One common task in many data sciences applications is to answer questions about the effect of new interventions, like: 'what would happen to Y if we make X equal to x while observing covariates Z = z?'. Formally, this is known as conditional effect identification, where the goal is to determine whether a post-interventional distribution is computable from the combination of an observational distribution and assumptions about the underlying domain represented by a causal diagram. A plethora of methods was developed for solving this problem, including the celebrated do-calculus [Pearl, 1995]. In practice, these results are not always applicable since they require a fully specified causal diagram as input, which is usually not available. In this paper, we assume as the input of the task a less informative structure known as a partial ancestral graph (PAG), which represents a Markov equivalence class of causal diagrams, learnable from observational data.

A plethora of methods was developed for solving this problem, including the celebrated do-calculus [Pearl, 1995]. In practice, these results are not always applicable since they require a fully specified causal diagram as input, which is usually not available.

Weconsidertwoscenarios where causal effects are estimable.

A.2 Proof of Theorem 1 We restate the theorem for completeness: Theorem 1. Assume Any ODE's solution, if it exists and converges, converges to an's estimate of the conditional effect is We now bound the remaining term. 's computation of the surrogate intervention involved Thus, such error does not accumulate even with large step sizes. Theorem 4. Effect Connectivity is necessary for nonparametric effect estimation in Let Effect Connectivity be violated, i.e. there exists a Thus, nonparametric effect estimation is impossible. The effect threshold here is 0.1.Figure 7: True positive vs. False negative rate as we vary the threshold on average

Causal inference relies on two fundamental assumptions: ignorability and positivity .

(Pearl and Robins, 1995).

We have repeated all experiments three times.

In finding causal effects, researchers may want to know the effect across an entire population, sometimes called a total or unconditional causal effect. For example, does free access to pre-kindergarten (pre-K) improve children's socio-emotional skills throughout elementary school (Moffett et al., 2023)? However, researchers may want to know the effect within subgroups of the population, or a conditional causal effect. For instance, is there a subgroup of children who particularly benefit from free access to pre-K? Our research considers identifying these conditional effects from observational data.