From Christos Dimitrakakis:<\/p>\n
>> To be honest, there is such a plethora of causal models, that it is not entirely clear what subsumes what, and which one is equivalent to what. Is there a simple taxonomy somewhere? I thought that influence diagrams were sufficient for all causal questions, for example, but one of Pearl’s papers asserts that this is not the case.<\/p>\n
Reply from J. Pearl:<\/p>\n
Dear Christos,<\/p>\n
From my perspective, I do not see a plethora of causal\u00a0models at all, so it is hard for me to answer your question in\u00a0specific terms. What I do see is a symbiosis of all\u00a0causal models in one framework, called Structural Causal\u00a0Model (SCM) which unifies structural equations, potential\u00a0outcomes, and graphical models. So, for me, the world appears\u00a0simple, well organized, and smiling.\u00a0Perhaps you can tell us what models lured your\u00a0attention and caused you to see a plethora of models\u00a0lacking subsumption taxonomy.<\/p>\n
The taxonomy that has helped me immensely is the three-level\u00a0hierarchy described in chapter 1 of my book Causality:\u00a01. association, 2. intervention, and 3 counterfactuals.\u00a0It is a useful hierarchy because it has an objective\u00a0criterion for the classification: You cannot answer\u00a0questions at level i unless you have assumptions from\u00a0level i or higher.<\/p>\n
As to influence diagrams, the relations between\u00a0them and SCM is discussed in Section 11.6 of my book\u00a0Causality (2009),\u00a0Influence diagrams belong to the 2nd layer of the causal\u00a0hierarchy, together with Causal Bayesian Networks.\u00a0They lack however two facilities:<\/p>\n
1. The ability to process counterfactuals.
\n2. The ability to handle novel actions.<\/p>\n
To elaborate,<\/p>\n
1. Counterfactual sentences (e.g., Given what I see,\u00a0I should have acted differently) require functional models.\u00a0Influence diagrams are built on conditional and interventional probabilities, that is,\u00a0p(y|x) or p(y|do(x)).\u00a0There is no interpretation of E(Y_x| x’) in\u00a0this framework.<\/p>\n
2. The probabilities that annotate\u00a0links emanating from Action Nodes\u00a0are interventional type, p(y|do(x)),\u00a0that must be assessed judgmentally by the user.\u00a0No facility is provided for deriving these\u00a0probabilities from data together with the structure of the graph.\u00a0Such a derivation is developed in chapter 3\u00a0of Causality, in the context of\u00a0Causal Bayes Networks where every node\u00a0can turn into an action node.<\/p>\n
Using the causal hierarchy, the 1st Law of\u00a0Counterfactuals and the unification provided\u00a0by SCM, the space of causal models should\u00a0shine in clarity and simplicity.\u00a0Try it, and let us know of any questions remaining.<\/p>\n
Judea<\/p>\n","protected":false},"excerpt":{"rendered":"
From Christos Dimitrakakis: >> To be honest, there is such a plethora of causal models, that it is not entirely clear what subsumes what, and which one is equivalent to what. Is there a simple taxonomy somewhere? I thought that influence diagrams were sufficient for all causal questions, for example, but one of Pearl’s papers […]<\/p>\n","protected":false},"author":6,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5,6,37],"tags":[],"class_list":["post-1658","post","type-post","status-publish","format-standard","hentry","category-causal-effect","category-counterfactual","category-structural-equations"],"_links":{"self":[{"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/posts\/1658","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/comments?post=1658"}],"version-history":[{"count":6,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/posts\/1658\/revisions"}],"predecessor-version":[{"id":1664,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/posts\/1658\/revisions\/1664"}],"wp:attachment":[{"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/media?parent=1658"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/categories?post=1658"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/causality.cs.ucla.edu\/blog\/index.php\/wp-json\/wp\/v2\/tags?post=1658"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}