Geodesic
Characterisation of conditional independence structures for polymatroids using vanishing sets
Kybernetika, Tome 56 (2020) no. 6, pp. 1022-1044
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper, we characterise and classify a list of full conditional independences via the structure of the induced set of vanishing atoms. Construction of Markov random subfield and minimal characterisation of polymatroids satisfying a MRF will also be given.
In this paper, we characterise and classify a list of full conditional independences via the structure of the induced set of vanishing atoms. Construction of Markov random subfield and minimal characterisation of polymatroids satisfying a MRF will also be given.
DOI : 10.14736/kyb-2020-6-1022
Classification : 62-09, 62B10
Keywords: full conditional independence; markov random field; polymatroids 
@article{10_14736_kyb_2020_6_1022,
     author = {Chan, Terence and Chen, Qi and Yeung, Raymond},
     title = {Characterisation of conditional independence structures for polymatroids using vanishing sets},
     journal = {Kybernetika},
     pages = {1022--1044},
     year = {2020},
     volume = {56},
     number = {6},
     doi = {10.14736/kyb-2020-6-1022},
     mrnumber = {4199901},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2020-6-1022/}
}
TY  - JOUR
AU  - Chan, Terence
AU  - Chen, Qi
AU  - Yeung, Raymond
TI  - Characterisation of conditional independence structures for polymatroids using vanishing sets
JO  - Kybernetika
PY  - 2020
SP  - 1022
EP  - 1044
VL  - 56
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2020-6-1022/
DO  - 10.14736/kyb-2020-6-1022
LA  - en
ID  - 10_14736_kyb_2020_6_1022
ER  - 
%0 Journal Article
%A Chan, Terence
%A Chen, Qi
%A Yeung, Raymond
%T Characterisation of conditional independence structures for polymatroids using vanishing sets
%J Kybernetika
%D 2020
%P 1022-1044
%V 56
%N 6
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2020-6-1022/
%R 10.14736/kyb-2020-6-1022
%G en
%F 10_14736_kyb_2020_6_1022
Chan, Terence; Chen, Qi; Yeung, Raymond. Characterisation of conditional independence structures for polymatroids using vanishing sets. Kybernetika, Tome 56 (2020) no. 6, pp. 1022-1044. doi: 10.14736/kyb-2020-6-1022

[1] Blake, A., Kohli, P., Rother, C.: Markov random fields for vision and image processing. MIT Press, 2011. | DOI | MR

[2] Chan, T. H., Thakor, S., Grant, A.: Minimal characterisation of Shannon-type inequalities under functional dependence and full conditional independence structures. IEEE Trans. Inform. Theory 65 (2019), 7, 4041-4051. | DOI | MR

[3] Chen, M., Cho, J., Zhao, H.: Incorporating biological pathways via a Markov random field model in genome-wide association studies. PLOS Genetics 7 (2011), 1-13. | DOI

[4] Doyle, L. E., Kokaram, A. C., Doyle, S. J., Forde, T. K.: Ad hoc networking, Markov random fields, and decision making. IEEE Signal Process. Mag. 23 (2006), 63-73. | DOI

[5] Geiger, D., Pearl, J.: Logical and algorithmic properties of conditional independence and graphical models. Ann. Statist. 21 (1993), 4, 2001-2021. | DOI | MR

[6] Malvestuto, F.: A unique formal system for binary decompositions of database relations, probability distributions, and graphs. Inform. Sci. 59 (1992), 1, 21-52. | DOI | MR

[7] Snijders, T. A.: Statistical models for social networks. Ann. Rev. Sociology 37 (2011), 1, 131-153. | DOI | MR

[8] Wang, T., Krim, H., Viniotis, Y.: A generalized Markov graph model: Application to social network analysis. IEEE J. Selected Topics Signal Process. 7 (2013), 318-332. | DOI

[9] Yeung, R. W.: A new outlook on Shannon's information measures. IEEE Trans. Inform. Theory 37 (1991), 466-474. | DOI | MR

[10] Yeung, R. W.: Information Theory and Network Coding. Springer, 2008.

[11] Yeung, R. W., Al-Bashabsheh, A., Chen, C., Chen, Q., Moulin, P.: On information-theoretic characterizations of Markov random fields and subfields. IEEE Trans. Inform. Theory 65 (2019), 1493-1511. | DOI | MR

[12] Yeung, R. W., Lee, T. T., Ye, Z.: Information-theoretic characterizations of conditional mutual independence and markov random fields. IEEE Trans. Inform. Theory 48 (2002), 1996-2011. | DOI | MR

Cité par Sources :