Graphical Criteria for Inequality Constraints in Directed Acyclic Graphs with Hidden Variables
Talkat Quantum Physics and Statistical Causal Models (Simons Institute workshop, 2022) · 2022-04-27..04-29
summary
Shows that e-separation => entropic inequalities gives explicit, testable entropy bounds that reproduce some quantifier-elimination results and are computationally cheaper; uses mutual information to bound information flow (example mutual information values lead to a 2^(1.549) type bound) and defines MME minimal mediary entropy as a measure of arrow strength; shows known hidden-variable cardinalities imply non-negative rank bounds (non-negative rank bound) and points to a quantum analogue via PSD rank, enabling causal discovery beyond conditional independences.
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chapters (14)
- 0:00Graphical Criteria for Inequality Constraints in Directed Acyclic Graphs with Hidden Variables
- 1:08d-separation
- 4:22Equality constraints implied by DAGS
- 6:02Constraints in hidden variable models
- 10:16Entropic constraints from e-separation
- 14:27Related results
- 15:06Causal discovery
- 17:24Latent variables Y
- 20:29Quantifying causal influence
- 25:39Restricted cardinality
- 26:22Measure of dependence
- 29:42Applications Distribution generation
- 34:10Psd-rank
- 34:41Quantum generalization