# Probabilistic Graphical Models Course Notes

# Preliminaries

## Distributions

Suppose A has 2, B has 2 and C has 3 possible values. Their **Joint
Probability Distribution** will contain 2x2x3=12 values.

We can *condition* the values by setting a variable to a certain value.

We can also *marginalize* the values to a certain variable and check the
distribution of this single variable.

# Factors

A *factor* $\phi$ is a function that takes values for A, B and C and
returns a real value.

The arguments that the factor takes are called the *scope* of the
factor.

Both normalized and unnormalized measures are factors. But the scope of each can change.

CPD (Conditional Probability Distribution) is another example of a factor.