SCM
- Graph of M G(M)
- Observation VS Intervention
- (perfect) intervention
Markov property
- (conditional) independence: in terms of prob.
- d-separation (visual graph example)
- Markov equivalence (covered edge reversal)
Tasks:
-
Global inference -> MEC
-
Local inference -> feature of SCM
-
Identifiable?, Total causal effect?, cause & direct cause
(example how it can be exploited? example method?; image to visualize assumptions in graph?) Reichenbach's principle
- Selection bias (unbiased data selection)
- LCD: combination of (in)dependences only works if they cannot be the cause of conditioning on a hidden variable Faithfulness
- Independence oracle
- causal minimality (follow from faithf.)
- identifiability
- ASD: add (in)dep. as soft constraints in an ASP solver Causal sufficiency (absence of Latent Confounders)
- IC: infer edge if there is no set of variables that makes a dependence a conditional independence Acyclicity
- Topological order (reference)
- SP: restrict the search space of DAGs Exogeneity
- ICP: exploit invariance to the exogenous variables of the conditional distribution of a variable given it's parents
Focus here on independence, but there are other patterns that can be exploited, such as
- “Verma constraints” (Shpitser et al.,2014),
- algebraic constraints in the linear-Gaussian case (van Ommen and Mooij, 2017),
- non-Gaussianity in linear models (Kano and Shimizu, 2003), and
- non-additivity of noise in nonlinear models (Peters et al., 2014) can also be exploited.
ADD/REWRITE RElATED WORK:
- disadvantages of constraint-based
- other constraints
Backdoor criterion?
% SECTIONS % Definitions of concepts (including topological ordering) % Causal principles (Reichenbach, independence (correlation), …) % Related methods % Width: categories % Depth: SotA on Kemmeren
% NOTES % SCMs % Cycles, latent confounding, selection bias, interventions, constraint VS score-based, faithfulness, causal sufficiency (Markov properties), graph types, evt. independence oracle (Chickering et al., 2004? [according to \citeauthor{claassen2013learning}])
\subsection{Mathematical Definitions} % TODO: list of priorities in concepts/definitions/propositions
\subsection{Principles of Causal Inference} % Assumptions: faithfulness, selection bias, confounding