Algebraic Statistics and the Study of Multistate Models: Theory and Applications

This multidisciplinary project is funded by University of Helsinki, Aalto University and KU Leuven Seed Fund. It aims to advance novel applications of algebraic statistics within the framework of multistate models for complex time-to-event processes. There will be two workshops organized as part of this project: one in Espoo/Helsinki in spring 2025 and one in Leuven in fall 2025.

Seminar series

We run a monthly online series within this project. Everyone is welcome to join!

Talks

Monday 05 May 2025, 17:00 (EEST) / 16:00 (CEST)

Speaker: Sarah Lumpp (Technical University of Munich)

Title: Introduction to graphical continuous Lyapunov models

Abstract: Stationary distributions of multivariate diffusion processes have recently been proposed as probabilistic models of causal systems in statistics and machine learning. By assuming each observation to arise as a one-time cross-sectional snapshot of a temporal process in equilibrium, they allow to model dependence structures that may include feedback loops. Specifically, the graphical continuous Lyapunov model consists of steady-state distributions of multivariate Ornstein-Uhlenbeck processes where sparsity assumptions on the drift matrices are represented with a directed graph. These distributions are Gaussian with covariance matrices that are parametrized as solutions of the continuous Lyapunov equation. In this talk, I will give an introduction to the model with a focus on the conditional independence structure as well as identifiability of the drift parameters in specific cases.

Zoom link: https://aalto.zoom.us/j/61505481430

Tuesday 02 December 2025, 11:15 (EET) / 10:15 (CET)

Speaker: Signe Lundqvist (KU Leuven)

Title: Scenes over non-generic pictures of hypergraphs

Abstract: The central problem in scene analysis is finding the space of d-dimensional polyhedral caps with a fixed projection to (d-1)-dimensional space. In particular, we are interested in which sets of points in (d-1)-dimensional space are the projections of non-trivial polyhedral caps, in the sense that the hyperplanes of the polyhedral cap are distinct. Given the combinatorial structure of the polyhedral cap, studying the space of d-dimensional polyhedral caps with a fixed generic projection becomes a combinatorial problem. Specifically, liftings of generic projections can be studied via a lifting matrix. Whiteley characterised independence in the row-matroid of the lifting matrix for generic projections. The dual problem to studying scenes over generic projections is the problem of studying the space of parallel redrawings of hyperplane arrangements. In this talk, we will focus on liftability of non-generic projections, or, dually, parallel redrawings of non-generic hyperplane arrangements. For a class of polyhedral caps, we will see that the set of projections that lift to non-generic polyhedral caps with the correct combinatorial structure is given as the zero-set of a single polynomial, called the pure condition. We will see some basic properties of the pure condition, and how to easily compute it. The talk will be based on joint work with Daniel Bernstein.

Location: Aalto University, Otakaari 1, M2 (M233) and https://aalto.zoom.us/j/69981271101

Workshop April 1-4, 2025

This workshop will be held at Aalto University and the University of Helsinki from April 1–4, 2025, bringing together experts in algebraic statistics and survival and event history analysis. The primary goal is to introduce participants to the fundamental concepts of both fields. The program includes introductory mini-courses on April 2–3, while April 1 and 4 will focus on discussions aimed at fostering connections between the two areas. This workshop is open to researchers at all levels who are interested in exploring the intersection of algebraic statistics and survival and event history analysis.

Tentative program

Tuesday, April 1 (Aalto University)

Room M233 (M2), Otakaari 1, Espoo

We have 15-minutes What is …? talks that are introductory talks introducing basic notions related to the project.

10:00 Kaie Kubjas: What is algebraic geometry?

10:30 Nataliia Kushnerchuk: What is a graphical model?

11:00 Sangita Kulathinal: What is survival analysis?

11:30 Fatemeh Mohammadi: What is algebraic statistics?

12:00-13:00 Lunch Break

13:00 Joel Siurua: What are compartmental models for infectious disease modelling?

13:30 Etienne Sebag: What are hidden Markov models and how they are used for longitudinal data?

14:00–16:00 Discussion and collaboration

Wednesday, April 2 (University of Helsinki)

Room A127, Chemicum Building, Kumpula Campus, University of Helsinki

10:00–10:45 Marina Garrote-López: Algebraic Statistical Models in Phylogenetics

11:15–12:00 Marina Garrote-López: Algebraic Statistical Models in Phylogenetics

12:15–13:15 Lunch break

13:30–14:15 Hakon K. Gjessing: Survival and event history analysis using multistate models as a framework

14:45–15:30 Hakon K. Gjessing: Survival and event history analysis using multistate models as a framework

18:00–20:00 Workshop dinner at Fat Lizard Töölö (self-pay)

Thursday, April 3 (University of Helsinki)

Room B321, Exactum Building, Kumpula Campus, University of Helsinki

10:00–10:45 Hakon K. Gjessing: Survival and event history analysis using multistate models as a framework

11:15–12:00 Hakon K. Gjessing: Survival and event history analysis using multistate models as a framework

12:15–13:15 Lunch break

13:30–14:15 Aida Maraj: Algebraic Approaches to Staged Tree Models and Maximum Likelihood Estimation

14:45–15:30 Carlotta Langer: Algebraic Approaches to Staged Tree Models and Maximum Likelihood Estimation

Friday, April 4 (University of Helsinki)

Room D340, Exactum Building, Kumpula Campus, University of Helsinki

10:00–13:00 Brainstorming session on future research ideas on the intersection of algebraic statistics and survival and event history analysis (by invitation only)

Registration

Please register for the workshop here. The registration deadline is March 23, 2025. There is no registration fee.

Contacts

Kaie Kubjas (Aalto U.)

Sangita Kulathinal (U. Helsinki)

Fatemeh Mohammadi (KU Leuven)