Review of Causal Discovery Methods Based on Graphical Models

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## Graph & Causality Review of Causal Discovery Methods Based on Graphical Models --- ## Intro A fundamental task in various disciplines of science, including biology, is to find underlying causal relations and make use of them. Causal relations can be seen if interventions are properly applied; however, in many cases they are difficult or even impossible to conduct. --- A traditional way to discover causal relations is to use interventions or randomized experiments, which is in many cases too expensive, too time-consuming, or even impossible. --- Therefore,revealing causal information by analyzing purely observational data, known as **causal discovery**,has drawn much attention. --- ## DGCM Directed Graphical Causal Models  --- ### Chain Structure Dependence flows in the direction of the arrows. The greater the causal expertise, the greater your chances of getting a promotion.  --- As a general rule, the dependence flow in the direct path from A to C is blocked when we condition on an intermediary variable B. $$ A \not \perp C $$ $$ A \perp C | B $$ --- ### Fork Structure As a general rule, two variables that share a common cause are dependent, but independent when we condition on the common cause.  --- $$ A \not \perp B $$ $$ A \perp B | C $$ --- ### Collider structure As a general rule, conditioning on a collider opens the dependence path. Not conditioning on it leaves it closed.  --- $$ A \perp B $$ $$ A \not \perp B | C $$ --- ## Methods Some methods using to build CAUSAL MODELS. --- ### The PC Algorithm - Form a complete undirected graph - Eliminate edges between variables that are unconditionally independent - For each pair of variables (A, B) having an edge between them,and for each variable C with an edge connected to either of them, eliminate the edge between A and B if $A \not \perp B | C$ - Keep on more pair --- ### The FCI Algorithm - FCI orients edges by a procedure similar to PC but without assuming that every edge is directed one way or the other. - Have a 'o' mark,means can be an arrow head or an arrow tail. - Bidirected edge between Y and Z indicates that there is at least one unmeasured confounder between Y and Z.

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Intro

A fundamental task in various disciplines of science, including biology, is to find underlying causal relations and make use of them. Causal relations can be seen if interventions are properly applied; however, in many cases they are difficult or even impossible to conduct.

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A traditional way to discover causal relations is to use interventions or randomized experiments, which is in many cases too expensive, too time-consuming, or even impossible.

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Therefore,revealing causal information by analyzing purely observational data, known as causal discovery,has drawn much attention.

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DGCM

Directed Graphical Causal Models

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Chain Structure

Dependence flows in the direction of the arrows. The greater the causal expertise, the greater your chances of getting a promotion.

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As a general rule, the dependence flow in the direct path from A to C is blocked when we condition on an intermediary variable B.

$$A\perp ̸C$$$$A\perp C|B$$

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Fork Structure

As a general rule, two variables that share a common cause are dependent, but independent when we condition on the common cause.

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$$A\perp ̸B$$$$A\perp B|C$$

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Collider structure

As a general rule, conditioning on a collider opens the dependence path. Not conditioning on it leaves it closed.

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$$A\perp B$$$$A\perp ̸B|C$$

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Methods

Some methods using to build CAUSAL MODELS.

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The PC Algorithm

• Form a complete undirected graph
• Eliminate edges between variables that are unconditionally independent
• For each pair of variables (A, B) having an edge between them,and for each variable C with an edge connected to either of them, eliminate the edge between A and B if $A\perp ̸B|C$
• Keep on more pair

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The FCI Algorithm

• FCI orients edges by a procedure similar to PC but without assuming that every edge is directed one way or the other.
• Have a 'o' mark,means can be an arrow head or an arrow tail.
• Bidirected edge between Y and Z indicates that there is at least one unmeasured confounder between Y and Z.

参考来源

• 图模型简介
• 论文综述