New Approaches To Learning Nonparametric (Latent) Causal Graphical Models
summary
Proves that under a subset condition on which latents connect to which observables and mild nondegeneracy, the bipartite graph and discrete latent distribution P(H) are identifiable from marginal mixtures given a mixture oracle; reduction splits the problem into estimating small-set mixture models (use tensor decomposition on triples, needs column linear independence) and then running fully observed causal discovery. Implements a practical pipeline with K-means + GES recovering small graphs and a six-component nonparametric mixture; sample/computational complexity remains open.
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chapters (7)
- 0:00Introduction and problem setup
- 6:06Assumptions and framework
- 9:16Reduction to known problems
- 14:38Algorithmic approach
- 20:04Identifiability and mixtures
- 25:06Implementation and complexity
- 30:55Final Q&A
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