causal structure

Causal Structure

The directed graph of mechanisms relating the variables of a system. Each variable $V_i$ is generated from its direct causes (its parents $\mathrm{pa}(V_i)$) and an exogenous noise term $U_i$ via a fixed assignment, plus the mechanism $f_i$:

$$V_i:=f_i(\mathrm{pa}(V_i),U_i).$$

Each mechanism $f_i$ is invariant under interventions on variables outside $\mathrm{pa}(V_i)$.
The DAG alone (without the $f_i$) is the causal skeleton; together with the mechanisms it forms a structural causal model (SCM).

modularity assumption Mechanisms correspond to separate physical processes and can be changed independently. You can shift the distribution of the parents, perturb cousins, swap environments but the rule mapping parents to $V_i$ doesn't change.

Causal structure = code

Mechanisms are functions, the DAG is the call graph, noise terms are random inputs.

Invariant Causal Prediction

Across environments, find the variable set whose conditional distribution of $Y$ stays invariant $⟹\mathrm{pa}(Y)$.

There is no gods-eye view on this graph

Taking seriously the perspective of intelligence as relational implies something far more mind-bending than merely acknowledging the social origins of consciousness. It implies that relationships themselves are the building blocks of reality. There is no God’s-eye “view from nowhere” in a relationship graph. In fact there isn’t even a God’s-eye view of what the nodes in the graph are.

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See also: observer-dependent