Welcome to RKHS-Seminars! - Tentative Content

The purpose of this seminar series is an introduction to the theory and application of RKHS in connection with machine learning.

The tentative outline of the (learning part of the) seminars is as follows.

• Introduction and Motivation: kernels, kernel principle component analysis, kernel ridge regression (See RKHS in Machine Learning and (Ghojogh et al., 2023))
• Finite Dimensional RKHSs (See (Manton & Amblard, 2015))
• Prerequisites: metric, normed, and unitary spaces; Cauchy sequences and Completion, Banach and Hilbert spaces, bounded linear operators and the Riesz Theorem (See Lecture Notes of Aydın Aytuna)
• Finite and Infinite Dimensional RKHSs (See (Manton & Amblard, 2015) and (Okutmuştur, 2020))
• Applications to Stochastic Processes (See (Manton & Amblard, 2015))

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1. Ghojogh, B., Crowley, M., Karray, F., & Ghodsi, A. (2023). Elements of Dimensionality Reduction and Manifold Learning. Springer International Publishing. https://doi.org/10.1007/978-3-031-10602-6

   @book{Ghojogh23,
     title = {Elements of Dimensionality Reduction and Manifold Learning},
     author = {Ghojogh, B. and Crowley, M. and Karray, F. and Ghodsi, A.},
     year = {2023},
     doi = {10.1007/978-3-031-10602-6},
     publisher = {Springer International Publishing}
   }
   

2. Manton, J. H., & Amblard, P.-O. (2015). A Primer on Reproducing Kernel Hilbert Spaces. https://doi.org/10.1561/2000000050

   @misc{Manton15,
     title = {A Primer on Reproducing Kernel {H}ilbert Spaces},
     author = {Manton, Jonathan H. and Amblard, Pierre-Olivier},
     year = {2015},
     eprint = {1408.0952},
     archiveprefix = {arXiv},
     primaryclass = {math.HO},
     doi = {10.1561/2000000050}
   }
   

3. Okutmuştur, B. (2020). A Survey on Hilbert Spaces and Reproducing Kernels. In K. Shah & B. Okutmuştur (Eds.), Functional Calculus. IntechOpen. https://doi.org/10.5772/intechopen.91479

   @incollection{Baver20,
     author = {Okutmu\c{s}tur, Baver},
     title = {A Survey on {H}ilbert Spaces and Reproducing Kernels},
     booktitle = {Functional Calculus},
     publisher = {IntechOpen},
     address = {Rijeka},
     year = {2020},
     editor = {Shah, Kamal and Okutmu\c{s}tur, Baver},
     chapter = {5},
     doi = {10.5772/intechopen.91479}
   }