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Tree-structured models are a powerful alternative to parametric regression models if non-linear effects and interactions are present in the data. Yet, classical tree-structured models might not be appropriate if data comes in clusters of…

Stochastic network design is a general framework for optimizing network connectivity. It has several applications in computational sustainability including spatial conservation planning, pre-disaster network preparation, and river network…

We introduce and study the problem of posterior inference on tree-structured graphical models in the presence of a malicious adversary who can corrupt some observed nodes. In the well-studied broadcasting on trees model, corresponding to…

The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference,…

The dynamical phenomena of complex networks are very difficult to predict from local information due to the rich microstructures and corresponding complex dynamics. On the other hands, it is a horrible job to compute some stochastic…

Understanding propagation structures in graph diffusion processes, such as epidemic spread or misinformation diffusion, is a fundamental yet challenging problem. While existing methods primarily focus on source localization, they cannot…

While normalizing flows for continuous data have been extensively researched, flows for discrete data have only recently been explored. These prior models, however, suffer from limitations that are distinct from those of continuous flows.…

Modern language models address complex questions through chain-of-thought (CoT) reasoning (Wei et al., 2023) and retrieval augmentation (Lewis et al., 2021), yet struggle with error propagation and knowledge integration. Tree-structured…

The varying-coefficient model is a strong tool for the modelling of interactions in generalized regression. It is easy to apply if both the variables that are modified as well as the effect modifiers are known. However, in general one has a…

Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network.…

In classification and forecasting with tabular data, one often utilizes tree-based models. Those can be competitive with deep neural networks on tabular data and, under some conditions, explainable. The explainability depends on the depth…

Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution…

Diffusion is a key element of a large set of phenomena occurring on natural and social systems modeled in terms of complex weighted networks. Here, we introduce a general formalism that allows to easily write down mean-field equations for…

Regression models for supervised learning problems with a continuous target are commonly understood as models for the conditional mean of the target given predictors. This notion is simple and therefore appealing for interpretation and…

D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…

Decision trees are ubiquitous in machine learning for their ease of use and interpretability. Yet, these models are not typically employed in reinforcement learning as they cannot be updated online via stochastic gradient descent. We…

Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer.…

Variable trees are a new method for the exploration of discrete multivariate data. They display nested subsets and corresponding frequencies and percentages. Manual calculation of these quantities can be laborious, especially when there are…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

Many of the distributed localization algorithms are based on relaxed optimization formulations of the localization problem. These algorithms commonly rely on first-order optimization methods, and hence may require many iterations or…