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Definitions

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

Principles of causal inference

Assumptions: causal knowledge/assumptions

(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