Related papers: Diversity-multiplexing Gain Tradeoff: a Tool in Al…

Cylindrical algebraic decomposition (CAD) is a key tool for solving problems in real algebraic geometry and beyond. In recent years a new approach has been developed, where regular chains technology is used to first build a decomposition in…

Zhang twists are a common tool for deforming graded algebras over a field in a way that preserves important ring-theoretic properties. We generalize Zhang twists to the setting of closed monoidal categories equipped with their self-enriched…

Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of probability distributions is of fundamental importance in…

An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study various problems in combinatorial algebraic geometry and…

This work explores the deformation theory of algebraic structures in a very general setting. These structures include commutative, associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy…

The minority model was introduced to study the competition between agents with limited information. It has the remarkable feature that, as the amount of information available increases, the collective gain made by the agents is reduced.…

While consolidation strategies form the backbone of many supply chain optimisation problems, exploitation of multi-tier material relationships through consolidation remains an understudied area, despite being a prominent feature of…

The combination of the group ring setting with the methods of character theory allows an elegant and powerful analysis of various combinatorial structures, via their character sums. These combinatorial structures include difference sets,…

Zheng and Tse have shown that over a quasi-static channel, there exists a fundamental tradeoff, known as the diversity-multiplexing gain (D-MG) tradeoff. In a realistic system, to avoid inefficiently operating the power amplifier, one…

This work introduces a novel interpretable machine learning method called Mixture of Decision Trees (MoDT). It constitutes a special case of the Mixture of Experts ensemble architecture, which utilizes a linear model as gating function and…

For a matrix *-algebra B, consider the matrix *-algebra A consisting of the symmetric tensors in the n-fold tensor product of B. Examples of such algebras in coding theory include the Bose-Mesner algebra and Terwilliger algebra of the…

Distributed optimization algorithms are widely used in machine learning. This paper investigates how a small amount of data sharing can improve their performance. Focusing on general linear models, we analyze the effects of data sharing on…

Dempster-Shafer theory is widely applied to uncertainty modelling and knowledge reasoning due to its ability of expressing uncertain information. However, some conditions, such as exclusiveness hypothesis and completeness constraint, limit…

A new seemingly weak axiomatic formulation of information algebras is given. It is shown how such information algebras can be embedded into set (information) algebras. In set algebras there is a natural relation of conditional independence…

Let $A$ be a finite dimensional algebra of finite global dimension over a finite field. In the present paper, we introduce certain elements in Bridgeland's Hall algebra of $A$, and give a multiplication theorem of these elements. In…

Many fundamental statistical methods have become critical tools for scientific data analysis yet do not scale tractably to modern large datasets. This paper will describe very recent algorithms based on computational geometry which have…

Recent studies have introduced the worst-case quantum divergence as a key measure in quantum information. Here we show that such divergences can be understood from the perspective of the resource theory of asymmetric distinguishability,…

As multi-task models gain popularity in a wider range of machine learning applications, it is becoming increasingly important for practitioners to understand the fairness implications associated with those models. Most existing fairness…

A practical notation can convey valuable intuitions and concisely express new ideas. Information theory is of importance to machine learning, but the notation for information-theoretic quantities is sometimes opaque. We propose a practical…

Information theory is an outstanding framework to measure uncertainty, dependence and relevance in data and systems. It has several desirable properties for real world applications: it naturally deals with multivariate data, it can handle…