Improved Guarantees for Heterogeneous Treatment-Effect Estimation via Matrix Completion

2026-05-28

AI Summary

This study addresses the estimation of heterogeneous treatment effects for individual units in panel data under unknown and non-uniform treatment assignment, formulating the problem as a low-rank matrix completion task without requiring propensity score information. By integrating spectral analysis with row-wise perturbation theory, the authors propose a computationally efficient estimator and, under standard low-rank and regularity assumptions, establish the first sharp row-wise ℓ₂ perturbation bound. This theoretical advance overcomes the limitation of existing results that apply only to average treatment effects. The resulting error bound scales as Õ(√(1/n + n/m²)), substantially improving both the theoretical guarantees and practical accuracy for estimating individual-level treatment effects.

Abstract

A central goal of modern causal inference is estimating heterogeneous treatment effects to answer questions like "how does an intervention affect each unit," rather than only on average. We study this problem with panel-data where we observe $n$ units across $m$ times under unknown, non-uniform treatment assignments. The data in this setting is naturally represented as a matrix of all unit--time treatment effects. Estimating heterogeneous treatment effects can then be expressed as obtaining a good estimation of each row's average in this matrix. This allows us to formulate the problem as matrix completion, which can be solved under natural low-rankness assumptions. However, existing matrix-completion guarantees are not powerful enough to get meaningful bounds for the per-row guarantee required for estimating the heterogeneous treatment effect; roughly speaking, they are only useful for estimating average treatment effect bounds, as also illustrated in a recent line of work. We give a simple, computationally efficient estimator that, without knowledge of the propensities and under standard low-rankness and regularity assumptions, achieves a row-wise $\ell_2$ error of $\tilde{O}(\sqrt{\frac{1}{n} + \frac{n}{m^2}})$. Technically, our analysis establishes the first sharp row-wise $\ell_2$-perturbation bound for low-rank approximation, complementing existing spectral-, Frobenius-, and entrywise perturbation theory.

Problem

• heterogeneous treatment effects
• matrix completion
• panel data
• causal inference
• low-rank approximation

Innovation

• heterogeneous treatment effects
• matrix completion
• row-wise error bound
• low-rank approximation
• causal inference