On the influence of the kernel on the consistency of support vector machines
The Journal of Machine Learning Research
Kernel independent component analysis
The Journal of Machine Learning Research
Dimensionality Reduction for Supervised Learning with Reproducing Kernel Hilbert Spaces
The Journal of Machine Learning Research
Kernel Methods for Measuring Independence
The Journal of Machine Learning Research
Statistical Consistency of Kernel Canonical Correlation Analysis
The Journal of Machine Learning Research
Nonparametric Independence Tests: Space Partitioning and Kernel Approaches
ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
Measuring statistical dependence with hilbert-schmidt norms
ALT'05 Proceedings of the 16th international conference on Algorithmic Learning Theory
On the asymptotic properties of a nonparametric L1-test statistic of homogeneity
IEEE Transactions on Information Theory
DirectLiNGAM: A Direct Method for Learning a Linear Non-Gaussian Structural Equation Model
The Journal of Machine Learning Research
Hi-index | 0.00 |
Three simple and explicit procedures for testing the independence of two multi-dimensional random variables are described. Two of the associated test statistics (L1, log-likelihood) are defined when the empirical distribution of the variables is restricted to finite partitions. A third test statistic is defined as a kernel-based independence measure. Two kinds of tests are provided. Distribution-free strong consistent tests are derived on the basis of large deviation bounds on the test statistics: these tests make almost surely no Type I or Type II error after a random sample size. Asymptotically α-level tests are obtained from the limiting distribution of the test statistics. For the latter tests, the Type I error converges to a fixed non-zero value α, and the Type II error drops to zero, for increasing sample size. All tests reject the null hypothesis of independence if the test statistics become large. The performance of the tests is evaluated experimentally on benchmark data.