ICML 2025

Learning Joint Interventional Effects from Single-Variable Interventions
in Additive Models
Armin Keki´c 1 Sergio Hernan Garrido Mejia 1 2 Bernhard Sch¨olkopf 1 3 4
Abstract
Estimating causal effects of joint interventions on
multiple variables is crucial in many domains, but
obtaining data from such simultaneous interven-
tions can be challenging. Our study explores how
to learn joint interventional effects using only ob-
servational data and single-variable interventions.
We present an identifiability result for this prob-
lem, showing that for a class of nonlinear additive
outcome mechanisms, joint effects can be inferred
without access to joint interventional data. We
propose a practical estimator that decomposes the
causal effect into confounded and unconfounded
contributions for each intervention variable. Ex-
periments on synthetic data demonstrate that our
method achieves performance comparable to mod-
els trained directly on joint interventional data,
outperforming a purely observational estimator.
1. Introduction
Understanding the effects of interventions is fundamental
across many domains, from designing public health policies
to optimizing business operations and administering medical
treatments. Particularly challenging and important are joint
interventional effects, where simultaneous interventions on
multiple action variables influence a target outcome. Such
scenarios are common in fields like epidemiology (Keki´c
et al., 2023a), e-commerce (Kunz et al., 2023; Schultz et al.,
2023), and medicine (Prosperi et al., 2020).
Consider a company trying to optimize their marketing strat-
egy across multiple channels like social media, email cam-
paigns, and display advertising. While the ultimate goal is
to understand how these channels work together to drive
sales, running experiments for every possible combination
1Max Planck Institute for Intelligent Systems, T¨ubingen, Ger-
many 2Amazon Research, T¨ubingen, Germany 3T¨ubingen AI Cen-
ter, T¨ubingen, Germa...