Elements of Causal Inference: Reading Notes 2/N

1.3 Causal Modeling and Learning

A causal structure entails a probability model and has additional information.

Causal reasoning is the process of drawing conclusions from a causal model.

Probability model allows us to reason about the outcomes of random experiments.

Causal models, in addition to probability model, also allows us to reason about the effect of interventions or distribution changes.

Structure learning = causal discovery

Structure identifiability = “which parts of the causal structure can in principle be inferred from the joint distribution”. Even full knowledge of $P$ does not make the solution trivial, see Section 1.2.

Correlation does not imply causation.

Principle 1.1 (Reichenbach’s common cause principle)

If two random variables $X$ and $Y$ are statistically dependent ( $X \not \!\perp\!\!\! \perp Y$ ), then there exists a third variable $Z$ that causally influences both. (As a special case, $Z$ may coincide with either $X$ or $Y$.) Furthermore, this variable $Z$ screens $X$ and $Y$ from each other in the sense that given $Z$, they become independent, $X \!\perp\!\!\!\perp Y \mid Z$.

Caveats: Dependences may also arise from (other than Reichenbach’s common cause principle)

  1. The random variables we observe are conditioned on others.
  2. The random variables only appear to be dependent.
  3. both random variables may inherit a time dependence and follow a simple physical law.

1.4 Two Examples

1.4.1 Pattern Recognition

Structural causal models (SCMs) = structural equation models

Same distribution can be generated by different SCMs.

Causality can only be discussed when taking into account the notion of time. But time is often ignored in probabistic model or causal model.

Note to self: time is an intrinsic part of RL (Reinformcement Learning) problems. RL problems also allows agent to perform intervention. RL seems to be perfect framework for applying Causal learning.

Note to self: It would be nice if RL agent can learn causal relationship model of its action and environments.

1.4.2 Gene Perturbation

In this example, observational data cannot tell apart of the actual underlying mechansim and cannot predict outcomes of an intervention (“phenotype after deletion of a gene” in this case).

References