arXiv Open Access 2021

Information cohomology of classical vector-valued observables

Juan Pablo Vigneaux

Lihat Sumber

Abstrak

We provide here a novel algebraic characterization of two information measures associated with a vector-valued random variable, its differential entropy and the dimension of the underlying space, purely based on their recursive properties (the chain rule and the nullity-rank theorem, respectively). More precisely, we compute the information cohomology of Baudot and Bennequin with coefficients in a module of continuous probabilistic functionals over a category that mixes discrete observables and continuous vector-valued observables, characterizing completely the 1-cocycles; evaluated on continuous laws, these cocycles are linear combinations of the differential entropy and the dimension.

Topik & Kata Kunci

cs.IT math.CT math.PR

Penulis (1)

Juan Pablo Vigneaux

Format Sitasi

APA MLA BibTeX

Vigneaux, J.P. (2021). Information cohomology of classical vector-valued observables. https://arxiv.org/abs/2107.04377

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2021
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