Causal Inference for Sequential Settings under Interference and Latent Confounding

Constantinos Daskalakis; Devavrat Shah; Phevos Paschalidis

REVIEW 2 major objections 5 minor 1 cited by

Causal Inference for Sequential Settings under Interference and Latent Confounding

T0 review · 2 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

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

Pith's one-line read From a single observational panel, this paper proves that a sequential pseudo-likelihood estimator recovers both the Ising-model parameters and generalized treatment effects under network interference, temporal dependence, and low-rank late

desk verdict Solid theory paper: new combination, sound proof under assumptions, but the real-data causal estimate and several experiments step outside those assumptions. read the letter →

arxiv 2607.14940 v1 pith:3YGQGTG4 submitted 2026-07-16 cs.LG math.PR

Phevos Paschalidis , Constantinos Daskalakis , Devavrat Shah This is my paper · ORCID

classification cs.LGmath.PR MSC 62F1262M10

keywords causalinferenceinterferencelatentconfoundingIsingmodelmaximumpseudo-likelihoodlow-rankfactorgeneralizedtreatmenteffectsequentialobservationaldata

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that causal inference is possible from one sequential observational dataset even when three complications appear together: each unit's outcome depends on other units' outcomes (interference), on the previous time step, and on unmeasured confounders that evolve with a low-rank factor structure. The proposed learning rule is sequential maximum pseudo-likelihood estimation (MPLE), which is convex and computationally easy to evaluate. The authors prove non-asymptotic bounds on parameter error and on the error of estimated generalized treatment effects, showing the error vanishes in reasonable regimes. A sympathetic reader would care because previous work handled these complications in pairs, not all at once, and none offered provable guarantees from a single sample.

What carries the argument

The central object is the sequential pseudo-likelihood φ(θ), built from one-step conditional distributions of the Ising model; it is a convex surrogate for the intractable likelihood and its curvature in θ controls identifiability. Three assumptions carry the argument: low rank of the latent field A (so its covering entropy is O(k(N+T))), Dobrushin's uniqueness condition (which supplies concentration, fast Gibbs mixing, and a perturbation bound on counterfactual means), and an 'excitability' assumption on Z that guarantees the treatment effect β cannot be absorbed into a change in the low-rank field A. The proof combines martingale concentration for dependent Ising blocks, covering arguments

What would settle it

Generate synthetic data under the paper's model with a rank-one or near-rank-one treatment matrix Z (e.g., all columns identical after some switch-on time) and a rank-k latent field A* whose leading singular vectors align with Z; if the sequential MPLE still recovers β close to its true value, then Assumption 3 is not necessary as stated, whereas if β-error grows with the alignment, the assumption is doing the identified work. A second check on real data: fit the model to the COVID-19 panel but hold out the later time steps; if the learned β and GTE change materially when the post-switch perio

Watch

Extended reading notes

Core claim

Under a Markovian Ising model for binary outcomes, a single observed trajectory (x,z) suffices to estimate the latent confounder matrix A, the direct treatment effect β, the spatial-interaction strength ξ, and the temporal-interaction strength η, provided the latent field has rank at most k, the interactions satisfy a Dobrushin-type weak-dependence condition, and the intervention matrix Z is 'excitable' enough relative to the low-rank field. The sequential MPLE estimate θ̂ obeys a non-asymptotic error bound, and a corollary transfers this to a squared-error bound on any generalized treatment effect. This gives the first computationally efficient, provable framework for observational causal e

Load-bearing premise

The whole identification of the treatment effect rests on Assumption 3—that the observed intervention pattern Z is 'excitable' enough that changes in β cannot be mimicked by changes in the low-rank latent field; the paper itself notes the COVID-19 vaccination rollout, where counties stay above the threshold once crossed, may violate exactly this condition.

Editorial extensions

If this is right

If the theorem holds, a researcher with one observational panel—no repeated draws, no randomized assignments—can estimate counterfactuals under arbitrary intervention patterns, not just all-on/all-off.
Treatment-effect estimation inherits the same error rate as parameter estimation, so identifiability of β is both necessary and sufficient for generalized treatment effect estimation.
The error rate vanishes when T||Γ||_F² dominates k(N+T)logT; in particular, a connected graph with bounded maximum degree and growing T suffices.
Because inference under Dobrushin's condition is fast via Gibbs sampling, the method is computationally efficient end to end: fit once, then sample counterfactuals.
Empirically, modeling interference and latent confounding together yields materially larger estimated vaccine effects on COVID-19 county death rates than logistic-regression baselines that ignore either.

