Causal Networks

3203. Introduction to Artificial Intelligence

Causal Networks

1. Correlation vs. Causation

Causation (Causality) is a relationship between two events in which a change in one (the cause) brings about a change in the other (the effect).

It has been widely acknowledged that correlation does not imply causation. Two variables may be correlated because:

The first causes the second.
The second causes the first.
A third factor causes both.
The correlation is purely accidental.

Therefore, additional assumptions, experiments, or causal models are needed to establish causation. In particular, interventions and conterfactuals are considered as important in identifying causal relations.

2. Causal Networks

A Causal Networks is a graphical model that extends a Bayesian Network by explicitly representing causal relationships and supporting reasoning about interventions. It enables prediction, explanation, and the analysis of actions and their consequences.

An intervention sets a variable to a specific value directly, rather than influencing it indirectly through its normal causes in the model. Interventions allow us to reason about the effects of actions and answer "What if we do X?" questions.

A causal model is constructed using observational data, experimental or interventional data, and domain knowledge expressed as modeling assumptions. This is not referring to "the (unique) cause" of an effect, but all of the factors that together lead to the effect. An effect typically has multiple causes, and their relations are probabilistic.

A direct cause of variable Y is a variable X such that intervening on X, holding all other variables constant, can affect Y.

The do-notation adds interventions to the language of probability: P(x|do(z), y) where x, y, and z are propositions is the probability that x is true after doing z and then observing y. Unlike ordinary conditional probabilities, do-expressions represent the effects of actions rather than passive observations.

Intervening after observing is counterfactual reasoning because the intervention could make the observation no longer true.

3. An Example

Example 11.11. The effect of a drug on a disease.