Efficient Symbolic Computations for Identifying Causal Effects
Benjamin Hollering, Pratik Misra, Nils Sturma
TLDR
An efficient quasi-polynomial time algorithm is presented for identifying causal effects using symbolic computation, outperforming traditional methods.
Key contributions
- Presents an efficient algorithm for deciding rational identifiability of causal effects.
- Overcomes the computational infeasibility of standard Gröbner bases methods.
- Provably finds the lowest degree identifying formulas for causal effects.
- Achieves quasi-polynomial time complexity for finding formulas up to a specified degree.
Why it matters
Causal effect identifiability is crucial for drawing valid conclusions from observational data. Traditional symbolic computation methods are too slow for practical use. This paper provides a much-needed efficient algorithm, making complex causal inference problems tractable.
Original Abstract
Determining identifiability of causal effects from observational data under latent confounding is a central challenge in causal inference. For linear structural causal models, identifiability of causal effects is decidable through symbolic computation. However, standard approaches based on Gröbner bases become computationally infeasible beyond small settings due to their doubly exponential complexity. In this work, we study how to practically use symbolic computation for deciding rational identifiability. In particular, we present an efficient algorithm that provably finds the lowest degree identifying formulas. For a causal effect of interest, if there exists an identification formula of a prespecified maximal degree, our algorithm returns such a formula in quasi-polynomial time.
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