Reading between the lines

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

The necessity of Assumption 3 suggests a practical design lesson the paper leaves implicit: intervention schedules that are more 'rank-rich'—staggered, reversible, or with within-unit variation—make the treatment effect identifiable against low-rank confounding, whereas one-way monotone rollouts like vaccination campaigns are exactly the hard case.
Because the identifiability mechanism separates β from A through the interaction with Z, a natural extension is to multiple treatment arms or continuous treatments, where the analogous condition would require the treatment matrix to span directions outside the latent factor space.
A testable refinement: with synthetic data where Z's top singular value carries, say, 90% of its energy and A* is partially aligned with Z's leading singular vectors, the estimator's β error should degrade relative to the experiments reported here; quantifying that degradation would map the boundary of Assumption 3.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

First thing to know: the theoretical core is real. I read the proof of Theorem 1 and Corollary 2 carefully and did not find a load-bearing error. The proof is a clean extension of the established Dagan-Daskalakis-Kandiros template, with Assumption 3 explicitly doing the identifiability work. The combination of outcome interference, temporal dependence, and low-rank latent confounding in a single-sample panel is genuinely new relative to Bhattacharya-Sen and Shah et al. The paper also deserves credit for being upfront about what it cannot validate: real-data counterfactuals are not testable, and Assumption 3 is a substantive identifiability condition, not a regularity footnote.

The soft spots are mostly on the empirical side, and the paper half-admits them. The COVID case study explicitly says the intervention pattern may not satisfy Assumption 3, and the once-vaccinated-always rollout looks like exactly the low-rank Z that lets a low-rank A absorb β. The hybrid experiment uses an A* sharing the top singular direction with Z, which is the favorable case, not the adversarial one, so it does little to reassure me that β is identified for the real data. The reported GTE (-0.108) should be read as an illustration under strong assumptions, not as a measured effect. Add the mismatch between theory (global minimizer over rank-constrained Θ) and implementation (alternating minimization, no global guarantee), and the synthetic experiments running with |ξ*|+|η*|=1.1 > 1, outside Theorem 2's regime. The fitted ξ̂=1.11 on real data also violates the Dobrushin condition; the B=100 vs B=500 check is a reasonable sanity check, but it does not restore the theoretical guarantees.

The test-set recovery experiment is weaker than the text suggests: a constant predictor achieves lower aggregate error than their model (0.002 vs 0.015). That is a real omission, though it does not affect the theoretical claims.

None of this is fatal to the main contribution. The theory is a legitimate step forward, and the paper is honest about many of its own limitations. It just asks the reader to keep theory and application separate. If revised to add in-regime experiments, a baseline in the recovery study, and more careful framing of the COVID estimate as conditional on a suspicious assumption, it will be a useful paper for people working at the intersection of high-dimensional Ising estimation and causal inference. I would send it to a serious referee.

Referee Report

2 major / 5 minor

Summary. The paper studies causal inference for sequential binary outcomes under network interference and low-rank latent confounding. Outcomes evolve according to a temporal Ising model with a known interaction graph Γ, an unknown low-rank external field A (latent confounders), a scalar treatment effect β, a spatial coupling ξ, and a temporal coupling η. The observed data are a single panel (x,z). The authors propose sequential maximum pseudo-likelihood estimation (MPLE) and prove non-asymptotic bounds on the parameter error and on the squared error of generalized treatment effect (GTE) estimates under three assumptions: low rank of A*, a Dobrushin-type boundedness condition, and an 'excitability' condition on the intervention matrix Z (Assumption 3). The proofs follow the established single-sample Ising template: pointwise curvature, identifiability separation, and an ε-net union bound. Synthetic experiments, hybrid experiments based on the real Z, and a COVID-19 vaccination case study are used to illustrate the method. The paper claims the first computationally efficient estimator with provable guarantees in this combined setting.

