Related papers: Mixture Models: Building a Parameter Space

The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…

Identifiability is a necessary condition for successful parameter estimation of dynamic system models. A major component of identifiability analysis is determining the identifiable parameter combinations, the functional forms for the…

Large information sizes in samples and features can be encoded to speed up the learning of statistical models based on linear algebra and remove unwanted signals. Encoding information can reduce both sample and feature dimension to a…

Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating…

High-throughput computational materials design promises to greatly accelerate the process of discovering new materials and compounds, and of optimizing their properties. The large databases of structures and properties that result from…

A concept of "evolving categories" is suggested to build a simple, scalable, mathematically consistent framework for representing in uniform way both data and algorithms. A state machine for executing algorithms becomes clear, rich and…

Many nonequilibrium systems, such as biochemical reactions and socioeconomic interactions, can be described by reaction-diffusion equations that demonstrate a wide variety of complex spatiotemporal patterns. The diversity of the morphology…

Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems. Although modern models are trained on massive datasets, they still cover only a tiny fraction of the…

Embedding spaces contain interpretable dimensions indicating gender, formality in style, or even object properties. This has been observed multiple times. Such interpretable dimensions are becoming valuable tools in different areas of…

The practice of evolutionary algorithms involves the tuning of many parameters. How big should the population be? How many generations should the algorithm run? What is the (tournament selection) tournament size? What probabilities should…

Pre-trained large foundation models play a central role in the recent surge of artificial intelligence, resulting in fine-tuned models with remarkable abilities when measured on benchmark datasets, standard exams, and applications. Due to…

High dimensional superposition models characterize observations using parameters which can be written as a sum of multiple component parameters, each with its own structure, e.g., sum of low rank and sparse matrices, sum of sparse and…

Synthetic polymers are versatile and widely used materials. Similar to small organic molecules, a large chemical space of such materials is hypothetically accessible. Computational property prediction and virtual screening can accelerate…

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.…

Over the past decades, linear mixed models have attracted considerable attention in various fields of applied statistics. They are popular whenever clustered, hierarchical or longitudinal data are investigated. Nonetheless, statistical…

Recent research in molecular discovery has primarily been devoted to small, drug-like molecules, leaving many similarly important applications in material design without adequate technology. These applications often rely on more complex…

Polymer materials have the characteristic feature that they are multiscale systems by definition. Already the description of a single molecules involves a multitude of different scales, and cooperative processes in polymer assemblies are…

High-throughput data generation methods and machine learning (ML) algorithms have given rise to a new era of computational materials science by learning relationships among composition, structure, and properties and by exploiting such…

Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…

Linear compartmental models are a widely used tool for analyzing systems arising in biology, medicine, and more. In such settings, it is essential to know whether model parameters can be recovered from experimental data. This is the…