Perfilado de sección

    • Lecture: slides part I - 7-17
    • Assignments
      1. Let's consider 3 variables A, B and C, what directed acyclic graphs encode the following assumptions ? Provide some realistic examples for all these scenarios.
        • A, B and C are all independent.
        • A and B are "directly" dependent (they are dependent, and dependent conditionally to any other variable), B and C are independent, A and C are independent.
        • A and B are "directly" dependent, B and C are "directly" dependent, A and C are dependent but independent given B.
        • A and B are "directly" dependent, B and C are "directly" dependent, A and C are independent but dependent given B.
      2. Write the decomposition of the joint distribution as a product of local conditional distributions for the graph depicted below
      3. Markov Equivalence :
        • definition : "inferred edges" are the arcs which are not members of a V-structure, but whose orientation is also constrained (if we inverted them, we could for example create a new V-structure not present in the original graph)
        • Let us consider 3 variables. How many different DAGs with 3 variables exist? Which ones are Markov equivalent? And how many different CPDAGs exist with these 3 variables?
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