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PreprintCC BY 4.0arXiv

Matrix Φ-Entropic Measures of Dependence

  • Chenyu Wang
  • Amin Gohari
Open at sourcePDFDOICite

Abstract

We introduce matrix Φ-ribbons, extending the scalar Φ-ribbons to the matrix case. For Φ in the subadditivity class, we establish data processing and tensorization properties of matrix Φ-ribbons. We establish scalar and matrix Φ-entropy inequalities and use them to show that both Φ-ribbons characterize the corresponding Φ-strong data processing inequality (SDPI) constants. We obtain exact evaluations of the SDPI constants for several sources. We provide examples showing that the matrix Φ-SDPI constant can exceed the scalar counterpart. Finally, we derive inner bounds for Φ-ribbons from prescribed independence structures and prove that these bounds are optimal when Φ(t)=tlog t.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026matrix,
  title = {{Matrix $Φ$-Entropic Measures of Dependence}},
  author = {Chenyu Wang and Amin Gohari},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29576},
  eprint = {2610.29576},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29576},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Matrix Φ-Entropic Measures of Dependence
AU  - Chenyu Wang
AU  - Amin Gohari
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29576
UR  - https://arxiv.org/abs/2610.29576
AB  - We introduce matrix Φ-ribbons, extending the scalar Φ-ribbons to the matrix case. For Φ in the subadditivity class, we establish data processing and tensorization properties of matrix Φ-ribbons. We establish scalar and matrix Φ-entropy inequalities and use them to show that both Φ-ribbons characterize the corresponding Φ-strong data processing inequality (SDPI) constants. We obtain exact evaluations of the SDPI constants for several sources. We provide examples showing that the matrix Φ-SDPI constant can exceed the scalar counterpart. Finally, we derive inner bounds for Φ-ribbons from prescribed independence structures and prove that these bounds are optimal when Φ(t)=tlog t.
ER  -