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Local transfer learning from one data space to another | | H. N. Mhaskar
; Ryan O'Dowd
; | | Date: |
1 Feb 2023 | | Abstract: | A fundamental problem in manifold learning is to approximate a functional
relationship in a data chosen randomly from a probability distribution
supported on a low dimensional sub-manifold of a high dimensional ambient
Euclidean space. The manifold is essentially defined by the data set itself
and, typically, designed so that the data is dense on the manifold in some
sense. The notion of a data space is an abstraction of a manifold encapsulating
the essential properties that allow for function approximation. The problem of
transfer learning (meta-learning) is to use the learning of a function on one
data set to learn a similar function on a new data set. In terms of function
approximation, this means lifting a function on one data space (the base data
space) to another (the target data space). This viewpoint enables us to connect
some inverse problems in applied mathematics (such as inverse Radon transform)
with transfer learning. In this paper we examine the question of such lifting
when the data is assumed to be known only on a part of the base data space. We
are interested in determining subsets of the target data space on which the
lifting can be defined, and how the local smoothness of the function and its
lifting are related. | | Source: | arXiv, 2302.00160 | | Services: | Forum | Review | PDF | Favorites | |
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