Distinguishing Between Cause and Effect via Kernel-Based Complexity Measures for Conditional Distributions
We propose a method to evaluate the complexity of probability measures from data that is based on a reproducing kernel Hilbert space seminorm of the logarithm of conditional probability densities. The motivation is to provide a tool for a causal inference method which assumes that conditional probabilities for effects given their causes are typically simpler and smoother than vice-versa. We present experiments with toy data where the quantitative results are consistent with our intuitive understanding of complexity and smoothness. Also in some examples with real-world data the probability measure corresponding to the true causal direction turned out to be less complex than those of the reversed order.
| Author(s): | Sun, X. and Janzing, D. and Schölkopf, B. |
| Book Title: | Proceedings of the 15th European Symposium on Artificial Neural Networks |
| Journal: | Proceedings of the 15th European Symposium on Artificial Neural Networks (ESANN 2007) |
| Pages: | 441-446 |
| Year: | 2007 |
| Month: | April |
| Day: | 0 |
| Editors: | M Verleysen |
| Publisher: | D-Side Publications |
| Bibtex Type: | Conference Paper (inproceedings) |
| Address: | Evere, Belgium |
| Event Name: | ESANN 2007 |
| Event Place: | Brugge, Belgium |
| Digital: | 0 |
| Electronic Archiving: | grant_archive |
| Language: | en |
| Organization: | Max-Planck-Gesellschaft |
| School: | Biologische Kybernetik |
| Links: | |
BibTex
@inproceedings{4454,
title = {Distinguishing Between Cause and Effect via Kernel-Based Complexity Measures for Conditional Distributions},
journal = {Proceedings of the 15th European Symposium on Artificial Neural Networks (ESANN 2007)},
booktitle = {Proceedings of the 15th European Symposium on Artificial Neural Networks
},
abstract = {We propose a method to evaluate the complexity of probability measures from data that is based on a reproducing kernel Hilbert space seminorm of the logarithm of conditional probability densities. The motivation is to provide a tool for a causal inference method which assumes that conditional probabilities for effects given their causes are typically simpler and smoother than vice-versa. We present experiments with toy data where the quantitative results are consistent with our intuitive understanding of complexity and smoothness. Also in some examples with real-world data the probability measure corresponding to the true causal direction turned out to be less complex than those of the reversed order.},
pages = {441-446},
editors = {M Verleysen},
publisher = {D-Side Publications},
organization = {Max-Planck-Gesellschaft},
school = {Biologische Kybernetik},
address = {Evere, Belgium},
month = apr,
year = {2007},
slug = {4454},
author = {Sun, X. and Janzing, D. and Sch{\"o}lkopf, B.},
month_numeric = {4}
}