Significance. If the results hold, the paper makes a useful theoretical contribution: it extends the single-sample Ising estimation line of work to a sequential setting with low-rank latent confounding and provides end-to-end guarantees from parameter estimation to causal estimands, under explicit assumptions. The proof structure is detailed and largely follows established techniques, and the synthetic/hybrid experiments provide supporting evidence for the method's finite-sample behavior. The real-data case study, however, is the weakest part: the headline causal estimate is presented as a substantive finding despite the paper's own acknowledgment that the actual intervention pattern may violate the identifiability assumption, and the fitted model violates the Dobrushin condition used by the GTE bound. These issues are fixable by honest reframing and additional diagnostics, but they currently overstate what is established.

major comments (2)

[Assumption 3; §4.2, Table 5] Assumption 3 is the load-bearing identifiability condition that separates β from the low-rank field A; it is used explicitly in Lemma 7, Eq. (30). It fails when the observed Z can be absorbed into a rank-k perturbation of A*: for example, taking A=A*−δZ gives LHS zero while the RHS is positive. The COVID-19 rollout Z is monotone (Figure E1) and nearly rank-one (the top singular value carries 77% of its energy, Section 4.2), which is exactly the regime in which Assumption 3 is suspect. The paper itself states that the interventional pattern 'may not satisfy Assumption 3.' The hybrid experiments construct an A* whose leading factor is the top singular feature of Z, a favorable partially-confounded case; they do not test the worst-case direction. Consequently Corollary 2 does not support the headline GTE=−0.108 in Table 5. Please (i) report the singular-value spectrum / effective rank of Z,
[§4.2, Table 3; Theorem 2/Corollary 2] The real-data fit violates the Dobrushin condition required by Theorem 2: the test-set-recovery model reports ξ̂=1.11, and with |η̂| positive, |ξ̂|+|η̂|>1. Corollary 2's GTE perturbation bound requires |ξ|+|η|<1 for both the estimated and the true parameters. The B=100 vs. B=500 mixing comparison in Table E2 is a useful heuristic, but it does not restore the formal guarantee. Either constrain the real-data fit to the theoretically covered regime, or present the COVID causal estimate as heuristic and explicitly outside the scope of Theorem 2.

minor comments (5)

[Abstract, §1] The abstract and introduction describe Assumptions 1–3 as 'mild assumptions.' Assumption 3 is a substantive identifiability condition on the observed intervention matrix, not a mild regularity condition. Suggest rephrasing to 'structural assumptions'.
[Notation] The symbol B is used both for the ℓ∞ bound in Assumption 2 and for the number of Gibbs sweeps in the experiments (e.g., 'B=100'). This is confusing; consider renaming the Gibbs sweep parameter (e.g., 'R' or 'sweeps').
[§4.2, Table 5] The threshold choices ('more than 2 deaths per 100,000' and '30% vaccinated') are justified only by 'ensuring diversity.' A small sensitivity analysis over these thresholds would strengthen the case study.
[§4.2] Typos: 'Generalized Treatement Effect' in Eq. (2), 'outerperfoms' in Section 4.2, and 'unqiueness' in Appendix C. Also Figure E1 is referenced but the caption does not fully describe the plotted quantity.
[Appendix D, Theorem 3 proof] Step 3 of the Theorem 3 proof, bounding derivatives with respect to α_i^{(t)}, is terse. A few lines showing the oscillation bound δ_j(g)=2 I{j=i} and the summation would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the central bound follows from explicit assumptions; Assumption 3 is a genuine identifiability premise, not a repackaged conclusion.

full rationale

The derivation chain is not circular. The paper specifies the model (1) and states Assumptions 1-3. Theorem 1 is proven from these by Taylor-expanding the sequential MPLE objective and bounding the random curvature terms via Lemmas 1-8. Assumption 3 is used explicitly in Lemma 7 to lower-bound the conditional expectation of the external-field deviation by ||A−A*||_F^2 + NT(β−β*)²; this is an input assumption, not the theorem's conclusion. No parameter is fitted to the quantity later called a prediction: the GTE bound (Corollary 2) follows from the parameter bound plus Theorem 2, which is proven from Dobrushin correlation decay (Lemmas 18-19), and the GTE estimates in the case study are model outputs evaluated on held-out test outcomes and synthetic hybrid data, not refitted targets. The self-citations ([20], [21], [29], [37]) are prior general Ising-model concentration/correlation results whose assumptions do not include the target sequential-MPLE or GTE claim, so they count as independent support under the review rules. The admitted possibility that the COVID-19 intervention pattern violates Assumption 3 (Section 4.2) is a validity/identifiability limitation, not circularity: if the premise fails, the theorem's applicability fails, but the theorem does not assume its conclusion. The hybrid experiment tests only a favorable (A*, Z) pair, but it is an empirical sanity check rather than a load-bearing derivation step. Overall, no equation reduces by construction to its own input.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central results rest on three paper-stated premises (exact rank-k confounding structure, Dobrushin-type boundedness, uniform excitability of interventions) plus the parametric form of Eq (1) itself. Assumption 3 is the most fragile: the paper admits the real intervention pattern likely violates it, and the near-rank-one Z means β identification on the COVID data is assumed rather than established. Hyperparameters k and λ are selected by cross-validation, and the real-data thresholds are data-dependent design choices whose influence on the headline GTE is not analyzed. No invented entities: the latent confounders A=UV^T are a standard panel-data construct, and θ parameters are estimands, not free fitting constants.

