Exploring the causal order of binary variables via exponential hierarchies of Markov kernels
We propose a new algorithm for estimating the causal structure that underlies the observed dependence among n (n>=4) binary variables X_1,...,X_n. Our inference principle states that the factorization of the joint probability into conditional probabilities for X_j given X_1,...,X_{j-1} often leads to simpler terms if the order of variables is compatible with the directed acyclic graph representing the causal structure. We study joint measures of OR/AND gates and show that the complexity of the conditional probabilities (the so-called Markov kernels), defined by a hierarchy of exponential models, depends on the order of the variables. Some toy and real-data experiments support our inference rule.
| Author(s): | Sun, X. and Janzing, D. |
| Book Title: | ESANN 2007 |
| Journal: | Proceedings of the 15th European Symposium on Artificial Neural Networks (ESANN 2007) |
| Pages: | 465-470 |
| Year: | 2007 |
| Month: | April |
| Day: | 0 |
| Publisher: | D-Side |
| Bibtex Type: | Conference Paper (inproceedings) |
| Address: | Evere, Belgium |
| Event Name: | 15th European Symposium on Artificial Neural Networks |
| Event Place: | Brugge, Belgium |
| Digital: | 0 |
| Electronic Archiving: | grant_archive |
| Language: | en |
| Organization: | Max-Planck-Gesellschaft |
| School: | Biologische Kybernetik |
| Links: | |
BibTex
@inproceedings{4456,
title = {Exploring the causal order of binary variables via exponential hierarchies of Markov kernels},
journal = {Proceedings of the 15th European Symposium on Artificial Neural Networks (ESANN 2007)},
booktitle = {ESANN 2007},
abstract = {We propose a new algorithm for estimating the causal structure that underlies the observed dependence among n (n>=4) binary variables X_1,...,X_n. Our inference principle states that the factorization of the joint probability into conditional probabilities for X_j given X_1,...,X_{j-1} often leads to simpler terms if the order of variables is compatible with the directed acyclic graph representing the causal structure. We study joint measures of OR/AND gates and show that the complexity of the conditional probabilities (the so-called Markov kernels), defined by a hierarchy of exponential models, depends on the order of the variables. Some toy and real-data experiments support our inference rule.},
pages = {465-470},
publisher = {D-Side},
organization = {Max-Planck-Gesellschaft},
school = {Biologische Kybernetik},
address = {Evere, Belgium},
month = apr,
year = {2007},
slug = {4456},
author = {Sun, X. and Janzing, D.},
month_numeric = {4}
}