| Title:
|
On solution sets of information inequalities (English) |
| Author:
|
Ay, Nihat |
| Author:
|
Wenzel, Walter |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
48 |
| Issue:
|
5 |
| Year:
|
2012 |
| Pages:
|
845-864 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce structural properties of Bayesian networks, which is important within causal inference. (English) |
| Keyword:
|
linear inequalities |
| Keyword:
|
polyhedral sets |
| Keyword:
|
Bayesian networks |
| Keyword:
|
information |
| Keyword:
|
entropy |
| MSC:
|
15A39 |
| MSC:
|
52Bxx |
| MSC:
|
94A17 |
| idMR:
|
MR3086855 |
| . |
| Date available:
|
2012-12-17T13:26:34Z |
| Last updated:
|
2013-09-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143085 |
| . |
| Reference:
|
[1] Ay, N.: A refinement of the common cause principle..Discrete Appl. Math. 157 (2009), 2439-2457. MR 2527961, 10.1016/j.dam.2008.06.032 |
| Reference:
|
[2] Ay, N., Polani, D.: Information flows in causal networks..Adv. Complex Systems 11 (2008), 1, 17-41. Zbl 1163.94417, MR 2400125, 10.1142/S0219525908001465 |
| Reference:
|
[3] Martini, H., Soltan, V.: Combinatorial problems on the illumination of convex bodies..Aequationes Math. 57 (1999), 121-152. Zbl 0937.52006, MR 1689190, 10.1007/s000100050074 |
| Reference:
|
[4] Martini, H., Wenzel, W.: Illumination and visibility problems in terms of closure operators..Beiträge zur Algebra und Geometrie 45 (2004), 2, 607-614. Zbl 1074.52001, MR 2093030 |
| Reference:
|
[5] Pearl, J.: Causality: Models, Reasoning and Inference..Cambridge University Press 2000. Zbl 1188.68291, MR 1744773 |
| Reference:
|
[6] Steudel, B., Ay, N.: Information-theoretic inference of common ancestors..Submitted. ArXiv preprint (2010) arXiv:1010.5720. |
| Reference:
|
[7] Valentine, F. A.: Visible shorelines..Amer. Math. Monthly 77 (1970), 146-152. Zbl 0189.52903, MR 0257881, 10.2307/2317326 |
| Reference:
|
[8] Webster, R.: Convexity..Oxford University Press 1994. Zbl 1052.68785, MR 1443208 |
| Reference:
|
[9] Ziegler, G.: Lectures on Polytopes..Springer Verlag Berlin 1997. Zbl 0823.52002, MR 1311028 |
| . |