free parameters (4)

rank k of the latent factor matrix A = k=3 (synthetic), k=5 (hybrid), k=5 or 8 (real data, grid search)
The low-rank dimension in Assumption 1 is selected by cross-validation (Appendix F.1.3); the theory treats k as known.
regularization λ for (||U||_F² + ||V||_F²) = 0.001-0.05 depending on setting
λ is chosen by cross-validation from Λ={0.001,0.005,0.01,0.05,0.1,0.5}. The estimator analyzed in Theorem 1 has no λ; the implemented estimator in Eq (6) does.
binarization thresholds for the real-world study = >2 deaths per 100,000 residents per week; >30% vaccinated with a two-week lag
Thresholds are 'chosen to ensure diversity in x and z' (Section 4.2); the headline COVID GTE depends on these data-dependent choices.
interaction graph construction Γ = 8 nearest neighbors, weights w_ij = e^{-d(i,j)/d̄}, normalized so ||Γ||_∞ = 1
Γ is assumed known in the model, but in the application it is a distance-kernel heuristic; all theoretical rates depend on ||Γ||_F².

assumptions (6)

domain assumption Assumption 1: the N×T matrix of latent confounders A* has rank at most k
Central structural assumption imported from synthetic-controls and panel-data literature (Section 2); if the true confounding is not exactly low-rank, α is not identifiable as specified.
domain assumption Assumption 2: ||Γ||_∞=1, |ξ*|<1, and all fields bounded by B≥1
Sufficient for Dobrushin uniqueness, which underpins concentration, fast Gibbs mixing, and correlation decay (Section 2, Lemma 2.6 of [29]). Violated by the real-data fit where ξ̂=1.11.
ad hoc to paper Assumption 3: uniform excitability of the intervention matrix Z separating β from the low-rank field
Paper-specific identifiability condition; the sole mechanism separating treatment effect from the latent field (used in Lemma 7 / Eq (30)). The paper states the monotone COVID rollout 'may not satisfy' it, and Z's top singular value carries 77% of its energy (near rank-one).
domain assumption The data-generating process is exactly the Markovian Ising model (Eq 1), with no unobserved confounders beyond the low-rank A
The causal estimands GTE_θ are defined and identified within this model; violations of the model form would invalidate the counterfactuals.
standard math Ising concentration, anti-concentration, and affine-concentration lemmas from [20,39] (Lemmas 11-14 in Appendix C)
Borrowed results under Dobrushin's condition; used as black boxes in the proof of Theorem 1.
standard math Covering-number bound for low-rank matrices (Lemma 3.1 of [53])
Used for the ε-net over Θ in the proof of Lemma 3.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Causal Inference for Sequential Settings under Interference and Latent Confounding." pith.science (2026). https://pith.science/paper/3YGQGTG4

@misc{pith2026260714940,
  author       = {Pith},
  title        = {Pith review of: Causal Inference for Sequential Settings under Interference and Latent Confounding},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3YGQGTG4}},
  note         = {Machine review of arXiv:2607.14940}
}

read the original abstract

We study causal inference under outcome interference for sequential, observational settings. Specifically, we consider settings where the binary outcomes over N units are Markovian across T time steps. At each time step, the outcomes of N units have dependencies captured through an Ising model; each outcome is also impacted through an external field capturing the effects of its treatment as well as latent confounders. Similar to panel data literature, these latent confounders are modeled to have a low-rank factor structure. Our data is a single sample from this high-dimensional distribution. To estimate causal quantities of interest, we provide a computationally efficient method based on Maximum Pseudo-Likelihood Estimation (MPLE) for learning the model parameters. Under mild assumptions, we establish non-asymptotic consistency for parameter estimation and show this translates to faithful estimation of causal quantities of interest after sampling from the learned model. We demonstrate the efficacy of the method through synthetic experiments as well as a real-world case-study investigating causal effects of vaccine rates on COVID-19 death rates within US counties nationwide.

