Rick Quax

Alex Gabel, Victoria Klein, Riccardo Valperga et al.

The problem of detecting and quantifying the presence of symmetries in datasets is useful for model selection, generative modeling, and data analysis, amongst others. While existing methods for hard-coding transformations in neural networks require prior knowledge of the symmetries of the task at hand, this work focuses on discovering and characterizing unknown symmetries present in the dataset, namely, Lie group symmetry transformations beyond the traditional ones usually considered in the field (rotation, scaling, and translation). Specifically, we consider a scenario in which a dataset has been transformed by a one-parameter subgroup of transformations with different parameter values for each data point. Our goal is to characterize the transformation group and the distribution of the parameter values. The results showcase the effectiveness of the approach in both these settings.

Leon Lang, Clélia de Mulatier, Rick Quax et al.

Markov random fields are known to be fully characterized by properties of their information diagrams, or I-diagrams. In particular, for Markov random fields, regions in the I-diagram corresponding to disconnected vertex sets in the graph vanish. Recently, I-diagrams have been generalized to F-diagrams, for a larger class of functions F satisfying the chain rule beyond Shannon entropy, such as Kullback-Leibler divergence and cross-entropy. In this work, we generalize the notion and characterization of Markov random fields to this larger class of functions F and investigate preliminary applications. We define F-independences, F-mutual independences, and F-Markov random fields and characterize them by their F-diagram. In the process, we also define F-dual total correlation and prove that its vanishing is equivalent to F-mutual independence. We then apply our results to information functions F that are applied to probability mass functions. We show that if the probability distributions of a set of random variables are Markov random fields for the same graph, then we formally recover the notion of an F-Markov random field for that graph. We then study the Kullback-Leibler diagrams on specific Markov chains, leading to a visual representation of the second law of thermodynamics and a simple explicit derivation of the decomposition of the evidence lower bound for diffusion models.

Frederike Oetker, Vittorio Nespeca, Rick Quax

Agent Based Models (ABMs) often deal with systems where there is a lack of quantitative data or where quantitative data alone may be insufficient to fully capture the complexities of real-world systems. Expert knowledge and qualitative insights, such as those obtained through interviews, ethnographic research, historical accounts, or participatory workshops, are critical in constructing realistic behavioral rules, interactions, and decision-making processes within these models. However, there is a lack of systematic approaches that are able to incorporate both qualitative and quantitative data across the entire modeling cycle. To address this, we propose FREIDA (FRamework for Expert-Informed Data-driven Agent-based models), a systematic mixed-methods framework to develop, train, and validate ABMs, particularly in data-sparse contexts. Our main technical innovation is to extract what we call Expected System Behaviors (ESBs) from qualitative data, which are testable statements that can be evaluated on model simulations. Divided into Calibration Statements (CS) for model calibration and Validation Statements (VS) for model validation, they provide a quantitative scoring mechanism on the same footing as quantitative data. In this way, qualitative insights can inform not only model specification but also its parameterization and assessment of fitness for purpose, which is a long standing challenge. We illustrate the application of FREIDA through a case study of criminal cocaine networks in the Netherlands.

Jeroen F. Uleman, Loes Crielaard, Leonie K. Elsenburg et al.

Causal loop diagrams (CLDs) are widely used in health and environmental research to represent hypothesized causal structures underlying complex problems. However, as qualitative and static representations, CLDs are limited in their ability to support dynamic analysis and inform intervention strategies. We propose Diagrams-to-Dynamics (D2D), a method for converting CLDs into exploratory system dynamics models (SDMs) in the absence of empirical data. With minimal user input - following a protocol to label variables as stocks, flows or auxiliaries, and constants - D2D leverages the structural information already encoded in CLDs, namely, link existence and polarity, to simulate hypothetical interventions and explore potential leverage points under uncertainty. Results suggest that D2D helps distinguish between high- and low-ranked leverage points. We compare D2D to a data-driven SDM constructed from the same CLD and variable labels. D2D showed greater consistency with the data-driven model compared to static network centrality analysis, while providing uncertainty estimates and guidance for future data collection. The D2D method is implemented in an open-source Python package and a web-based application to support further testing and lower the barrier to dynamic modeling for researchers working with CLDs. We expect that additional validation studies will further establish the approach's utility across a broad range of cases and domains.