## 17.06.2024 09:00 Saber Salehkaleybar (Leiden University): Causal Inference in Linear Structural Causal Models

The ultimate goal of causal inference is so-called causal effect identification (ID), which refers to quantifying the causal influence of a subset of variables on a target set. A stepping stone towards performing ID is learning the causal relationships among the variables which is commonly called causal structure learning (CSL). In this talk, I mainly focus on the problems pertaining to CSL and ID in linear structural causal models, which serve as the basis for problem abstraction in various scientific fields. In particular, I will review the identifiability results and algorithms for CSL and ID in the presence of latent confounding. Then, I will present our recent result on the ID problem using cross-moments among observed variables and discuss its applications to natural experiments and proximal causal inference. Finally, I conclude the presentation with possible future research directions.

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## 17.06.2024 15:00 Tomer Berlinski: "Modelling SIS Epidemics on Small-World Networks Using Moment Closures"

"The spread of infectious diseases is significantly influenced by the underlying structure of social and contact networks. Epidemic models often use moment systems to describe the evolution of the expected average prevalence of infections. Employing moment closures, which commonly involve network structure, simplifies the moment system by reducing the number of coupled ODEs. The clustering of nodes accelerates disease spread through dense local connections, suggesting the use of closures that account for this phenomenon. Closures for networks with highly heterogeneous degree distributions, such as the Super Compact Pairwise (SCP) closure, may more accurately predict the spread of diseases on real-world complex networks.
We explore the dynamics of Susceptible-Infected-Susceptible (SIS) epidemics on small-world networks, characterized by high clustering and low average path length. Using the Watts–Strogatz model, we investigate how topological features of networks, such as clustering and degree distribution, impact epidemic spread, thresholds, and endemic prevalence. We provide an overview of various closures and compare their effectiveness in modelling disease dynamics. Results indicate that the closure involving clustering shows better agreement with stochastic simulations, particularly near critical epidemic thresholds."

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## 17.06.2024 16:30 Timo Vilkas: The level of information is pivotal in Maker-Breaker games on trees

Maker-Breaker is a two player game performed on a graph, in which Breaker tries to cut off a special vertex (e.g. origin or root) by erasing edges while Maker tries to prevent that by fixing them. In this talk we consider the game to be played on supercritical Galton-Watson trees and determine the corresponding winning probabilities given different information regimes.

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## 18.06.2024 16:00 Lars Rohwedder: Sensitivity, Proximity and FPT Algorithms for Exact Matroid Problems

We consider the problem of finding a basis of a matroid with weight exactly equal to a given target. Here weights can be small discrete values or more generally m-dimensional vectors of small discrete values. We resolve the parameterized complexity completely, by presenting an FPT algorithm parameterized by the maximum weight and m for arbitrary matroids. Prior to our work, no such algorithms were known even when weights are in 0/1, or arbitrary and m = 1. Our main technical contributions are new proximity and sensitivity bounds for matroid problems, independent of the number of elements. These bounds imply FPT algorithms via matroid intersection. This is joint work with Friedrich Eisenbrand and Karol Węgrzycki.

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## 20.06.2024 16:30 Ulrich Riegel: Separation of Attritional and Large Losses in Chain Ladder Calculations

Insurance claims are often not paid out immediately. In long-tail lines such as liability or motor liability, it can take years or even decades until a claim is settled. In order to set up adequate reserves, so-called IBNR methods are used to predict future payments. Chain ladder is probably the most popular IBNR method worldwide. Since large losses behave quite differently from attritional losses, it is advisable to separate the two loss categories in the IBNR calculation.
We introduce a stochastic model for the development of attritional and large claims in long-tail lines of business and present a corresponding chain ladder-like IBNR method that predicts attritional and large losses in a consistent way.

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