Kernel-Based Functional Balancing for Causal Inference with Compositional Treatments

Sungbum Kim; Jiayi Wang

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arXiv · 2606.17308

Kernel-Based Functional Balancing for Causal Inference with Compositional Treatments

Sungbum Kim·Jiayi Wang

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Abstract

We study causal effect estimation with compositional treatments, where the exposure lies on a simplex and the estimand is defined over compositions rather than scalar or binary values. By considering a projection of the average potential outcome onto the treatment space, a kernel-based covariate functional balancing approach is adopted for weight construction. The weights are obtained by directly minimizing a worst-case balancing error over a reproducing kernel Hilbert space (RKHS) defined on the joint space of treatments and covariates, instead of being estimated under a treatment assignment model. Building on these weights, an augmented weighted estimator (AWE) is proposed, where the outcome function is estimated via kernel ridge regression and combined with a marginal augmentation over the covariate distribution. Despite the complex structure of the resulting objective, a finite-dimensional convex optimization problem is formulated via a representer theorem and a low-rank approximation. The proposed estimator achieves $\sqrt{n}$-consistency without requiring consistent estimation or smoothness of the weights. An asymptotic normality result is established around a sample-specific target. Empirical performance is demonstrated through simulation studies and a real data application.

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BibTeX RIS

Sungbum Kim, Jiayi Wang. 2026-06-17. Kernel-Based Functional Balancing for Causal Inference with Compositional Treatments. https://arxiv.org/abs/2606.17308

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