Inflation: Python implementations of the Inflation Technique for causal inference

Inflation is a package, written in Python, that implements inflation algorithms for causal inference. In causal inference, the main task is to determine which causal relationships can exist between different observed random variables. Inflation algorithms are a class of techniques designed to solve the causal compatibility problem, that is, test compatibility between some observed data and a given causal relationship.

This package implements the inflation technique for classical, quantum, and post-quantum causal compatibility. By relaxing independence constraints to symmetries on larger graphs, it develops hierarchies of relaxations of the causal compatibility problem that can be solved using linear and semidefinite programming. For details, see Wolfe et al. “The inflation technique for causal inference with latent variables.” Journal of Causal Inference 7 (2), 2017-0020 (2019), Wolfe et al. “Quantum inflation: A general approach to quantum causal compatibility.” Physical Review X 11 (2), 021043 (2021), and references therein.

Examples of use of this package include:

• Causal compatibility with classical, quantum, non-signaling, and hybrid models.

• Feasibility problems and extraction of certificates.

• Optimization of Bell operators.

• Optimization over classical distributions.

• Handling of bilayer (i.e., networks) and multilayer causal structures.

• Standard Navascues-Pironio-Acin hierarchy.

• Scenarios with partial information.

• Possibilistic compatibility with a causal network.

• Estimation of do-conditionals and causal strengths.