A Unifying Framework for Causal Modeling With Infinitely Many Variables
Authors: Spencer Peters, Joseph Y. Halpern
JAIR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We propose a class of models that are, in a certain natural sense, the most expressive generalization of SEMs. Our generalized SEMs (GSEMs) can be viewed as a unifying framework that recovers structural dynamical causal models, causal constraints models, counterfactual resimulation, and common-sense causal interpretations of systems of ODEs and hybrid automata (Alur et al. 1992) as special cases. The input-output behavior, or interface , of GSEMs is exactly that of SEMs, which means that definitions of concepts like actual cause, responsibility, blame, and explanation, can be immediately lifted from SEMs to GSEMs. The generality of GSEMs also makes them ideally suited to studying causality in the abstract; for example, they have been used to establish independence relationships among Halpern s axioms for SEMs (Peters and Halpern 2022). In a follow-up paper [15], we give sound and complete axiomatizations for GSEMs and several subclasses of GSEMs, building from Halpern s axiomatization for SEMs [9]. |
| Researcher Affiliation | Academia | SPENCER PETERS , Cornell University, USA JOSEPH Y. HALPERN, Cornell University, USA. Authors Contact Information: Spencer Peters, orcid: 0000-0002-9248-107X, EMAIL, Cornell University, Ithaca, New York, USA; Joseph Y. Halpern, orcid: 0000-0002-9229-1663, EMAIL, Cornell University, Ithaca, New York, USA. |
| Pseudocode | Yes | In Appendix A, we give an algorithm that computes the outcomes of M_ODE by solving the underlying differential equations, further reinforcing the view that the outcomes of M_ODE correspond to the natural causal semantics of the underlying equations. Algorithm A (1) For 1 i n, define X_i(0) = X_0i. (2) For i= 1, . . . ,l: (a) For j= 1, . . . ,n, if X_j is set to f on (t_i-1,t_i), define X_j(t) = f(t) for all t (t_i-1,t_i). (b) Define the remaining (intervention-free) dynamical variables on (t_i-1,t_i) so that for j= 1, . . . ,n, if X_j is intervention-free, then X_j is right-continuous at t_i-1, differentiable on (t_i-1,t_i), and its derivative X_j satisfies X_j(t) = F_j(X_1(t), . . . , X_m(t)) for all t (t_i-1,t_i). If there is no way to do this, output No solution . (c) For j= 1, . . . ,n, define X_j(t_i) as follows. (i) If X_t_i_j X, define X_j(t_i) = x[X_t_i_j]. (ii) If X_t_i_j X, define X_j(t_i) = lim_t_t_i X_j(t). (3) Define the functions X_i, 1 i n, on (t_l, ) so that X_1, X_2, . . . , X_n solve the initial-value problem on (t_l, ), as defined in ODE3 . Again, if there is no way to do this, output No solution . (4) Output the outcome v defined by v[X_t_i] = X_i(t) for all 1 i n, t> 0. |
| Open Source Code | No | The paper does not provide any explicit statements about code availability, links to repositories, or mention of supplementary materials containing code for the described methodology. |
| Open Datasets | No | The paper uses illustrative examples (LC circuit, thermostat) to demonstrate its theoretical framework and does not mention or provide access to any publicly available or open datasets for empirical evaluation. |
| Dataset Splits | No | The paper does not conduct empirical studies with datasets, therefore, there is no information regarding dataset splits for training, testing, or validation. |
| Hardware Specification | No | The paper is theoretical and does not involve empirical experiments requiring specific hardware; therefore, no hardware specifications are provided. |
| Software Dependencies | No | The paper is theoretical and does not describe implementation details that would require specific software dependencies with version numbers. A reference mentions MATLAB, but not as a dependency for the paper's methodology. |
| Experiment Setup | No | The paper is theoretical and focuses on formal definitions and modeling. It does not describe any empirical experiments, and therefore, no experimental setup details such as hyperparameters or training configurations are provided. |