Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Connections and Equivalences between the Nystr\"om Method and Sparse
  Variational Gaussian Processes   We investigate the connections between sparse approximation methods for
making kernel methods and Gaussian processes (GPs) scalable to massive data,
focusing on the Nystr\"om method and the Sparse Variational Gaussian Processes
(SVGP). While sparse approximation methods for GPs and kernel methods share
some algebraic similarities, the literature lacks a deep understanding of how
and why they are related. This is a possible obstacle for the communications
between the GP and kernel communities, making it difficult to transfer results
from one side to the other. Our motivation is to remove this possible obstacle,
by clarifying the connections between the sparse approximations for GPs and
kernel methods. In this work, we study the two popular approaches, the
Nystr\"om and SVGP approximations, in the context of a regression problem, and
establish various connections and equivalences between them. In particular, we
provide an RKHS interpretation of the SVGP approximation, and show that the
Evidence Lower Bound of the SVGP contains the objective function of the
Nystr\"om approximation, revealing the origin of the algebraic equivalence
between the two approaches. We also study recently established convergence
results for the SVGP and how they are related to the approximation quality of
the Nystr\"om method.

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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: eess
6
The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: econ