How deeply does Causal AI cover structural causal model?

Defines variables and deterministic assignments, then works through a linear mechanism; later causal inferences are deferred.

Structural causal model

As explained in Causal AI

A causal model is a statistical model built on assumptions about the causal process that generates data and supports reasoning about interventions.

Suppose femur length helps determine height. A causal graph can say that femur length causes height; a structural causal model (SCM) also specifies how it does so. That extra assumption can support causal inferences that a graph alone cannot, but it creates another way for the model to be wrong. section 6.0 section 6.1

An SCM starts with a causal directed acyclic graph (DAG). Its endogenous variables are the quantities modeled explicitly. Exogenous, or noise, variables stand for causes left outside that model. Each endogenous variable has a structural assignment: a function that determines its value from its parents. In the formulation here, each endogenous variable has its own latent exogenous parent; those exogenous variables are independent root nodes. Their values come from probability distributions, while the assignments determine endogenous values. section 6.1.3

Height from femur length

Let x be femur length in centimeters and y be height in centimeters. One proposed mechanism is nᵧ ~ N(0, 3.3) and y = 25 + 3x + nᵧ. The equation asserts that changing femur length changes height proportionally; nᵧ represents other causal determinants. Linearity is a causal claim to justify, not merely a convenient curve to fit. section 6.1.1

This differs from fitting a conditional probability table or neural-network component to each node. Those components can describe how a child varies with its parents without asserting a particular mechanism. A structural assignment deliberately makes a stronger claim about that mechanism. Stronger assumptions may enable stronger inferences, but also increase the risk of modeling error. section 6.1

Use the model to reason about setting a cause to a hypothetical value when a real experiment is infeasible. First make the graph and assignment assumptions explicit; then ask whether their implications survive contact with data. Conditional-independence checks can refute a proposed DAG, but failure to refute it does not establish that its causal claims are true. section 1.5.3 section 4.3

How Causal AI covers it

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Causal Inference for Data ScienceA causal model is a conceptual representation of causal relationships that accounts for variables influencing both a cause and an effect.

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Related concepts

endogenous variablehas part · An endogenous variable is a variable in a structural causal model whose value is determined by the model’s relationships and exogenous inputs.
exogenous variablehas part · An exogenous variable is a causal input whose variation originates outside the endogenous system represented by a structural causal model.
assignment functionhas part · An assignment function is a deterministic rule in a structural causal model that determines an endogenous variable from its causal parents and exogenous inputs.
causal graphical modelkind of · A causal graphical model is a probabilistic or structural model whose graph represents causal relationships and whose mechanisms support reasoning about interventions.
directed acyclic graphuses · A directed acyclic graph is a graph with directed edges and no directed cycles.
experimentationmeasured by · Experimentation is the deliberate testing of an idea, intervention, or alternative by observing outcomes to gather evidence or compare effects.

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