Reproducing kernel Banach spaces for machine learning

By Haizhang Zhang, Yuesheng Xu, Jun Zhang. 2009

205 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Kenji Fukumizu
2. Bernhard Schölkopf
3. Bharath K. Sriperumbudur
4. Gert R. G. Lanckriet
5. Haizhang Zhang
6. Jun Zhang
7. Krikamol Muandet
8. Clint Scovel

In Computer Vision and Pattern Recognition

1. Bharath K. Sriperumbudur
2. Kenji Fukumizu
3. Krikamol Muandet
4. Bernhard Schölkopf
5. Gert R. G. Lanckriet
6. Jun Zhang
7. Haizhang Zhang
8. Clint Scovel

In Statistical and Nonlinear Physics

1. Kenji Fukumizu
2. Bharath K. Sriperumbudur
3. Bernhard Schölkopf
4. Krikamol Muandet
5. Gert R. G. Lanckriet
6. Jun Zhang
7. Haizhang Zhang
8. Arthur Gretton

Citations in the corpus

• Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “data, Zhang et al. (2008) proposes a Structured-HSIC where P satisfies the conditional independence spec-”
• Learning in Hilbert vs. Banach Spaces: A Measure Embedding Viewpoint (2011, methodology): “structure does not allow closed form representation s in terms of the kernel K (also see [24] where regularization algorithms derived in RKBS are not sol vable unlike in an RKHS), and therefore could limit its practical viability.”
• Frames, Riesz bases, and sampling expansions in Banach spaces via semi-inner products☆ (2011, methodology): “With the aid of semi-inner products, Der and Lee [9] studied hard margin classification in Banach spaces, and we established the theory of reproducing kernel Banach spaces (RKBS) in a recent work [45].”
• Separability of reproducing kernel spaces (2015, background): “In their generalization to reproducing kernel Banach spaces (RKBS), Zhang, Xu, and Zhang [40] stipulate that a RKBS on a set X is a reflexive Banach space of real-valued functions on X whose dual space is isometric with a Banach space of functions on X such that pointwise evaluation is continuous fo”