Dr. Kayvan Sadeghi, University College London

Probabilistic Independence, Graphs, and Random Networks
The main purpose of this talk is to explore the relationship between the set of conditional independence statements induced by a probability distribution and the set of separations induced by graphs as studied in graphical models. I introduce the concepts of Markov property and faithfulness, and provide conditions under which a given probability distribution is Markov or faithful to a graph in a general setting. I discuss the implications of these conditions in devising structural learning algorithms, in understanding exchangeabile vectors, and in random network analysis.