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Painless Embeddings of Distributions: the Function Space View (Part 1)




This tutorial will give an introduction to the recent understanding and methodology of the kernel method: dealing with higher order statistics by embedding painlessly random variables/probability distributions. In the early days of kernel machines research, the "kernel trick" was considered a useful way of constructing nonlinear algorithms from linear ones. More recently, however, it has become clear that a potentially more far reaching use of kernels is as a linear way of dealing with higher order statistics by embedding distributions in a suitable reproducing kernel Hilbert space (RKHS). Notably, unlike the straightforward expansion of higher order moments or conventional characteristic function approach, the use of kernels or RKHS provides a painless, tractable way of embedding distributions. This line of reasoning leads naturally to the questions: what does it mean to embed a distribution in an RKHS? when is this embedding injective (and thus, when do different distributions have unique mappings)? what implications are there for learning algorithms that make use of these embeddings? This tutorial aims at answering these questions. There are a great variety of applications in machine learning and computer science, which require distribution estimation and/or comparison.

Author(s): Fukumizu, K. and Gretton, A. and Smola, A.
Year: 2008
Month: July
Day: 0

Department(s): Empirical Inference
Bibtex Type: Talk (talk)

Digital: 0
Event Name: 25th International Conference on Machine Learning (ICML 2008)
Event Place: Helsinki, Finland
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF


  title = {Painless Embeddings of Distributions: the Function Space View (Part 1)},
  author = {Fukumizu, K. and Gretton, A. and Smola, A.},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = jul,
  year = {2008},
  month_numeric = {7}