Related papers: Algebraic Databases
Providing machine learning (ML) over relational data is a mainstream requirement for data analytics systems. While almost all the ML tools require the input data to be presented as a single table, many datasets are multi-table, which forces…
Recent advances with in-memory columnar database techniques have increased the performance of analytical queries on very large databases and data warehouses. At the same time, advances in artificial intelligence (AI) algorithms have…
This paper presents the current version of our (Elementary) Mathematical Data Model ((E)MDM), which is based on the na\"ive theory of sets, relations, and functions, as well as on the first-order predicate calculus with equality. Many…
One of the challenging problems in the multidatabase systems is to find the most viable solution to the problem of interoperability of distributed heterogeneous autonomous local component databases. This has resulted in the creation of a…
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…
Neural networks excel at pattern recognition but struggle with reliable logical reasoning, often violating basic logical principles during inference. We address this limitation by developing a categorical framework that systematically…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
We present a novel framework for integrating prior knowledge into discriminative classifiers. Our framework allows discriminative classifiers such as Support Vector Machines (SVMs) to utilize prior knowledge specified in the generative…
In this paper, we introduce a novel approach to deductive databases meant to take into account the needs of current applications in the area of data integration. To this end, we extend the formalism of standard deductive databases to the…
Kernel classifiers and regressors designed for structured data, such as sequences, trees and graphs, have significantly advanced a number of interdisciplinary areas such as computational biology and drug design. Typically, kernels are…
Multi-class classification problem is among the most popular and well-studied statistical frameworks. Modern multi-class datasets can be extremely ambiguous and single-output predictions fail to deliver satisfactory performance. By allowing…
Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
Applied process calculi include advanced programming constructs such as type systems, communication with pattern matching, encryption primitives, concurrent constraints, nondeterminism, process creation, and dynamic connection topologies.…
Graph neural networks (GNNs) are powerful deep learning models for graph-structured data, demonstrating remarkable success across diverse domains. Recently, the database (DB) community has increasingly recognized the potentiality of GNNs,…
In modern data analytics, analysts frequently face the challenge of searching for desirable entities by evaluating, for each entity, a collection of its feature relations to derive key analytical properties. This search is challenging…
Purpose: This study extends the structural theory of finite commutative ternary $\Gamma$-semirings into a computational and categorical framework for explicit classification and constructive reasoning. Methods: Constraint-driven enumeration…
Set-valued prediction is a well-known concept in multi-class classification. When a classifier is uncertain about the class label for a test instance, it can predict a set of classes instead of a single class. In this paper, we focus on…
The business model represents an increasingly important management concept. However, progress in research related to the concept is currently inhibited from inconsistencies in terms of formalizing and therewith also empirically measuring…
Recent work on database application development platforms has sought to include a declarative formulation of a conceptual data model in the application code, using annotations or attributes. Some recent work has used metadata to include the…