Petr Ryšavý

Mengjia Niu, Xiaoyu He, Petr Ryšavý et al.

Clustering of time series is a well-studied problem, with applications ranging from quantitative, personalized models of metabolism obtained from metabolite concentrations to state discrimination in quantum information theory. We consider a variant, where given a set of trajectories and a number of parts, we jointly partition the set of trajectories and learn linear dynamical system (LDS) models for each part, so as to minimize the maximum error across all the models. We present globally convergent methods and EM heuristics, accompanied by promising computational results. The key highlight of this method is that it does not require a predefined hidden state dimension but instead provides an upper bound. Additionally, it offers guidance for determining regularization in the system identification.

Petr Ryšavý, Pavel Rytíř, Xiaoyu He et al.

In mixed graphs, there are both directed and undirected edges. An extension of acyclicity to this mixed-graph setting is known as maximally ancestral graphs. This extension is of considerable interest in causal learning in the presence of confounders. There, directed edges represent a clear direction of causality, while undirected edges represent confounding. We propose a score-based branch-and-cut algorithm for learning maximally ancestral graphs. The algorithm produces more accurate results than state-of-the-art methods, while being faster to run on small and medium-sized synthetic instances.

Vyacheslav Kungurtsev, Fadwa Idlahcen, Petr Rysavy et al.

In this paper, we present a guide to the foundations of learning Dynamic Bayesian Networks (DBNs) from data in the form of multiple samples of trajectories for some length of time. We present the formalism for a generic as well as a set of common types of DBNs for particular variable distributions. We present the analytical form of the models, with a comprehensive discussion on the interdependence between structure and weights in a DBN model and their implications for learning. Next, we give a broad overview of learning methods and describe and categorize them based on the most important statistical features, and how they treat the interplay between learning structure and weights. We give the analytical form of the likelihood and Bayesian score functions, emphasizing the distinction from the static case. We discuss functions used in optimization to enforce structural requirements. We briefly discuss more complex extensions and representations. Finally we present a set of comparisons in different settings for various distinct but representative algorithms across the variants.

Petr Ryšavý, Xiaoyu He, Jakub Mareček

Learning causal relationships between a set of variables is a challenging problem in computer science. Many existing artificial benchmark datasets are based on sampling from causal models and thus contain residual information that the ${R} ^2$-sortability can identify. Here, we present a benchmark for methods in causal learning using time series. The presented dataset is not ${R}^2$-sortable and is based on a real-world scenario of the Krebs cycle that is used in cells to release energy. We provide four scenarios of learning, including short and long time series, and provide guidance so that testing is unified between possible users.