Learning via Hilbert Space Embedding of Distributions

By Yasemin Altun, Karsten M. Borgwardt, Tim Dwyer, P. Eades, Kenji Fukumizu, E. Gordon, Arthur Gretton, Seok-Hee Hong, Bernhard Sch ölkopf, Alex Smola and 10 more. 2007

64 citations recorded by the source corpus.

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “Such a condition, however, is often impractically strong: as noted in Song et al. (2009) and”
Computing functions of random variables via reproducing kernel Hilbert space representations (2015, neutral): “One can show that μ [ ˆ p m ] converges at rate m − 1 / 2 [cf. Smola et al. (2007), (Song 2008, Theorem 27), and Lopez-Paz et al. (2015)]: Independent of the requirement of injectivity, μ can be used to compute expectations of arbitrary functions f living in the RKHS, using the identity which…”
Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithm (2019, background): “Empirical measures converge in MMD metric to their target distribution [46].”
From Dependence to Causation (2016, methodology): “The statement (Song, 2008, Theorem 27) assumed f ∈ [0, 1], but we let these functions to take negative values.”
Transfer Learning via Dimensionality Reduction (2008, unknown): “To do this, we first recall the following property of universal kernels (Song 2007):”
Feature-based transfer learning with real-world applications (2010, background): “Note that in practice, the corresponding kernel may not need to be universal [173].”
Towards a Learning Theory of Cause-Effect Inference (2015, methodology): “Using the well known dual relation between the norm in RKHS and sup-norm of empirical process which can be found in Theorem 28 of (Song, 2008) we can write: ‖µk(P )− µk(PS)‖Hk = sup ‖f‖Hk≤1 ( E z∼P [f(z)]− 1 n n∑ i=1 f(zi) ) .”