Nonlinear additive noise model

As explained in Causal AI

A nonlinear additive noise model is an additive structural causal model with nonlinear assignment functions and additive exogenous noise.

A nonlinear additive noise model (ANM) is a structural causal model whose assignment function combines a nonlinear function of endogenous parents with additive exogenous noise: V = g(Vpa) + Nv. The noise may be Gaussian or non-Gaussian. section 6.4.6 section 6.4.3

Use ANMs when qualitative causal knowledge must become an explicit function class and noise distribution. Additivity makes model parameters more tractable to learn, and some learned parameters can have causal interpretations. section 6.4.3

A practical ANM workflow connects domain mechanisms to an SCM:

• Specify the causal variables and their parent relationships in a DAG. section 6.4.3
• Choose a nonlinear assignment function from domain knowledge, then add an exogenous noise term. section 6.4.6
• Use a dynamic model, such as an ODE, to derive the assignment function when the mechanism is naturally expressed over time. section 6.4.6

Enzyme and protein synthesis

Let X be the enzyme amount and Y the measured target-protein amount. An enzyme biologist can use an ODE describing biochemical reactions, derive its equilibrium, and choose the resulting nonlinear relationship as g(X), with additive noise representing unexplained variation. section 6.4.6 section 6.4.3

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

Browse the causal diagram linking enzyme amount X to measured protein amount Y. section 6.4.3

How Causal AI covers it

How deep it goes

Explains the structural equation and mechanistic ODE example, but stops short of detailed parameter-learning or inference procedures.

Examples

Uses enzyme concentration, protein synthesis, biochemical equilibrium, and an ODE-derived assignment function.

What it assumes

Assumes familiarity with structural causal models, assignment functions, endogenous parents, exogenous variables, and causal graphs.

What you can do after

Build an SCM by translating a nonlinear domain mechanism into an assignment function with additive exogenous noise.

How it connects

Connects structural causal models, additive models, directed acyclic graphs, dynamic modeling, ordinary differential equations, and exogenous variables.

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Related concepts

• additive structural causal modelkind of · 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.
• structural causal modelpart 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.