Related papers: The (Elementary) Mathematical Data Model Revisited

Multi-Entity Bayesian Network (MEBN) is a knowledge representation formalism combining Bayesian Networks (BN) with First-Order Logic (FOL). MEBN has sufficient expressive power for general-purpose knowledge representation and reasoning.…

Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…

Rank-order relational data, in which each actor ranks the others according to some criterion, often arise from sociometric measurements of judgment (e.g., self-reported interpersonal interaction) or preference (e.g., relative liking). We…

Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…

Energy-Based Models (EBMs) are an important class of probabilistic models, also known as random fields and undirected graphical models. EBMs are un-normalized and thus radically different from other popular self-normalized probabilistic…

Language models and specialized table embedding models have recently demonstrated strong performance on many tasks over tabular data. Researchers and practitioners are keen to leverage these models in many new application contexts; but…

Energy-based models (EBMs) are powerful probabilistic models, but suffer from intractable sampling and density evaluation due to the partition function. As a result, inference in EBMs relies on approximate sampling algorithms, leading to a…

Existential rules, a.k.a. dependencies in databases, and Datalog+/- in knowledge representation and reasoning recently, are a family of important logical languages widely used in computer science and artificial intelligence. Towards a deep…

Without any doubt, the relational paradigm has been a huge success. At the same time, we believe that the time is ripe to rethink how database systems could look like if we designed them from scratch. Would we really end up with the same…

Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…

Data modeling is a process of developing a model to design and develop a data system that supports an organization s various business processes. A conceptual data model represents a technology-independent specification of structure of data…

We look at equivalence relations on the set of models of a theory -- MERs, for short -- such that the class of equivalent pairs is itself an elementary class, in a language appropriate for pairs of models. We provide many examples of…

Feature-importance methods show promise in transforming machine learning models from predictive engines into tools for scientific discovery. However, due to data sampling and algorithmic stochasticity, expressive models can be unstable,…

This is an up-to-date introduction to and overview of the Minimum Description Length (MDL) Principle, a theory of inductive inference that can be applied to general problems in statistics, machine learning and pattern recognition. While MDL…

This article analyzes the use of Large Language Models (LLMs) as support for the conceptual modeling of relational databases through the automatic generation of Entity-Relationship (ER) diagrams from natural language requirements. The…

Presented are algorithms for enforcing function diagram commutativity and anti-commutativity database constraints, using the database software application constraint-driven design and development methodology, in the realm of the…

Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…

Exponential-family random graph models (ERGMs) provide a principled and flexible way to model and simulate features common in social networks, such as propensities for homophily, mutuality, and friend-of-a-friend triad closure, through…

This paper rigorously and concisely defines, in the context of our (Elementary) Mathematical Data Model ((E)MDM), the mathematical concepts of self-map, composite mapping, totality, one-to-oneness, non-primeness, ontoness, bijectivity,…

This tutorial overviews the state of the art in learning models over relational databases and makes the case for a first-principles approach that exploits recent developments in database research. The input to learning classification and…