Related papers: The (Elementary) Mathematical Data Model Revisited

Matrix regression plays an important role in modern data analysis due to its ability to handle complex relationships involving both matrix and vector variables. We propose a class of regularized regression models capable of predicting both…

Separate programming models for data transformation (declarative) and computation (procedural) impact programmer ergonomics, code reusability and database efficiency. To eliminate the necessity for two models or paradigms, we propose a…

Current state-of-the-art generative models map noise to data distributions by matching flows or scores. A key limitation of these models is their inability to readily integrate available partial observations and additional priors. In…

This paper addresses the current lack of a unified formal framework in machine learning theory, as well as the absence of robust theoretical foundations for interpretability and ethical safety assurance. We first construct a formal…

This paper reviews, classifies and compares recent models for social networks that have mainly been published within the physics-oriented complex networks literature. The models fall into two categories: those in which the addition of new…

Algebraic statistics is a recently evolving field, where one would treat statistical models as algebraic objects and thereby use tools from computational commutative algebra and algebraic geometry in the analysis and computation of…

Modern scientific computational methods are undergoing a transformative change; big data and statistical learning methods now have the potential to outperform the classical first-principles modeling paradigm. This book bridges this…

Energy-Based Models (EBMs), also known as non-normalized probabilistic models, specify probability density or mass functions up to an unknown normalizing constant. Unlike most other probabilistic models, EBMs do not place a restriction on…

Every major data modality now has a foundation model that understands it natively: text has language models, images have vision models, audio has audio models. Tabular data, the modality on which many consequential real-world AI decisions…

Modern successes of diffusion models in learning complex, high-dimensional data distributions are attributed, in part, to their capability to construct diffusion processes with analytic transition kernels and score functions. The…

Relational databases play a central role in many information systems. Their schema contains structural (e.g. tables and columns) and behavioral (e.g. stored procedures or views) entity descriptions. Then, just like for ``normal'' software,…

The rapid proliferation of artificial intelligence (AI) models and methods presents growing challenges for research software engineers and researchers who must select, integrate, and maintain appropriate models within complex research…

Multilevel models (MLMs) are a central building block of the Bayesian workflow. They enable joint, interpretable modeling of data across hierarchical levels and provide a fully probabilistic quantification of uncertainty. Despite their…

Entity matching (EM) is a critical step in entity resolution (ER). Recently, entity matching based on large language models (LLMs) has shown great promise. However, current LLM-based entity matching approaches typically follow a binary…

Constrained sequential pattern mining aims at identifying frequent patterns on a sequential database of items while observing constraints defined over the item attributes. We introduce novel techniques for constraint-based sequential…

We explore a method of statistical estimation called Maximum Entropy on the Mean (MEM) which is based on an information-driven criterion that quantifies the compliance of a given point with a reference prior probability measure. At the core…

Word embeddings are a powerful approach for capturing semantic similarity among terms in a vocabulary. In this paper, we develop exponential family embeddings, a class of methods that extends the idea of word embeddings to other types of…

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 present a pseudocode algorithm for translating our (Elementary) Mathematical Data Model schemes into relational ones and associated sets of non-relational constraints, used by MatBase, our intelligent data and knowledge base management…

A common approach for knowledge-base entity search is to consider an entity as a document with multiple fields. Models that focus on matching query terms in different fields are popular choices for searching such entity representations. An…