## A Kernel-based Causal Learning Algorithm

### Cached

### Download Links

- [imls.engr.oregonstate.edu]
- [www.kyb.tuebingen.mpg.de]
- [www.machinelearning.org]
- [www.kyb.mpg.de]
- DBLP

### Other Repositories/Bibliography

Citations: | 7 - 4 self |

### BibTeX

@MISC{Sun_akernel-based,

author = {Xiaohai Sun and Dominik Janzing and Bernhard Schölkopf},

title = {A Kernel-based Causal Learning Algorithm},

year = {}

}

### OpenURL

### Abstract

We describe a causal learning method, which employs measuring the strength of statistical dependences in terms of the Hilbert-Schmidt norm of kernel-based cross-covariance operators. Following the line of the common faithfulness assumption of constraint-based causal learning, our approach assumes that a variable Z is likely to be a common effect of X and Y, if conditioning on Z increases the dependence between X and Y. Based on this assumption, we collect “votes” for hypothetical causal directions and orient the edges by the majority principle. In most experiments with known causal structures, our method provided plausible results and outperformed the conventional constraint-based PC algorithm. 1.

### Citations

2210 | Learning with Kernels
- Schölkopf, Smola
- 2002
(Show Context)
Citation Context ...iance operators to measuring conditional dependences. 2. Measuring Statistical Dependences with Kernels The idea of measuring dependences by reproducing kernel Hilbert spaces (RKHS) (Aronszajn, 1950; =-=Schölkopf & Smola, 2002-=-) is that statistical dependences can always be detected by correlations after data are mapped into an appropriate feature space which is implicitly given by a kernel. 2.1. Cross-Covariance Operator a... |

1342 | Local computations with probabilities on graphical structures and their application to expert systems - Lauritzen, Spiegelhalter - 1988 |

1247 | Causality: models, reasoning, and inference - Pearl |

1135 | Nonlinear component analysis as a kernel eigenvalue problem
- Scholkopf, Smola, et al.
- 1998
(Show Context)
Citation Context ... HY X|Z after finite sampling. It has been shown by Gretton et al. (2005) that �H (n) Y X := 1 � Tr �KY (n − 1) 2 � � KX . is a consistent estimator for HY X. Here � K is the centralized Gram matrix (=-=Schölkopf et al., 1998-=-). Fukumizu et al. (2007) showed that the estimator of the cross-covariance operator guarantees to converge in HS norm at rate n −1/2 . In some analogy to the construction of an estimator for Σ XX|Z g... |

1132 | A Bayesian method for the induction of probabilistic networks from data - Cooper, Herskovits - 1992 |

948 | Learning bayesian networks: The combination of knowledge and statistical data - Heckerman, Geiger, et al. - 1995 |

832 |
Theory of Reproducing kernels
- Aronszajn
(Show Context)
Citation Context ...rm of cross-covariance operators to measuring conditional dependences. 2. Measuring Statistical Dependences with Kernels The idea of measuring dependences by reproducing kernel Hilbert spaces (RKHS) (=-=Aronszajn, 1950-=-; Schölkopf & Smola, 2002) is that statistical dependences can always be detected by correlations after data are mapped into an appropriate feature space which is implicitly given by a kernel. 2.1. Cr... |

682 | Approximating discrete probability distributions with dependence trees - Chow, Liu - 1968 |

339 | Kernel independent component analysis - Bach, Jordan |

198 | Efficient SVM training using low-rank kernel representations - Fine, Scheinberg - 2001 |

172 | Optimal structure identification with greedy search - Chickering |

122 | Dimensionality reduction for supervised learning with reproducing kernel hilbert spaces - Fukumizu, Bach, et al. - 2004 |

102 | Learning bayesian networks from data: An informationtheory based approach - Cheng, Greiner, et al. - 2002 |

100 | Measuring statistical dependence with HilbertSchmidt norms - Gretton, Bousquet, et al. - 2005 |

88 | An algorithm for fast recovery of sparse causal graphs - Spirtes, Glymour, et al. - 1991 |

47 | Joint measures and cross-covariance operators
- Baker
- 1973
(Show Context)
Citation Context ...tions after data are mapped into an appropriate feature space which is implicitly given by a kernel. 2.1. Cross-Covariance Operator and Independence First, we introduce the cross-covariance operator (=-=Baker, 1973-=-) expressing correlations in the feature space and show its relation to independence of variables. Let (X, BX) and (Y, BY) be measurable spaces and (HX,kX),(HY,kY ) be RKHSs of functions on X and Y, w... |

30 | 2009 Kernel dimension reduction in regression - Fukumizu, Bach, et al. |

28 | Computer-based probabilistic network construction. Doctoral dissertation - COOPER, Herskovits, et al. - 1991 |

16 | BNT structure learning package: Documentation and experiments
- Francois, Leray
- 2004
(Show Context)
Citation Context ...ia network (left). Each node has two possible states representing responses “yes” and “no”. The graph on the right side is the structure discoved by KCL+K2. The performance of PC, see e.g. Fig. 2 of (=-=Leray & Francois, 2004-=-), is unsatisfactory in the sense that several edges are completely missing. Repeated experiments with a sample size from 500 to 5000 show that 3-5 from the total 8 edges are always missing. This resu... |

9 | Causation, prediction, and search. Lecture notes in statistics - Spirtes, Glymour, et al. - 1993 |

3 |
Cigarette Smoking and Cancers of the Urinary Tract: Geographic Variations in the United States
- Fraumeni
- 1968
(Show Context)
Citation Context ...s also quite competitive with PC and other Bayesian methods 7 . Most notably, our result can be reliably achieved with datasets of moderate sample size. The next experiment is a real-world dataset 8 (=-=Fraumeni, 1970-=-) containing the numbers of CIGARETTES (hundreds per capita) smoked (sold) in 43 states in the US and the District of Columbia in 1960 together with death rates per 100 thousand population from variou... |

2 | On the incompatibility of faithfulness and monotone DAG faithfulness - Chickering, Meek - 2006 |

1 | A Kernel-based Causal Learning Algorithm Fukumizu - Bach, F, et al. - 2007 |