Learning in Hilbert vs. Banach Spaces: A Measure Embedding Viewpoint

NeurIPS 2011 Kenji FukumizuGert R. LanckrietBharath K. Sriperumbudur

The goal of this paper is to investigate the advantages and disadvantages of learning in Banach spaces over Hilbert spaces. While many works have been carried out in generalizing Hilbert methods to Banach spaces, in this paper, we consider the simple problem of learning a Parzen window classifier in a reproducing kernel Banach space (RKBS)---which is closely related to the notion of embedding probability measures into an RKBS---in order to carefully understand its pros and cons over the Hilbert space classifier... (read more)

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