Related papers: Generalized Modeling: A survey and guide
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…
This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…
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.…
Data is a precious resource in today's society, and is generated at an unprecedented and constantly growing pace. The need to store, analyze, and make data promptly available to a multitude of users introduces formidable challenges in…
Development of several alternative mathematical models for the biological system in question and discrimination between such models using experimental data is the best way to robust conclusions. Models which challenge existing theories are…
Mathematical models are vital to the field of metrology, playing a key role in the derivation of measurement results and the calculation of uncertainties from measurement data, informed by an understanding of the measurement process. These…
This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the sets and functions which comprise the…
Deep learning models have gained great popularity in statistical modeling because they lead to very competitive regression models, often outperforming classical statistical models such as generalized linear models. The disadvantage of deep…
We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. We envision this method being generally applicable…
A substantial volume of research has been devoted to studies of community structure in networks, but communities are not the only possible form of large-scale network structure. Here we describe a broad extension of community structure that…
While there are many applications of ML to scientific problems that look promising, visuals can be deceiving. Using numerical analysis techniques, we rigorously quantify the accuracy, convergence rates, and generalization bounds of certain…
The advent of modern technology, permitting the measurement of thousands of characteristics simultaneously, has given rise to floods of data characterized by many large or even huge datasets. This new paradigm presents extraordinary…
During modeling of dynamical systems, often two or more model architectures are combined to obtain a more powerful or efficient model regarding a specific application area. This covers the combination of multiple machine learning…
The increasing integration of renewable energy sources has introduced complex dynamic behavior in power systems that challenge the adequacy of traditional continuous-time modeling approaches. These developments call for modeling frameworks…
Multi-model ensembles provide a pragmatic approach to the representation of model uncertainty in climate prediction. However, such representations are inherently ad hoc, and, as shown, probability distributions of climate variables based on…
The current science of cities can provide a useful foundation for future urban policies, provided that these proposals have been validated by correct observations of the diversity of situations in the world. However, international…
Estimation of density functions supported on general domains arises when the data is naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching…
The standard procedures for analysing hierarquical or grouped data are by (non)linear mixed models or generalized mixed models. However, the generalized additive models for location, scale and shape (GAMLSSs) also allow different types of…
Generalized planning is concerned with the characterization and computation of plans that solve many instances at once. In the standard formulation, a generalized plan is a mapping from feature or observation histories into actions,…
Understanding the generalization behaviour of deep neural networks is a topic of recent interest that has driven the production of many studies, notably the development and evaluation of generalization "explainability" measures that…