相关论文: Diversity-multiplexing Gain Tradeoff: a Tool in Al…

We integrate information-theoretic concepts into the design and analysis of optimistic algorithms and Thompson sampling. By making a connection between information-theoretic quantities and confidence bounds, we obtain results that relate…

Many aspects of human learning have been proposed as a process of constructing mental programs: from acquiring symbolic number representations to intuitive theories about the world. In parallel, there is a long-tradition of using…

As the twin movements of open science and open source bring an ever greater share of the scientific process into the digital realm, new opportunities arise for the meta-scientific study of science itself, including of data science and…

The traditional approach to the quantitative study of segregation is to employ indices that are selected by ``desirable properties''. Here, we detail how information theory underpins entropy-based indices and demonstrate how desirable…

To improve diversity gain in an interference channel and hence to maximize diversity multiplexing tradeoff (DMT), we propose on-off switched interference alignment (IA) where IA is intermittently utilized by switching IA on/off. For on-off…

The data augmentation (DA) algorithm is a simple and powerful tool in statistical computing. In this note basic information theory is used to prove a nontrivial convergence theorem for the DA algorithm.

Differential graded (DG) commutative algebra provides powerful techniques for proving theorems about modules over commutative rings. These notes are a somewhat colloquial introduction to these techniques. In order to provide some motivation…

This paper is on developing some computer-assisted proof methods involving non-classical inequalities for Shannon entropy. Two areas of the applications of information inequalities are studied: Secret sharing schemes and hat guessing games.…

We view difference algebra as the study of algebraic objects in the topos of difference sets. The methods of topos theory and categorical logic enable us to develop difference homological algebra, identify a solid foundation for difference…

Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…

Algebraic space--time coding --- a powerful technique developed in the context of multiple-input multiple-output (MIMO) wireless communications --- has profited tremendously from tools from Class Field Theory and, more concretely, the…

Developments in Artificial Intelligence (AI) and Distributed Ledger Technology (DLT) currently lead to lively debates in academia and practice. AI processes data to perform tasks that were previously thought possible only for humans. DLT…

An extension of the popular diversity-multiplexing tradeoff framework to the low-SNR (or wideband) regime is proposed. The concept of diversity gain is shown to be redundant in this regime since the outage probability is SNR-independent and…

Many organizations rely on data from government and third-party sources, and those sources rarely follow the same data formatting. This introduces challenges in integrating data from multiple sources or aligning external sources with…

A strong link between information geometry and algebraic statistics is made by investigating statistical manifolds which are algebraic varieties. In particular it it shown how first and second order efficient estimators can be constructed,…

Fine-tuning large language models (LLMs) using diverse datasets is crucial for enhancing their overall performance across various domains. In practical scenarios, existing methods based on modeling the mixture proportions of data…

This is a survey of the diversity of problems in additive number theory. Equity requires the consideration of less currently popular problems, and suggests their inclusion in the additive canon. Of particular interest are problems about the…

This monograph offers a toolbox of mathematical techniques, which have been effective and widely applicable in information-theoretic analysis. The first tool is a generalization of the method of types to Gaussian settings, and then to…

Information theory is a mathematical theory of learning with deep connections with topics as diverse as artificial intelligence, statistical physics, and biological evolution. Many primers on information theory paint a broad picture with…

When developing peer-to-peer applications on Distributed Ledger Technology (DLT), a crucial decision is the selection of a suitable DLT design (e.g., Ethereum) because it is hard to change the underlying DLT design post hoc. To facilitate…