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Over the past decade network theory has turned out to be a powerful methodology to investigate complex systems of various sorts. Through data analysis, modeling, and simulation quite an unparalleled insight into their structure, function,…

Reinforcement learning practitioners often avoid hierarchical policies, especially in image-based observation spaces. Typically, the single-task performance improvement over flat-policy counterparts does not justify the additional…

Linear Software Models is a systematic effort to formulate a theory of software systems neatly based upon standard mathematics, viz. linear algebra. It has appeared in a series of papers dealing with various aspects of the theory. But one…

This chapter reviews the purpose and use of models from the field of complex systems and, in particular, the implications of trying to use models to understand or make decisions within complex situations, such as policy makers usually face.…

Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…

This paper shows how we combine and adapt methods from elite training, future studies, and collaborative design, and apply them to address significant problems in social networks. We focus on three such methods: we use Project Action…

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript…

Hierarchical Bayesian methods enable information sharing across multiple related regression problems. While standard practice is to model regression parameters (effects) as (1) exchangeable across datasets and (2) correlated to differing…

Large language models (LLMs) are increasingly deployed with hierarchical instruction schemes, where certain instructions (e.g., system-level directives) are expected to take precedence over others (e.g., user messages). Yet, we lack a…

The machine learning community has recently devoted much attention to the problem of inferring causal relationships from statistical data. Most of this work has focused on uncovering connections among scalar random variables. We generalize…

This text is a conceptual introduction to mixed effects modeling with linguistic applications, using the R programming environment. The reader is introduced to linear modeling and assumptions, as well as to mixed effects/multilevel…

A probabilistic model for random hypergraphs is introduced to represent unary, binary and higher order interactions among objects in real-world problems. This model is an extension of the Latent Class Analysis model, which captures…

Representing and navigating hierarchy is a fundamental primitive of reasoning. Large language models have demonstrated proficiency in a wide variety of tasks requiring hierarchical reasoning, but there exists limited analysis on how the…

It has long been noticed that high dimension data exhibits strange patterns. This has been variously interpreted as either a "blessing" or a "curse", causing uncomfortable inconsistencies in the literature. We propose that these patterns…

Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model.…

A common use of machine learning (ML) models is predicting the class of a sample. Object detection is an extension of classification that includes localization of the object via a bounding box within the sample. Classification, and by…

Future projection of climate is typically obtained by combining outputs from multiple Earth System Models (ESMs) for several climate variables such as temperature and precipitation. While IPCC has traditionally used a simple model output…

An important task for any large-scale organization is to prepare forecasts of key performance metrics. Often these organizations are structured in a hierarchical manner and for operational reasons, projections of these metrics may have been…

Modern sociology has profoundly uncovered many convincing social criteria for behavioural analysis. Unfortunately, many of them are too subjective to be measured and presented in online social networks. On the other hand, data mining…

Scientific journals are the repositories of the gradually accumulating knowledge of mankind about the world surrounding us. Just as our knowledge is organised into classes ranging from major disciplines, subjects and fields to increasingly…