Synthetic Interventions

Agarwal, Anish K.; Shah, Devavrat; Shen, Dennis

doi:10.48550/arxiv.2006.07691

Cited by 5 publications

(29 citation statements)

References 8 publications

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“…As a special case, this also provides novel entry-wise finite-sample consistency and asymptotic normality results for the traditional matrix completion with MCAR data literature. Collectively, our identification, consistency, and asymptotic normality results, coupled with SNN, can be seen as a generalization of the SI framework proposed in Agarwal et al (2021b).…”

Section: Contributions and Paper Organizationmentioning

confidence: 66%

“…We interpret Y as the matrix of potential outcomes and P as the matrix of intervention assignments. Building upon the recent work of Agarwal et al (2021b), we propose a framework that allows (i) correlation between D and Y , i.e., hidden confounding; (ii) correlation between the entries of D; (iii) the minimum value of P to be 0, i.e., entries of Y can be deterministically missing; (iv) P to not exhibit low-dimensional structure as is required in the panel data literature, i.e., we consider significantly more general missingness patterns. To the best of our knowledge, our framework, and associated algorithm, is the first within the MNAR matrix completion literature that allows for conditions (i)-(iv) to simultaneously hold.…”

Section: Contributions and Paper Organizationmentioning

confidence: 99%

“…To do so, we relate this task to the well-known problem of finding the "maximum" biclique in a bipartite graph. Since SNN is a generalization of the recently proposed synthetic interventions (SI) estimator of Agarwal et al (2021b), which itself is a generalization of the popular synthetic controls algorithm of Abadie and Gardeazabal (2003); Abadie et al (2010), this subroutine may be of independent interest to the synthetic controls and panel data literatures.…”

Section: Contributions and Paper Organizationmentioning

confidence: 99%

“…Comparison with synthetic interventions. Our proposed framework framework builds upon the recent work of Agarwal et al (2021b), called synthetic interventions (SI). SI is a causal inference method to do tensor completion with MNAR data, where the dimensions of the order-3 tensor of interest are units, measurements, and interventions.…”

Section: Panel Data and Matrix Completionmentioning

confidence: 99%

“…Their setup can be made a special case of ours by effectively flattening the tensor into a matrix, where the rows of the induced matrix still correspond to units, but a column is a double index for a measurement and an intervention, i.e., the (i, j, d)-th entry of the tensor corresponds to the (i, (j, d))-th entry of the induced matrix. Given this simple reduction, we generalize the framework, algorithm, and theoretical results in Agarwal et al (2021b) in the following ways. First, we formally extend the SI framework, to recover matrices under more general missingness patterns than that considered in Agarwal et al (2021b).…”

Section: Panel Data and Matrix Completionmentioning

confidence: 99%

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Causal Matrix Completion

Agarwal,

Dahleh,

Shah

et al. 2021

Preprint

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Matrix completion is the study of recovering an underlying matrix from a sparse subset of noisy observations. Traditionally, it is assumed that the entries of the matrix are "missing completely at random" (MCAR), i.e., each entry is revealed at random, independent of everything else, with uniform probability. This is likely unrealistic due to the presence of "latent confounders", i.e., unobserved factors that determine both the entries of the underlying matrix and the missingness pattern in the observed matrix. For example, in the context of movie recommender systems-a canonical application for matrix completion-a user who vehemently dislikes horror films is unlikely to ever watch horror films. In general, these confounders yield "missing not at random" (MNAR) data, which can severely impact any inference procedure that does not correct for this bias.We develop a formal causal model for matrix completion through the language of potential outcomes, and provide novel identification arguments for a variety of causal estimands of interest. We design a procedure, which we call "synthetic nearest neighbors" (SNN), to estimate these causal estimands. We prove finite-sample consistency and asymptotic normality of our estimator. Our analysis also leads to new theoretical results for the matrix completion literature. In particular, we establish entry-wise, i.e., max-norm, finite-sample consistency and asymptotic normality results for matrix completion with MNAR data. As a special case, this also provides entry-wise bounds for matrix completion with MCAR data. Across simulated and real data, we demonstrate the efficacy of our proposed estimator.

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Section: Contributions and Paper Organizationmentioning

confidence: 66%

Section: Contributions and Paper Organizationmentioning

confidence: 99%

Section: Contributions and Paper Organizationmentioning

confidence: 99%

Section: Panel Data and Matrix Completionmentioning

confidence: 99%

Section: Panel Data and Matrix Completionmentioning

confidence: 99%

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Causal Matrix Completion

Agarwal,

Dahleh,

Shah

et al. 2021

Preprint

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Causal Inference for Social and Engineering Systems

Agarwal

2022

SIGMETRICS Perform. Eval. Rev.

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What will happen to Y if we do A? A variety of meaningful social and engineering questions can be formulated this way: What will happen to a patient's health if they are given a new therapy? What will happen to a country's economy if policy-makers legislate a new tax? What will happen to a data center's latency if a new congestion control protocol is used? We explore how to answer such counterfactual questions using observational data-which is increasingly available due to digitization and pervasive sensors-and/or very limited experimental data. The two key challenges are: (i) counterfactual prediction in the presence of latent confounders; (ii) estimation with modern datasets which are high-dimensional, noisy, and sparse. The key framework we introduce is connecting causal inference with tensor completion. In particular, we represent the various potential outcomes (i.e., counterfactuals) of interest through an order-3 tensor. The key theoretical results presented are: (i) Formal identification results establishing under what missingness patterns, latent confounding, and structure on the tensor is recovery of unobserved potential outcomes possible. (ii) Introducing novel estimators to recover these unobserved potential outcomes and proving they are finite-sample consistent and asymptotically normal. Finally, we discuss connections between matrix/tensor completion and time series analysis and reinforcement learning; we believe this could serve as a basis to do counterfactual forecasting, and building data-driven simulators for reinforcement learning.

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Same Root Different Leaves: Time Series and Cross‐Sectional Methods in Panel Data

Shen,

Ding,

Sekhon

et al. 2023

ECTA

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One dominant approach to evaluate the causal effect of a treatment is through panel data analysis, whereby the behaviors of multiple units are observed over time. The information across time and units motivates two general approaches: (i) horizontal regression (i.e., unconfoundedness), which exploits time series patterns, and (ii) vertical regression (e.g., synthetic controls), which exploits cross‐sectional patterns. Conventional wisdom often considers the two approaches to be different. We establish this position to be partly false for estimation but generally true for inference. In the absence of any assumptions, we show that both approaches yield algebraically equivalent point estimates for several standard estimators. However, the source of randomness assumed by each approach leads to a distinct estimand and quantification of uncertainty even for the same point estimate. This emphasizes that researchers should carefully consider where the randomness stems from in their data, as it has direct implications for the accuracy of inference.

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Synthetic Interventions

Cited by 5 publications

References 8 publications

Causal Matrix Completion

Causal Matrix Completion

Causal Inference for Social and Engineering Systems

Same Root Different Leaves: Time Series and Cross‐Sectional Methods in Panel Data

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