This issue of Algebraic Statistics is a collection of research articles authored by groups of participants in the Apprenticeship Week within the research semester “Algebraic Statistics and Our Changing World”, held at the Institute for Mathematical and Statistical Innovation (IMSI). The participants, called apprentices, were selected from among graduate students and postdocs who had applied to IMSI to be part of this focused activity in Fall 2023. The research groups were formed during Summer 2023. As the leaders of the Apprenticeship Week, we suggested a list of research projects centered around the theme “varieties in statistics”. The articles you find in this issue are the product of intense (and fun) work the groups performed over about six months, including during a focused week in October 2023 when IMSI hosted us and the apprentices in Chicago. A subset of the apprentices spent a more extended period at IMSI and interacted with other members of the program. The articles were influenced and shaped by these interactions as well.

Working with the next generation of the scientists who will expand the frontiers of the field of algebraic statistics was tremendously rewarding. Their intellectual work resulted in papers with topics in log-linear models, Wasserstein distance, likelihood geometry of independence and Gaussian models, moment varieties, polynomial neural networks, mixtures of decomposable models, and cumulant tensors. The algebraic statistics community thrives on the eclectic mix of its participants and this was also true for the apprentices. The choice of the topics reflects the wide spectrum of their background and their interests. We think that you will find their results exciting and useful.

In addition, this issue includes an article that showcases three concrete research projects. They represent a sample of problems and directions that were discussed during the IMSI program.

In closing, we wish to express our gratitude to IMSI and its staff who made this fantastic experience possible for us and the young apprentices.

Keywords

Mathematical Subject Classification

Milestones

Authors