Additive structural causal model

As explained in Causal AI

An additive structural causal model is a structural causal model in which each variable is assigned by a function of its causal parents plus an additive exogenous disturbance.

When the causal question is how an intervention changes an outcome, an additive structural causal model (SCM) represents each variable as a function of its direct endogenous causes plus an exogenous disturbance. For a protein quantity Y caused by enzyme amount X, write N_Y ~ P(N_Y) and Y := f_Y(X) + N_Y. The function describes the systematic causal effect; the disturbance captures additional exogenous influence. Additive models provide a practical starting point because their parameters often have causal interpretations and can be learned with established software. section 6.4.3

Common additive SCM templates combine a constraint on the assignment function with one on the exogenous-variable distribution:

• LiGAM uses a linear assignment with Gaussian additive disturbances. section 6.4.3
• LiNGAM uses a linear assignment with non-Gaussian additive disturbances. section 6.4.3
• The nonlinear additive noise model (ANM) permits nonlinear assignments while retaining additive noise. section 6.4.3

Fit assignment-function parameters with linear or nonlinear regression tools, including generalized least squares, then inspect goodness-of-fit statistics. Unlike ordinary regression, an SCM restricts predictors to direct endogenous causes rather than adding any variables that improve prediction. A generalized linear model may resemble an additive SCM, but its link function is designed around a canonical distribution’s mean, not necessarily the causal relationship itself. section 6.4.7

Enzyme amount and protein production

Treat enzyme quantity X as a cause of measured protein quantity Y. Specify the causal graph, choose a function class for f_Y, choose a distribution for N_Y, and fit the resulting assignment from data. If the causal mechanism involves interactions between endogenous and exogenous causes, replace the additive form rather than forcing it to fit. section 6.4.3 section 6.4.8

Figure 6.21 The amount of enzyme (X) is a cause the measured quantity of protein (Y).

Use the causal diagram to trace enzyme quantity X into measured protein quantity Y before specifying the additive assignment. section 6.4.3

How Causal AI covers it

How deep it goes

Defines additive assignments, names LiGAM, LiNGAM, and ANM, and stops before multiplicative or deep-learning implementations.

Examples

Uses enzyme quantity as a cause of measured protein quantity and illustrates fitting through regression tools.

What it assumes

Assumes structural causal models, DAGs, endogenous variables, exogenous variables, and direct causal-parent relationships.

What you can do after

Builds additive SCM assignments from causal parents, fits parameters with regression, and evaluates explanatory fit.

How it connects

Connects structural causal models to DAGs, causal parents, regression, generalized linear models, and additive noise models.

liveBookmanning.com

Read Causal AI on liveBook Get the book at manning.com

Related concepts

• nonlinear additive noise modelincludes · A nonlinear additive noise model is an additive structural causal model with nonlinear assignment functions and additive exogenous noise.
• structural causal modelkind of · A structural causal model represents causal relationships among variables through equations that determine each variable from other variables and exogenous factors.

This explainer was generated by Manning's knowledge graph from the text of Causal AI. The section links point to the parts of the book it draws on.