,000 simulated points of $\\bigl(Y(1),U\\bigr)$ and $\\bigl(Y(0),U\\bigr)$ with\n   $\\beta = \\tfrac{10}{11}$, $\\theta_{0} = 0.5$, and $\\theta_{1} = 1$.  The scatter will fan out around the curves $Y(d)=\\theta_{d}\\,U^{2}$.  A steeper “fan” visually conveys a larger NETE, illustrating how the joint behavior of $(Y(d),U)$ encodes tail sensitivity.  \n\n*We were unable to upload the figure here, but will include it in the revised manuscript.*  \n\n\n3. Furthermore, the explanation of the results for the semi-synthetic dataset is limited. In most parts of the semi-synthetic application, the focus is primarily on the statistical properties of the estimators. However, more detailed interpretation of the results is needed to enhance the reader’s understanding of their practical implications.\n\nThanks for the suggestion. We will add result analysis in later versions. We can see from equation (4.1) that the treatment $D$ will only change the coefficient of $W^{\\alpha_1}S^{\\alpha_2}$, which is proportional to the NETE. As mentioned in the previous responses, a positive NETE means the treatment will make the tailed expected outcome grow faster with respect to the threshold t. \n\n4. From a statistical perspective, extreme value theory is well-established and well-motivated. However, researchers in the machine learning or causal inference community may be less familiar with this framework. Therefore, a more accessible explanation and stronger motivation would help broaden the impact and understanding of the work. In particular, the meaning of \\alpha may be important and warrants further clarification.\n\nThanks for the advice. We will add an extra section in the appendix to briefly introduce the extreme value theory. Besides, we will also add a paragraph in the introduction part to motivate EVT."}]

Author rebuttal:

Meta-review: The standard causal inference methods do not work for the data with extreme values. In this paper, the authors propose a method for treatment effects estimation in extreme data to capture the causal effect at the occurrence of rare events of interest. They define Normalized Extreme-value Treatment Effect (NETE) and use the theory of multivariate regular variation to model extremities. They also propose a doubly robust estimation method.

The work has its limitations: some assumptions such that observability of the extreme noise, independence Assumption  2.1, Pareto‑mixture Assumption 3.4 are limiting but do not render the methodology ineffective. The literature review can also be improved. Please address the rest of the reviewers' feedback in the final version of the paper.
Decision: Accept (poster)