Related papers: Lara: A Key-Value Algebra underlying Arrays and Re…
Conjunctive table algebras are introduced and axiomatically characterized. A conjunctive table algebra is a variant of SPJR algebra (a weaker form of relational algebra), which corresponds to conjunctive queries with equality. The table…
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 propose a graph-oriented attention-based explainability method for tabular data. Tasks involving tabular data have been solved mostly using traditional tree-based machine learning models which have the challenges of feature selection and…
This book dwells on mathematical and algorithmic issues of data analysis based on generality order of descriptions and respective precision. To speak of these topics correctly, we have to go some way getting acquainted with the important…
Data analysis often involves comparing subsets of data across many dimensions for finding unusual trends and patterns. While the comparison between subsets of data can be expressed using SQL, they tend to be complex to write, and suffer…
This paper uses typed linear algebra (LA) to represent data and perform analytical querying in a single, unified framework. The typed approach offers strong type checking (as in modern programming languages) and a diagrammatic way of…
We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…
Heterogeneous graphs are widely present in real-world complex networks, where the diversity of node and relation types leads to complex and rich semantics. Efforts for modeling complex relation semantics in heterogeneous graphs are…
We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…
Hybrid complex analytics workloads typically include (i) data management tasks (joins, selections, etc. ), easily expressed using relational algebra (RA)-based languages, and (ii) complex analytics tasks (regressions, matrix decompositions,…
Tabular data is the most abundant data type in the world, powering systems in finance, healthcare, e-commerce, and beyond. As tabular datasets grow and span multiple related targets, there is an increasing need to exploit shared task…
Biological network alignment (NA) aims to find a node mapping between species' molecular networks that uncovers similar network regions, thus allowing for transfer of functional knowledge between the aligned nodes. However, current NA…
Following our previous work, we suggest here a large class of algebras of scalars in which simultaneous and correlated computations can be performed owing to the existence of surjective algebra homomorphisms. This may replace the currently…
Reasoning, the ability to logically draw conclusions from existing knowledge, is a hallmark of human. Together with perception, they constitute the two major themes of artificial intelligence. While deep learning has pushed the limit of…
Mining patterns from multi-relational data is a problem attracting increasing interest within the data mining community. Traditional data mining approaches are typically developed for highly simplified types of data, such as an…
Complexity and decidability of logics is a major research area involving a huge range of different logical systems. This calls for a unified and systematic approach for the field. We introduce a research program based on an algebraic…
In order to efficiently learn with small amount of data on new tasks, meta-learning transfers knowledge learned from previous tasks to the new ones. However, a critical challenge in meta-learning is the task heterogeneity which cannot be…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
The OverRelational Manifesto (below ORM) proposes a possible approach to creation of data storage systems of the next generation. ORM starts from the requirement that information in a relational database is represented by a set of relation…
Language agents powered by large language models (LLMs) have demonstrated remarkable capabilities in understanding, reasoning, and executing complex tasks. However, developing robust agents presents significant challenges: substantial…