Figures

Figures reproduced from arXiv: 2607.14940 by the authors.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Scaling Limits for Ising Models on Inhomogeneous Random Graphs and Applications
math.PR 2026-08 conditional novelty 6.0 of 10

High-temperature Ising models on graphon random graphs have Gaussian spin statistics with covariance given by the graphon resolvent, yielding functional and Sobolev-space limits.

Reference graph

Works this paper leans on

55 extracted references · 1 linked inside Pith · cited by 1 Pith paper

[1]

G. W. Imbens and D. B. Rubin,Causal Inference for Statistics, Social, and Biomedical Sci- ences: An Introduction. Cambridge: Cambridge University Press, 2015

2015
[2]

Toward Causal Inference With Interference,

M. G. Hudgens and M. E. Halloran, “Toward Causal Inference With Interference,”Journal of the American Statistical Association, vol. 103, pp. 832–842, June 2008

2008
[3]

Estimating Average Causal Effects Under General Interference, with Application to a Social Network Experiment,

P. M. Aronow and C. Samii, “Estimating Average Causal Effects Under General Interference, with Application to a Social Network Experiment,”The Annals of Applied Statistics, vol. 11, Dec. 2017

2017
[4]

Average treatment effects in the presence of unknown interference,

F. Sävje, P. M. Aronow, and M. G. Hudgens, “Average treatment effects in the presence of unknown interference,”The Annals of Statistics, vol. 49, pp. 673–701, Apr. 2021

2021
[5]

Robust Inference for the Direct Average Treatment Effect with Treatment Assignment Interference,

M. D. Cattaneo, Y . He, Ruiqi, and Yu, “Robust Inference for the Direct Average Treatment Effect with Treatment Assignment Interference,” Feb. 2025

2025
[6]

The Conflict Graph Design: Estimating Causal Effects under Arbitrary Neighborhood Interference,

V . Kandiros, C. Pipis, C. Daskalakis, and C. Harshaw, “The Conflict Graph Design: Estimating Causal Effects under Arbitrary Neighborhood Interference,” Jan. 2025

2025
[7]

Auto-g-computation of causal effects on a network,

E. J. Tchetgen Tchetgen, I. R. Fulcher, and I. Shpitser, “Auto-g-computation of causal effects on a network,”Journal of the American Statistical Association, vol. 116, no. 534, pp. 833–844, 2021

2021
[8]

Causal effect estimation under network interference with mean- field methods,

S. Bhattacharya and S. Sen, “Causal effect estimation under network interference with mean- field methods,”The Annals of Statistics, vol. 53, no. 6, pp. 2430–2461, 2025

2025

Show all 55 references

[9]

Network Synthetic Interventions: A Causal Framework for Panel Data Under Network Interference,

A. Agarwal, S. H. Cen, D. Shah, and C. L. Yu, “Network Synthetic Interventions: A Causal Framework for Panel Data Under Network Interference,” Oct. 2023

2023
[10]

Designs for estimating the treatment effect in networks with interference,

R. Jagadeesan, N. S. Pillai, and A. V olfovsky, “Designs for estimating the treatment effect in networks with interference,”The Annals of Statistics, vol. 48, pp. 679–712, Apr. 2020

2020
[11]

Randomized graph cluster randomization,

J. Ugander and H. Yin, “Randomized graph cluster randomization,”Journal of Causal Infer- ence, vol. 11, Jan. 2023

2023
[12]

The economic costs of conflict: A case study of the basque country,

A. Abadie and J. Gardeazabal, “The economic costs of conflict: A case study of the basque country,”American economic review, vol. 93, no. 1, pp. 113–132, 2003

2003
[13]

Robust synthetic control,

M. Amjad, D. Shah, and D. Shen, “Robust synthetic control,”Journal of Machine Learning Research, vol. 19, no. 22, pp. 1–51, 2018

2018
[14]

