Matching for causal effects via multimarginal optimal transport

Gunsilius, Florian; Xu, Yang

doi:10.48550/arxiv.2112.04398

Cited by 4 publications

(8 citation statements)

References 50 publications

(94 reference statements)

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Section: Resultsmentioning

confidence: 99%

“…Remark 5 (Comparison with [GX21]). Theorem 1 in the latest update of [GX21] (updated on July 12, 2022 on arXiv) 3 states a limit distribution result for the EOT potentials in C(X 1 ) × C(X 2 ) (in fact [GX21] consider the multi-marginal setting, but we focus our discussion on the two-marginal case). Their proof differs from ours in that they do not derive Hadamard differentiability of EOT potentials (nor does the proof contain Hadamard differentiability results).…”

Section: Resultsmentioning

confidence: 99%

“…Importantly, the Hadamard differentiability result is stronger than just deriving a limit distribution, as it automatically yields bootstrap consistency and asymptotic efficiency of the empirical estimators; see Section 5 for further discussion. The question of asymptotic efficiency is not accounted for in [GX21]. Furthermore, Hadamard differentiability of the EOT potentials in C s (X 1 ) × C s (X 2 ) plays a crucial role in deriving the null limit distribution of the empirical Sinkhorn divergence which involves the second order Hadamard derivative of the EOT potentials in C(X 1 ) × C(X 2 ).…”

Section: Resultsmentioning

confidence: 99%

“…They analyzed the empirical EOT map and established the parametric convergence rate towards the EOT map for fixed ε > 0, but the rate toward the Brenier map itself when taking ε = ε n → 0 is sub-optimal; see also [RS22] for relevant results with ε > 0 fixed. CLTs for the empirical EOT plan were studied in [KTM20] for discrete distributions and [GX21] for more general cases. The latter work also obtained a limit theorem for the EOT potentials in the C-space, which is derived via a significantly different proof technique than ours (not relying on Hadamard differentiability) and is weaker than the convergence in Hölder spaces established herein.…”

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confidence: 99%

See 3 more Smart Citations

Limit Theorems for Entropic Optimal Transport Maps and the Sinkhorn Divergence

Goldfeld¹,

Kato²,

Rioux³

et al. 2022

Preprint

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We study limit theorems for entropic optimal transport (EOT) maps, dual potentials, and the Sinkhorn divergence. The key technical tool we use is a first and second order Hadamard differentiability analysis of EOT potentials with respect to the underlying distributions. Given the differentiability results, the functional delta method is used to obtain central limit theorems for empirical EOT potentials and maps. The second order functional delta method is leveraged to establish the limit distribution of the empirical Sinkhorn divergence under the null. Building on the latter result, we further derive the null limit distribution of the Sinkhorn independence test statistic and characterize the correct order. Since our limit theorems follow from Hadamard differentiability of the relevant maps, as a byproduct, we also obtain bootstrap consistency and asymptotic efficiency of the empirical EOT map, potentials, and Sinkhorn divergence.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Limit Theorems for Entropic Optimal Transport Maps and the Sinkhorn Divergence

Goldfeld¹,

Kato²,

Rioux³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Optimal transport with entropic regularization can be formulated as a convex optimization problem which can be solved efficiently using the alternating direction method (Sinkhorn-Knopp algorithm). Moreover, recent works have shown asymptotic properties of the entropy regularized optimal transport map for causal matching [31]. Entropy regularized optimal transport yields a probabilistic one-to-many matching for each point between two discrete distributions.…”

Section: Confounder Signal Matching Via Cinema-otmentioning

confidence: 99%

Causal identification of single-cell experimental perturbation effects with CINEMA-OT

Dong

Wang

Wei

et al. 2022

Preprint

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Recent advancements in single-cell technologies allow characterization of experimental perturbations at single-cell resolution. While methods have been developed to analyze data from such experiments, the application of a strict causal framework has not yet been explored for the inference of treatment effects at the single-cell level. In this work, we present a causal inference based approach to single-cell perturbation analysis, termed CINEMA-OT (Causal INdependent Effect Module Attribution + Optimal Transport). CINEMA-OT separates confounding sources of variation from perturbation effects to obtain an optimal transport matching that reflects counterfactual cell pairs. These cell pairs represent causal perturbation responses permitting a number of novel analyses, such as individual treatment effect analysis, response clustering, attribution analysis, and synergy analysis. We benchmark CINEMA-OT on an array of treatment effect estimation tasks for several simulated and real datasets and show that it outperforms other single-cell perturbation analysis methods. Finally, we perform CINEMA-OT analysis of two newly-generated datasets: (1) rhinovirus-infected airway organoids, and (2) combinatorial cytokine stimulation of immune cells. Using CINEMA-OT, we discover diverging treatment responses and their associated cellular sub-populations. By applying CINEMA-OT to combinatorial experimental designs, we infer the specific cell-gene programs driving syngergistic responses.

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Exploiting Geometry for Treatment Effect Estimation via Optimal Transport

Yan,

Yang,

Chen

et al. 2024

AAAI

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Estimating treatment effects from observational data suffers from the issue of confounding bias, which is induced by the imbalanced confounder distributions between the treated and control groups. As an effective approach, re-weighting learns a group of sample weights to balance the confounder distributions. Existing methods of re-weighting highly rely on a propensity score model or moment alignment. However, for complex real-world data, it is difficult to obtain an accurate propensity score prediction. Although moment alignment is free of learning a propensity score model, accurate estimation for high-order moments is computationally difficult and still remains an open challenge, and first and second-order moments are insufficient to align the distributions and easy to be misled by outliers. In this paper, we exploit geometry to capture the intrinsic structure involved in data for balancing the confounder distributions, so that confounding bias can be reduced even with outliers. To achieve this, we construct a connection between treatment effect estimation and optimal transport, a powerful tool to capture geometric information. After that, we propose an optimal transport model to learn sample weights by extracting geometry from confounders, in which geometric information between groups and within groups is leveraged for better confounder balancing. A projected mirror descent algorithm is employed to solve the derived optimization problem. Experimental studies on both synthetic and real-world datasets demonstrate the effectiveness of our proposed method.

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Matching for causal effects via multimarginal optimal transport

Cited by 4 publications

References 50 publications

Limit Theorems for Entropic Optimal Transport Maps and the Sinkhorn Divergence

Limit Theorems for Entropic Optimal Transport Maps and the Sinkhorn Divergence

Causal identification of single-cell experimental perturbation effects with CINEMA-OT

Exploiting Geometry for Treatment Effect Estimation via Optimal Transport

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