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The purpose of this paper is to provide a discussion, with illustrating examples, on Bayesian forecasting for dynamic generalized linear models (DGLMs). Adopting approximate Bayesian analysis, based on conjugate forms and on Bayes linear…

Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…

We consider problems of making sequences of decisions to accomplish tasks, interacting via the medium of language. These problems are often tackled with reinforcement learning approaches. We find that these models do not generalize well…

The proliferation of pretrained models, as a result of advancements in pretraining techniques, has led to the emergence of a vast zoo of publicly available models. Effectively utilizing these resources to obtain models with robust…

Mathematical modelling has a long history in the context of collective cell migration, with applications throughout development, disease and regenerative medicine. The aim of modelling in this context is to provide a framework in which to…

We analyze the properties of model food webs and of fifteen community food webs from a variety of environments. We first perform a theoretical analysis of the niche model of Williams and Martinez. We derive analytical expressions for the…

We introduce the Webworld model, which links together the ecological modelling of food web structure with the evolutionary modelling of speciation and extinction events. The model describes dynamics of ecological communities on an…

A challenge for practitioners of Bayesian inference is specifying a model that incorporates multiple relevant, heterogeneous data sets. It may be easier to instead specify distinct submodels for each source of data, then join the submodels…

As machine learning becomes more and more available to the general public, theoretical questions are turning into pressing practical issues. Possibly, one of the most relevant concerns is the assessment of our confidence in trusting machine…

Systematic Generalization refers to a learning algorithm's ability to extrapolate learned behavior to unseen situations that are distinct but semantically similar to its training data. As shown in recent work, state-of-the-art deep learning…

Generalization in generative modeling is defined as the ability to learn an underlying distribution from a finite dataset and produce novel samples, with evaluation largely driven by held-out performance and perceived sample quality. In…

Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…

Based on the law of mass action (and its microscopic foundation) and mass conservation, we present here a method to derive consistent dynamic models for the time evolution of systems with an arbitrary number of species. Equations are…

We advocate the use of qualitative models in the analysis of large biological systems. We show how qualitative models are linked to theoretical differential models and practical graphical models of biological networks. A new technique for…

This paper introduces a unified theoretical perspective that views deep generative models as probability transformation functions. Despite the apparent differences in architecture and training methodologies among various types of generative…

Scientists investigate the dynamics of complex systems with quantitative models, employing them to synthesize knowledge, to explain observations, and to forecast future system behavior. Complete specification of systems is impossible, so…

We analyze plankton-nutrient food chain models composed of phytoplankton, herbivorous zooplankton and a limiting nutrient. These models have played a key role in understanding the dynamics of plankton in the oceanic layer. Given the strong…

The basic mechanics of evolution have been understood since Darwin. But debate continues over whether macroevolutionary phenomena are driven primary by the fitness structure of genotype space or by ecological interaction. In this paper we…

Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility…

Predictive skill of complex models is often not uniform in model-state space; in weather forecasting models, for example, the skill of the model can be greater in populated regions of interest than in "remote" regions of the globe. Given a…