Estimating Individual Treatment Effects (ITE) in multi-treatment scenarios faces two critical challenges: the Hyperparameter Selection Dilemma for balancing weights and the Curse of Dimensionality in computational scalability. This paper derives a novel multi-treatment generalization bound and proposes a theoretical estimator for the optimal balancing weight α, eliminating expensive heuristic tuning. We investigate three balancing strategies: Pairwise, One-vs-All (OVA), and Treatment Aggregation. While OVA achieves superior precision in low-dimensional settings, our proposed Treatment Aggregation ensures both accuracy and O(1) scalability as the treatment space expands. Furthermore, we extend our framework to a generative architecture, Multi-Treatment CausalEGM, which preserves the Wasserstein geodesic structure of the treatment manifold. Experiments on semi-synthetic and image datasets demonstrate that our approach significantly outperforms traditional models in estimation accuracy and efficiency, particularly in large-scale intervention scenarios.
Figures & tables
Figure 1: Performance Comparison (PEHE). (a) All methods outperform baseline at K=4 . (b) At K=20 , Pairwise degrades while Aggregation remains robust. (See Appendix D.3 , Figure 5 for training efficiency)
Figure 2: Performance and Efficiency Analysis on Digits Dataset. (a) The estimated ADRF (blue) closely tracks the ground truth (red). (b) Dual-axis comparison showing PEHE error (bars) and Training Time (line).
Figure 3: Geometric Validation on Hierarchical Treatments. (a) The learned embeddings spontaneously recover the underlying tree structure, placing the Root centrally and separating the L/R branches. (b) Counterfactual interpolation from Leaf LL( Y=−3 ) to Leaf RR ( Y=+3 ) respects the causal topology by passing through the Root’s effect region ( Y≈0 ), whereas the linear baseline (grey) ignores the structure.
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 4: Detailed Architecture of Multi-Treatment CausalEGM. The left panel shows the original binary design, while the right panel highlights our proposed extensions (Embedding Layer and Softmax Activation) for complex treatment regimes.
Figure 5: Training Time Efficiency at K=20 . The Pairwise strategy incurs distinct computational costs due to (2K) constraints.
Figure 6: Latent Space Topology (Rotated MNIST). The model learns an isometric embedding of the treatments, recovering the cyclic order 0∘→45∘→⋯→315∘→0∘ .
Figure 7: Global Interpolation ( 0∘→180∘ ). The geodesic path correctly models the monotonic decrease in outcome Y as the digit rotates from upright to upside-down, tracking the cosine function.
Figure 8: Local Interpolation ( 0∘→315∘ ). Despite the large gap in discrete indices ( 0 vs 7 ), the model recognizes the topological proximity, yielding a smooth transition consistent with the periodic boundary condition.
Estimating heterogeneous single and interaction treatment effects from observational data under multiple simultaneous treatments is crucial for decision-making. To mitigate estimation variance, previous studies balance representation distributions between every pair of treatment patterns. However, such pairwise balancing scales quadratically with the number of treatment patterns and fails to preserve consistent local proximity structures across patterns, which degrades counterfactual estimation. To address these challenges, we propose the Causal Inference for Heterogeneous Single and Interaction Treatment Effects Network (CIHSI-Net), a deep learning framework built on a novel Barycentric Fused Gromov-Wasserstein Balancing (BFG-WB) objective. BFG-WB aligns the representation distribution of each treatment pattern with a shared Wasserstein barycenter, achieving global alignment while reducing the computational complexity from quadratic to linear, and its Fused Gromov-Wasserstein discrepancy preserves the local proximity structures essential for reliable heterogeneous effect estimation. Simulation studies show that CIHSI-Net consistently outperforms state-of-the-art baselines, and an application to real-world marketing data demonstrates its practical utility in complex multi-treatment scenarios.
Yuki Murakami, Takumi Hattori, Kohsuke Kubota
NTT DOCOMO, INC., Tokyo, Japan · Yokohama City University, Kanagawa, Japan
Predicting the effect of interventions with many possible variations, e.g., therapeutic content that affects mental health outcomes or an earnings call transcript that drives movement in share price, is useful across several domains. However, classical causal estimators tend to assume that all possible interventions are observed, which is infeasible when interventions vary widely, for instance, in the space of all text strings. We adapt a well-known approach of recasting causal inference as a learning problem to address such settings, assuming realizability of the learned function and no unobserved confounding. We show that causal error decomposes into moment-balancing errors of increasing order and exploit structure of the conditional outcome in the confounders to design objectives that directly improve causal estimation. We also show how to project the effect of a high-dimensional treatment onto coarser attributes, which allows a single model to answer several causal questions without additional attribute-specific training. We empirically evaluate our estimators in settings with high-dimensional continuous, discrete, and text treatments. Our experiments demonstrate generalization to held-out treatments, benefits of balancing higher-order moments when required, and projected causal estimates that are competitive with attribute-specific ones.
Nikita Dhawan, Arnav Paruthi, Andrew Kim +3
University of Toronto, Vector Institute · University of Toronto · Vanguard
Causal inference has become a central issue across various fields, including computer science, statistics, economics, education, healthcare, and medicine. The broad applicability of this discipline has garnered increased research funding and attention. In recent years, the estimation of causal effects from observational data has gained traction due to the vast amounts of collected data and the lower costs compared to randomized controlled trials. Advances in causal effect estimation methods have enhanced service personalization tools. For instance, these tools can help identify the most effective type of treatment (considering both cost and success rate) for each patient among different medical service options. This paper proposes an innovative method for estimating the heterogeneity of treatment effects. The structure of the proposed model is based on a deep neural network and a pseudo-single learner. The proposed method has been compared with other state-of-the-art methods on the IHDP benchmark. Acceptable results have been obtained by using one estimator to estimate the potential outcomes of two treatment groups. Accordingly, this paves the way for further development and improvement of the proposed method.
Ali Haghpanah Jahromi, Mohammad Taheri, Zohreh Azimifar
Department of Electrical and Computer Engineering, University of Shiraz, Shiraz, Iran