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Asymmetrical Latent Representation for Individual Treatment Effect Modeling

Armand Lacombe, Michèle Sebag

TL;DR

The paper tackles CATE estimation under distribution shifts between treated and control groups by introducing ALRITE, which uses asymmetrical latent representations in two dedicated pipelines to optimize counterfactual prediction for each group. It provides theoretical PEHE guarantees tied to counterfactualizability and latent distances, and demonstrates superior or competitive performance on IHDP and ACIC2016 benchmarks. The work bridges CATE-specific representation learning with a hybrid T-/X-learner framework, offering practical performance gains and new directions for robust counterfactual inference in real-world settings.

Abstract

Conditional Average Treatment Effect (CATE) estimation, at the heart of counterfactual reasoning, is a crucial challenge for causal modeling both theoretically and applicatively, in domains such as healthcare, sociology, or advertising. Borrowing domain adaptation principles, a popular design maps the sample representation to a latent space that balances control and treated populations while enabling the prediction of the potential outcomes. This paper presents a new CATE estimation approach based on the asymmetrical search for two latent spaces called Asymmetrical Latent Representation for Individual Treatment Effect (ALRITE), where the two latent spaces are respectively intended to optimize the counterfactual prediction accuracy on the control and the treated samples. Under moderate assumptions, ALRITE admits an upper bound on the precision of the estimation of heterogeneous effects (PEHE), and the approach is empirically successfully validated compared to the state-of-the-art

Asymmetrical Latent Representation for Individual Treatment Effect Modeling

TL;DR

The paper tackles CATE estimation under distribution shifts between treated and control groups by introducing ALRITE, which uses asymmetrical latent representations in two dedicated pipelines to optimize counterfactual prediction for each group. It provides theoretical PEHE guarantees tied to counterfactualizability and latent distances, and demonstrates superior or competitive performance on IHDP and ACIC2016 benchmarks. The work bridges CATE-specific representation learning with a hybrid T-/X-learner framework, offering practical performance gains and new directions for robust counterfactual inference in real-world settings.

Abstract

Conditional Average Treatment Effect (CATE) estimation, at the heart of counterfactual reasoning, is a crucial challenge for causal modeling both theoretically and applicatively, in domains such as healthcare, sociology, or advertising. Borrowing domain adaptation principles, a popular design maps the sample representation to a latent space that balances control and treated populations while enabling the prediction of the potential outcomes. This paper presents a new CATE estimation approach based on the asymmetrical search for two latent spaces called Asymmetrical Latent Representation for Individual Treatment Effect (ALRITE), where the two latent spaces are respectively intended to optimize the counterfactual prediction accuracy on the control and the treated samples. Under moderate assumptions, ALRITE admits an upper bound on the precision of the estimation of heterogeneous effects (PEHE), and the approach is empirically successfully validated compared to the state-of-the-art
Paper Structure (38 sections, 4 theorems, 38 equations, 8 figures, 5 tables, 1 algorithm)

This paper contains 38 sections, 4 theorems, 38 equations, 8 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. State of the art
  3. S-learners
  4. T-learners
  5. Other approaches
  6. Discussion
  7. Asymmetrical Latent Regularization for Individual Treatment Effect Modeling
  8. Intuition
  9. Overview of Alrite
  10. Counter-factualizability
  11. Model architecture
  12. Training loss
  13. Algorithm
  14. Formal guarantees
  15. Discussion
  16. ...and 23 more sections

Key Result

Theorem 1

Let $\phi: \mathcal{X} \rightarrow \mathcal{Z}$ be an embedding from $\mathcal{X}$ to a latent space $\mathcal{Z}$. Let us assume that the sought outcome models $\mu^0$ and $\mu^1$ can be expressed as $\mu^0 = \nu^0 \circ \phi$ and $\mu^1 = \nu^1 \circ \phi$, with $\nu^0$ and $\nu^1$ two functions d

Figures (8)

  • Figure 1: Average counter-factualizability (definition in section \ref{['subsub:counterfactualizability']}) for treated and control samples in latent space. Left: the distributions support a good counter-factual estimation for treated samples (but less so for control samples). Middle: the distributions support a decent ounter-factual estimation for both populations. Right: the distributions support a good counter-factual estimation for control samples (but less so for treated samples).
  • Figure 2: Contrasting the T- and X-learner architectures.
  • Figure 3: Treated and control samples in latent space. Left: the treated $x_i$ has a far mirror twin; the control $x_j$ has a close mirror twin. Right: the treated $x_\ell$ has counter-factual importance weight 0; the control sample $x_k$ has $w_k$=3.
  • Figure 4: Alrite architecture: Top: control-driven pipeline $\mathcal{P}_0$. Middle: propensity estimate $\hbox{$\hat{\eta}$}$. Bottom: treatment-driven pipeline $\mathcal{P}_1$. Right: overall CATE estimate.
  • Figure 5: Distribution of the control and treated samples. Top: covariate space $\mathbb{R}^2$. Bottom left: distribution of distances to mirror twins for $\phi =$Id. Bottom right: distribution of distances to mirror twins for $\phi =$projection on the $x$-axis.
  • ...and 3 more figures

Theorems & Definitions (9)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Lemma 4
  • proof
  • proof
  • proof
  • proof
  • proof