Doubly robust inference in causal latent factor models,

A. Abadie, A. Agarwal, R. Dwivedi, and A. Shah, “Doubly robust inference in causal latent factor models,”arXiv preprint arXiv:2402.11652, 2024

2024 arXiv
[15]

Synthetic interventions: Extending synthetic controls to multiple treatments,

A. Agarwal, D. Shah, and D. Shen, “Synthetic interventions: Extending synthetic controls to multiple treatments,”Operations Research, vol. 74, no. 2, pp. 840–859, 2026

2026
[16]

Estimation in spin glasses: A first step,

S. Chatterjee, “Estimation in spin glasses: A first step,”The Annals of Statistics, pp. 1931– 1946, 2007

1931
[17]

Inference in ising models,

B. B. Bhattacharya and S. Mukherjee, “Inference in ising models,”BERNOULLI, pp. 493–525, 2018

2018
[18]

Regression from dependent observations,

C. Daskalakis, N. Dikkala, and I. Panageas, “Regression from dependent observations,” in Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, pp. 881– 889, 2019

2019
[19]

Joint estimation of parameters in ising model,

P. Ghosal and S. Mukherjee, “Joint estimation of parameters in ising model,”The Annals of Statistics, vol. 48, no. 2, pp. 785–810, 2020

2020
[20]

Learning ising models from one or multiple samples,

Y . Dagan, C. Daskalakis, N. Dikkala, and A. V . Kandiros, “Learning ising models from one or multiple samples,” inProceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing, pp. 161–168, 2021

2021
[21]

Statistical Estimation from Dependent Data,

V . Kandiros, Y . Dagan, N. Dikkala, S. Goel, and C. Daskalakis, “Statistical Estimation from Dependent Data,” inProceedings of the 38th International Conference on Machine Learning, pp. 5269–5278, PMLR, July 2021

2021
[22]

Identification of treatment response with social interactions,

C. F. Manski, “Identification of treatment response with social interactions,”The Econometrics Journal, vol. 16, no. 1, pp. S1–S23, 2013. 10

2013
[23]

Causal Inference for a Population of Causally Connected Units,

M. J. van der Laan, “Causal Inference for a Population of Causally Connected Units,”Journal of causal inference, vol. 2, pp. 13–74, Mar. 2014

2014
[24]

Identification and estimation of causal effects from dependent data,

E. Sherman and I. Shpitser, “Identification and estimation of causal effects from dependent data,”Advances in neural information processing systems, vol. 31, 2018

2018
[25]

Causal inference under interference and net- work uncertainty,

R. Bhattacharya, D. Malinsky, and I. Shpitser, “Causal inference under interference and net- work uncertainty,” inProceedings of The 35th Uncertainty in Artificial Intelligence Conference (R. P. Adams and V . Gogate, eds.), vol. 115 ofProceedings of Machine Learning Research, ...

2020
[26]

Public health implications of opening National Football League stadiums during the COVID-19 pandemic,

B. García Bulle, D. Shen, D. Shah, and A. E. Hosoi, “Public health implications of opening National Football League stadiums during the COVID-19 pandemic,”Proceedings of the Na- tional Academy of Sciences, vol. 119, p. e2114226119, Apr. 2022

2022
[27]

Ding,A first course in causal inference

P. Ding,A first course in causal inference. Chapman and Hall/CRC, 2024

2024
[28]

Synthetic control methods for comparative case studies: Estimating the effect of california’s tobacco control program,

A. Abadie, A. Diamond, and J. Hainmueller, “Synthetic control methods for comparative case studies: Estimating the effect of california’s tobacco control program,”Journal of the American statistical Association, vol. 105, no. 490, pp. 493–505, 2010

2010
[29]

Learning from weakly dependent data under Dobrushin’s condition,

Y . Dagan, C. Daskalakis, N. Dikkala, and S. Jayanti, “Learning from weakly dependent data under Dobrushin’s condition,” inConference on Learning Theory, 2019

2019
[30]

Logistic regression with peer-group effects via inference in higher-order Ising models,

C. Daskalakis, N. Dikkala, and I. Panageas, “Logistic regression with peer-group effects via inference in higher-order Ising models,” inProceedings of the Twenty Third International Con- ference on Artificial Intelligence and Statistics, pp. 3653–3663, PMLR, June 2020

2020
[31]

