The Living Thing / Notebooks :

RKHS distribution embedding

The intersection of RKHS kernel methods and probability metrics; where you use a clever RKHS embedding to measure probability distributions.

A mere placeholder for now.


Gretton, A., Fukumizu, K., Teo, C. H., Song, L., Schölkopf, B., & Smola, A. J.(2008) A Kernel Statistical Test of Independence. In Advances in Neural Information Processing Systems 20: Proceedings of the 2007 Conference. Cambridge, MA: MIT Press
Muandet, K., Fukumizu, K., Sriperumbudur, B., Gretton, A., & Schölkopf, B. (2014) Kernel Mean Shrinkage Estimators. arXiv:1405.5505 [cs, Stat].
Muandet, K., Fukumizu, K., Sriperumbudur, B., & Schölkopf, B. (2016) Kernel Mean Embedding of Distributions: A Review and Beyonds. arXiv:1605.09522 [cs, Stat].
Reid, M. D., & Williamson, R. C.(2009) Generalised Pinsker Inequalities. In arXiv:0906.1244 [cs, math].
Reid, M. D., & Williamson, R. C.(2011) Information, Divergence and Risk for Binary Experiments. Journal of Machine Learning Research, 12(Mar), 731–817.
Schölkopf, B., Muandet, K., Fukumizu, K., & Peters, J. (2015) Computing Functions of Random Variables via Reproducing Kernel Hilbert Space Representations. arXiv:1501.06794 [cs, Stat].
Sejdinovic, D., Sriperumbudur, B., Gretton, A., & Fukumizu, K. (2012) Equivalence of distance-based and RKHS-based statistics in hypothesis testing. The Annals of Statistics, 41(5), 2263–2291. DOI.
Smola, A., Gretton, A., Song, L., & Schölkopf, B. (2007) A Hilbert Space Embedding for Distributions. In M. Hutter, R. A. Servedio, & E. Takimoto (Eds.), Algorithmic Learning Theory (pp. 13–31). Springer Berlin Heidelberg
Song, L., Huang, J., Smola, A., & Fukumizu, K. (2009) Hilbert Space Embeddings of Conditional Distributions with Applications to Dynamical Systems. In Proceedings of the 26th Annual International Conference on Machine Learning (pp. 961–968). New York, NY, USA: ACM DOI.
Sriperumbudur, B. K., Fukumizu, K., Gretton, A., Schölkopf, B., & Lanckriet, G. R. G.(2012) On the empirical estimation of integral probability metrics. Electronic Journal of Statistics, 6, 1550–1599. DOI.
Sriperumbudur, B. K., Gretton, A., Fukumizu, K., Lanckriet, G., & Schölkopf, B. (2008) Injective Hilbert Space Embeddings of Probability Measures. In Proceedings of the 21st Annual Conference on Learning Theory (COLT 2008).
Sriperumbudur, B. K., Gretton, A., Fukumizu, K., Schölkopf, B., & Lanckriet, G. R. G.(2010) Hilbert Space Embeddings and Metrics on Probability Measures. Journal of Machine Learning Research, 11, 1517−1561.
Zhang, K., Peters, J., Janzing, D., & Schölkopf, B. (2012) Kernel-based Conditional Independence Test and Application in Causal Discovery. arXiv:1202.3775 [cs, Stat].
Zhang, Q., Filippi, S., Gretton, A., & Sejdinovic, D. (2016) Large-Scale Kernel Methods for Independence Testing. arXiv:1606.07892 [stat].