Colloquium: Marginal Independence and Partial Set Partitions
November 21, 2024 11:00 am
Dr. Seth Sullivant, NC State University
Marginal Independence and Partial Set Partitions
Thursday, November 21 – 11 :00AM
Location: 018 Manchester Hall
Marginal Independence and Partial Set Partitions Independence models are widely used in probabilistic modeling, including in computational biology, statistics, and machine learning. In spite of their ubiquity, there is a large gap between the families of independence models that are easy to parametrize and completely general independence models. Focusing specifically on marginal independence models, we establish a bijection between marginal independence models on n random variables and split closed order ideals in the poset of partial set partitions. We also establish that every discrete marginal independence model is a toric variety in an appropriate coordinate system. Everything will be defined and the talk will be accessible to first year graduate students and advanced undergraduate students. This is joint work with Francisco Ponce Carrion.