Related papers: Ordered Sets for Data Analysis
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…
This document develops general concepts useful for extracting knowledge embedded in large graphs or datasets that have pair-wise relationships, such as cause-effect-type relations. Almost no underlying assumptions are made, other than that…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Ontologies order and interconnect knowledge of a certain field in a formal and semantic way so that they are machine-parsable. They try to define allwhere acceptable definition of concepts and objects, classify them, provide properties as…
We increasingly depend on a variety of data-driven algorithmic systems to assist us in many aspects of life. Search engines and recommender systems amongst others are used as sources of information and to help us in making all sort of…
Posets are discrete mathematical structures which are ubiquitous in a broad range of data analysis and machine learning applications. Research connecting posets to the data science domain has been ongoing for many years. In this paper, a…
Ranking entities such as algorithms, devices, methods, or models based on their performances, while accounting for application-specific preferences, is a challenge. To address this challenge, we establish the foundations of a universal…
The basic distinction between already known algorithmic characterizations of matroids and antimatroids is in the fact that for antimatroids the ordering of elements is of great importance. While antimatroids can also be characterized as set…
As datasets grow it becomes infeasible to process them completely with a desired model. For giant datasets, we frame the order in which computation is performed as a decision problem. The order is designed so that partial computations are…
Rough set theory is a new mathematical approach to imperfect knowledge. The notion of rough sets is generalized by using an arbitrary binary relation on attribute values in information systems, instead of the trivial equality relation. The…
Quantification, i.e., the task of training predictors of the class prevalence values in sets of unlabeled data items, has received increased attention in recent years. However, most quantification research has concentrated on developing…
TThe problem is to identify a probability associated with a set of natural numbers, given an infinite data sequence of elements from the set. If the given sequence is drawn i.i.d. and the probability mass function involved (the target)…
Dependencies have played a significant role in database design for many years. They have also been shown to be useful in query optimization. In this paper, we discuss dependencies between lexicographically ordered sets of tuples. We…
This paper introduces a new methodology for the complexity analysis of higher-order functional programs, which is based on three components: a powerful type system for size analysis and a sound type inference procedure for it, a ticking…
Neural compression is the application of neural networks and other machine learning methods to data compression. Recent advances in statistical machine learning have opened up new possibilities for data compression, allowing compression…
Formal definitions of quantities, quantity spaces, dimensions and dimension groups are introduced. Based on these concepts, a theoretical framework and a practical algorithm for dimensional analysis are developed, and examples of…
This paper seeks to apply categorical logic to the design of artificial intelligent agents that reason symbolically about objects more richly structured than sets. Using Johnstone's sequent calculus of terms- and formulae-in-context, we…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
We present a soundness theorem for a dependent type theory with context constants with respect to an indexed category of (finite, abstract) simplical complexes. The point of interest for computer science is that this category can be seen to…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…