Estimating Ising Models in Total Variation Distance,

C. Daskalakis, V . Kandiros, and R. Yao, “Estimating Ising Models in Total Variation Distance,” Nov. 2025

2025
[32]

The description of a random field by means of conditional probabilities and conditions of its regularity,

P. Dobruschin, “The description of a random field by means of conditional probabilities and conditions of its regularity,”Theory of Probability & Its Applications, vol. 13, no. 2, pp. 197– 224, 1968

1968
[33]

Spatial interaction and the statistical analysis of lattice systems,

J. Besag, “Spatial interaction and the statistical analysis of lattice systems,”Journal of the Royal Statistical Society: Series B (Methodological), vol. 36, no. 2, pp. 192–225, 1974

1974
[34]

Statistical analysis of non-lattice data,

J. Besag, “Statistical analysis of non-lattice data,”Journal of the Royal Statistical Society: Series D (The Statistician), vol. 24, no. 3, pp. 179–195, 1975

1975
[35]

On learning continuous pairwise markov random fields,

A. Shah, D. Shah, and G. Wornell, “On learning continuous pairwise markov random fields,” in International conference on artificial intelligence and statistics, pp. 1153–1161, PMLR, 2021

2021
[36]

A computationally efficient method for learning expo- nential family distributions,

A. Shah, D. Shah, and G. Wornell, “A computationally efficient method for learning expo- nential family distributions,”Advances in neural information processing systems, vol. 34, pp. 15841–15854, 2021

2021
[37]

On counterfactual inference with unob- served confounding,

A. Shah, R. Dwivedi, D. Shah, and G. W. Wornell, “On counterfactual inference with unob- served confounding,” Sept. 2023

2023
[38]

Why are big data matrices approximately low rank?,

M. Udell and A. Townsend, “Why are big data matrices approximately low rank?,”SIAM Journal on Mathematics of Data Science, vol. 1, no. 1, pp. 144–160, 2019

2019
[39]

Chatterjee,Concentration inequalities with exchangeable pairs

S. Chatterjee,Concentration inequalities with exchangeable pairs. Stanford University, 2005

2005
[40]

Concentration of multilinear functions of the ising model with applications to network data,

C. Daskalakis, N. Dikkala, and G. Kamath, “Concentration of multilinear functions of the ising model with applications to network data,”Advances in Neural Information Processing Systems, vol. 30, 2017

2017
[41]

A simple condition implying rapid mixing of single-site dynamics on spin sys- tems,

T. P. Hayes, “A simple condition implying rapid mixing of single-site dynamics on spin sys- tems,” inProceedings of the 47th Annual IEEE Symposium on Foundations of Computer Sci- ence, pp. 39–46, IEEE, 2006

2006
[42]

Decay of correlations under dobrushin’s uniqueness condition and its applica- tions,

H. Künsch, “Decay of correlations under dobrushin’s uniqueness condition and its applica- tions,”Communications in Mathematical Physics, vol. 84, no. 2, pp. 207–222, 1982

1982
[43]

A covariance estimate for Gibbs measures,

H. Föllmer, “A covariance estimate for Gibbs measures,”Journal of Functional Analysis, vol. 46, pp. 387–395, May 1982

1982
[44]

Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization,

B. Recht, M. Fazel, and P. A. Parrilo, “Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization,”SIAM review, vol. 52, no. 3, pp. 471–501, 2010. 11

2010
[45]

Low-rank matrix completion using alternating mini- mization,

P. Jain, P. Netrapalli, and S. Sanghavi, “Low-rank matrix completion using alternating mini- mization,” inProceedings of the forty-fifth annual ACM symposium on Theory of computing, pp. 665–674, 2013

2013
[46]

Nonconvex optimization meets low-rank matrix factorization: An overview,

Y . Chi, Y . M. Lu, and Y . Chen, “Nonconvex optimization meets low-rank matrix factorization: An overview,”IEEE Transactions on Signal Processing, vol. 67, no. 20, pp. 5239–5269, 2019

2019
[47]

Stochastic relaxation, gibbs distributions, and the bayesian restora- tion of images,

S. Geman and D. Geman, “Stochastic relaxation, gibbs distributions, and the bayesian restora- tion of images,”IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. PAMI- 6, no. 6, pp. 721–741, 1984

1984
[48]

Graphical Models, Exponential Families, and Variational Inference,

M. J. Wainwright and M. I. Jordan, “Graphical Models, Exponential Families, and Variational Inference,”Foundations and Trends in Machine Learning, vol. 1, pp. 1–305, Dec. 2008

