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Scriddie
Scriddie
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Additive noise models are an assumption

Additive noise models (ANM) express an assumption about the functional form of causal relationships. In your question, you say that "cancer <- f(smoking) + noise should be pretty similar to smoking <- f(cancer) + noise". In a way that's exactly what the ANM assumption is saying – they are pretty similar, except that in the causal direction the noise is independent. ANMs postulate that in the true causal model, noise is added to the effect, which leads to an asymmetry that can be exploited to learn the causal structure.

An intuition about additive noise models

Now you might say "why shouldwould the ANM assumption apply?" One motivation is to introduce stochasticity. Without noise of some form, the causal relationships would be completely deterministic, which would be hard to justify. Seeing that we need some stochasticity and having decided to use a noise term, why would it be additive? The intuition here is that the noise is some independent variation of the effect variable that does not interact with the values of the cause. Such variation could be caused by other variables that we have decided to view as outside our causal system but that still independently have some (usually weak) effect on our system variables.

Additive noise models are an assumption

Additive noise models (ANM) express an assumption about the functional form of causal relationships. In your question, you say that "cancer <- f(smoking) + noise should be pretty similar to smoking <- f(cancer) + noise". In a way that's exactly what the ANM assumption is saying – they are pretty similar, except that in the causal direction the noise is independent. ANMs postulate that in the true causal model, noise is added to the effect, which leads to an asymmetry that can be exploited to learn the causal structure.

An intuition about additive noise models

Now you might say "why should the ANM assumption apply?" One motivation is to introduce stochasticity. Without noise of some form, the causal relationships would be completely deterministic, which would be hard to justify. Seeing that we need some stochasticity and having decided to use a noise term, why would it be additive? The intuition here is that the noise is some independent variation of the effect variable that does not interact with the values of the cause. Such variation could be caused by other variables that we have decided to view as outside our causal system but that still independently have some (usually weak) effect on our system variables.

Additive noise models are an assumption

Additive noise models (ANM) express an assumption about the functional form of causal relationships. In your question, you say that "cancer <- f(smoking) + noise should be pretty similar to smoking <- f(cancer) + noise". In a way that's exactly what the ANM assumption is saying – they are pretty similar, except that in the causal direction the noise is independent. ANMs postulate that in the true causal model, noise is added to the effect, which leads to an asymmetry that can be exploited to learn the causal structure.

An intuition about additive noise models

Now you might say "why would the ANM assumption apply?" One motivation is to introduce stochasticity. Without noise of some form, the causal relationships would be completely deterministic, which would be hard to justify. Seeing that we need some stochasticity and having decided to use a noise term, why would it be additive? The intuition here is that the noise is some independent variation of the effect variable that does not interact with the values of the cause. Such variation could be caused by other variables that we have decided to view as outside our causal system but that still independently have some (usually weak) effect on our system variables.

Source Link
Scriddie
Scriddie
  • 2.4k
  • 7
  • 15

Additive noise models are an assumption

Additive noise models (ANM) express an assumption about the functional form of causal relationships. In your question, you say that "cancer <- f(smoking) + noise should be pretty similar to smoking <- f(cancer) + noise". In a way that's exactly what the ANM assumption is saying – they are pretty similar, except that in the causal direction the noise is independent. ANMs postulate that in the true causal model, noise is added to the effect, which leads to an asymmetry that can be exploited to learn the causal structure.

An intuition about additive noise models

Now you might say "why should the ANM assumption apply?" One motivation is to introduce stochasticity. Without noise of some form, the causal relationships would be completely deterministic, which would be hard to justify. Seeing that we need some stochasticity and having decided to use a noise term, why would it be additive? The intuition here is that the noise is some independent variation of the effect variable that does not interact with the values of the cause. Such variation could be caused by other variables that we have decided to view as outside our causal system but that still independently have some (usually weak) effect on our system variables.