David Rügamer:
Semi-Structured Regression: Current Advances and Challenges

Neural networks enable learning from various data modalities, such as images and text. This concept has been integrated into statistical modeling through semi-structured regression, which additively combines structured predictors with unstructured effects from arbitrary data modalities by embedding the statistical model into the neural network. This approach opens new opportunities for advancing regression models but also poses challenges, such as increased uncertainty, implicit regularization, and complexities in statistical inference. This presentation will introduce semi-structured regression, discuss recent advances, and highlight the challenges of embedding regression models into neural networks.

Various related papers: Paper 1, Paper 2, Paper 3, Paper 4, Paper 5

Sara Wade:
Understanding Uncertainty in Bayesian Cluster Analysis

The Bayesian approach to clustering is often appreciated for its ability to shed light on uncertainty in the partition structure. However, summarizing the posterior distribution on the partition space can be challenging. In previous work, we proposed to summarize the posterior samples using a single optimal clustering estimate, which minimizes the expected posterior Variation of Information (VI).  In instances where the posterior distribution is multimodal, it can be beneficial to summarize the posterior samples using multiple clustering estimates, each corresponding to a different part of the space of partitions that receives substantial posterior mass. In this work, we propose to find such clustering estimates by approximating the posterior distribution in a VI-based Wasserstein distance sense. An interesting byproduct is that this problem can be seen as using the k-mediods algorithm to divide the posterior samples into different groups, each represented by one of the clustering estimates. Using both synthetic and real datasets, we show that our proposal helps to improve the understanding of uncertainty, particularly when the data clusters are not well separated, or when the employed model is misspecified. 

Work in progress with Cecilia Balocchi (Edinburgh), building on previous work (see linked papers). 

Sascha Desmettre:
Equilibrium Control Theory for Kihlstrom-Mirman Preferences in Continuous Time

Introduced in 1974, Kihlstrom-Mirman preferences represent a multi-attribute generalization of the standard (univariate) expected utility theory. The main appeal of this class of utilities is that, by separating the choice of the elasticity of intertemporal substitution and risk aversion, they allow to disentangle attitudes towards time and risk. We discuss in detail how this approach differs from other classes of preferences exhibiting a similar feature (for instance, Epstein-Zin-Weil recursive utility). However, when solving intertemporal choice problems, the peculiar construction of Kihlstrom-Mirman preferences induces dynamic inconsistency - that is, the dynamic programming principle fails to hold. Our main contribution is therefore to address this challenge. In doing so, we provide a formal template to address the time-inconsistency of Kihlstrom-Mirman preferences in Markovian settings by means of equilibrium control theory. As an application, we study a consumption-investment problem for an agent with constant relative risk aversion and constant elasticity of substitution.