2008
[49]

On the hardness of sampling independent sets beyond the tree threshold,

E. Mossel, D. Weitz, and N. Wormald, “On the hardness of sampling independent sets beyond the tree threshold,”Probability Theory and Related Fields, vol. 143, no. 3, pp. 401–439, 2009

2009
[50]

Coronavirus (COVID-19) data in the United States

The New York Times, “Coronavirus (COVID-19) data in the United States.”https:// github.com/nytimes/covid-19-data, 2021. Accessed: 2024

2021
[51]

COVID data tracker: Vaccinations

Centers for Disease Control and Prevention, “COVID data tracker: Vaccinations.”https:// data.cdc.gov, 2021. Data endpoint: resource/8xkx-amqh

2021
[52]

Vaccine tracking data repository

S. Bansalet al., “Vaccine tracking data repository.”https://github.com/bansallab/ vaccinetracking, 2021. County-level time series vaccination data

2021
[53]

Tight oracle inequalities for low-rank matrix recovery from a min- imal number of noisy random measurements,

E. J. Candes and Y . Plan, “Tight oracle inequalities for low-rank matrix recovery from a min- imal number of noisy random measurements,”IEEE Transactions on Information Theory, vol. 57, no. 4, pp. 2342–2359, 2011

2011
[54]

Verification of forecasts expressed in terms of probability,

G. W. Brier, “Verification of forecasts expressed in terms of probability,”Monthly Weather Review, vol. 78, no. 1, pp. 1–3, 1950. A Representations of Causal Model Figure A1 represents the latent confounding for a singleiandt. Our consideration of latents vari- ables in (1) is...

1950
[55]

1 N X i x(s) i |x(t) =y # −E

Letc 6 = max{c′ 6, c′′ 6 }. The success probabil- ity of this event is at least1−C 6 exp(−e−c6Bd(θ))again sinced h dominatesd(θ)in this case. 17 B.3 Boundingd( ˆθ) In this section, we complete the proof of Theorem 1 by translating the pointwise bound of Lemma 2 into a uniform ...

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.

[1] [1]

G. W. Imbens and D. B. Rubin,Causal Inference for Statistics, Social, and Biomedical Sci- ences: An Introduction. Cambridge: Cambridge University Press, 2015

2015

[2] [2]

Toward Causal Inference With Interference,

M. G. Hudgens and M. E. Halloran, “Toward Causal Inference With Interference,”Journal of the American Statistical Association, vol. 103, pp. 832–842, June 2008

2008

[3] [3]

Estimating Average Causal Effects Under General Interference, with Application to a Social Network Experiment,

P. M. Aronow and C. Samii, “Estimating Average Causal Effects Under General Interference, with Application to a Social Network Experiment,”The Annals of Applied Statistics, vol. 11, Dec. 2017

2017

[4] [4]

Average treatment effects in the presence of unknown interference,

F. Sävje, P. M. Aronow, and M. G. Hudgens, “Average treatment effects in the presence of unknown interference,”The Annals of Statistics, vol. 49, pp. 673–701, Apr. 2021

2021

[5] [5]

Robust Inference for the Direct Average Treatment Effect with Treatment Assignment Interference,

M. D. Cattaneo, Y . He, Ruiqi, and Yu, “Robust Inference for the Direct Average Treatment Effect with Treatment Assignment Interference,” Feb. 2025

2025

[6] [6]

The Conflict Graph Design: Estimating Causal Effects under Arbitrary Neighborhood Interference,

V . Kandiros, C. Pipis, C. Daskalakis, and C. Harshaw, “The Conflict Graph Design: Estimating Causal Effects under Arbitrary Neighborhood Interference,” Jan. 2025

2025

[7] [7]

Auto-g-computation of causal effects on a network,

E. J. Tchetgen Tchetgen, I. R. Fulcher, and I. Shpitser, “Auto-g-computation of causal effects on a network,”Journal of the American Statistical Association, vol. 116, no. 534, pp. 833–844, 2021

2021

[8] [8]

Causal effect estimation under network interference with mean- field methods,

S. Bhattacharya and S. Sen, “Causal effect estimation under network interference with mean- field methods,”The Annals of Statistics, vol. 53, no. 6, pp. 2430–2461, 2025

2025