NEW FRONTIERS in CAUSAL INFERENCE: INEQUALITY CONSTRAINTS for LATENT VARIABLES with RESTRICTED CARDINALITY
Abstract
In this project, we aim to bring experts in latent variable causal modeling from the quantum physics, statistics, and computer science communities for an intensive week-long workshop. During this workshop we aim to create working groups that will work in the following four Ôgrand challengesÕ on causal models with latent variables with restricted cardinality: (a)Give an algorithm which, for a given distribution over the observed variables, can decide whether it is compatible with a given restricted-cardinality latent-variable causal structure. (b)Give a general algorithm for bounding arbitrary causal effects (or functionals of the full data for missing data problems) given a causal (missing data) model represented by a restricted cardinality latent-variable causal structure. (c)Provide criteria for deciding when a pair of restricted-cardinality latent-variable causal structures are observationally indistinguishable. (This problem is significantly harder than the corresponding problem for unrestricted cardinality.) (d)Give an explicit characterization of the inequality constraints on the distribution over the observed variables that are implied by a restricted-cardinality latent-variable causal structure. Advances in any of these problems will allow researches to find causal explanations for observed phenomena, make recommendations in decision support tools, and assess causal effects in the empirical sciences in settings not possible previously. In addition, increased understanding of these problems will lead to a better understanding of the quantum-classical gap in structured systems, a foundational problem in quantum theory with applications in quantum computing and cryptography. Though members of quantum physics, statistics, and computer science communities have worked on latent variable causal models, to date the communities have remained largely isolated from each other. Our proposal is the first, to our knowledge, that aims to explicitly bring the two communities together. We believe our project will lead to collaboration and exchange of ideas between the two communities, and new advances that were not possible otherwise.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 09, 2020
- Source ID
- W911NF2010164
Entities
People
- Ilya Shpitser
Organizations
- Army Contracting Command
- Defense Advanced Research Projects Agency
- Johns Hopkins University