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The notion of interpolation and extrapolation is fundamental in various fields from deep learning to function approximation.
On the inductive bias of neural tangent kernels
Bietti, A. and Mairal, J. (2019) · 1905
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Interpolation und extrapolation von stationaren zufalligen folgen
Kolmogoroff, A. (1941) · 1941
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Extrapolation, interpolation, and smoothing of stationary time series, with engineering applications
Wiener, N. (1949) · 1949
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Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis
Kruskal, J. B. (1964) · 1964
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Representation and analysis of signals part xxi. the intrinsic dimensionality of signal collections
Bennett, R. S. (1965) · 1965
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Extensions of lipschitz mappings into a hilbert space 26
Johnson, W. B. and Lindenstrauss, J. (1984) · 1984
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On a conjecture of re miles about the convex hull of random points
Buchta, C. (1986) · 1986
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On the shape of the convex hull of random points
Bárány, I. and Füredi, Z. (1988) · 1988
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Probability thatn random points are in convex position
Valtr, P. (1995) · 1995
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The probability that n random points in a triangle are in convex position
Valtr, P. (1996) · 1996
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Nonlinear approximation
DeVore, R. A. (1998) · 1998
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Nonlinear dimensionality reduction by locally linear embedding
Roweis, S. T. and Saul, L. K. (2000) · 2000
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The isomap algorithm and topological stability
Balasubramanian, M., Schwartz, E. L., Tenenbaum, J. B., de Silva, V., and Langford, J. C. (2002) · 2002
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Laplacian eigenmaps for dimensionality reduction and data representation
Belkin, M. and Niyogi, P. (2003) · 2003
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An elementary proof of a theorem of johnson and lindenstrauss
Dasgupta, S. and Gupta, A. (2003) · 2003
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Pattern recognition
Bishop, C. M. (2006) · 2006
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Mlle: Modified locally linear embedding using multiple weights
Zhang, Z. and Wang, J. (2007) · 2007
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Visualizing data using t-sne
Van der Maaten, L. and Hinton, G. (2008) · 2008
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Random convex hulls and extreme value statistics
Majumdar, S. N., Comtet, A., and Randon-Furling, J. (2010) · 2010
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To understand deep learning we need to understand kernel learning
Belkin, M., Ma, S., and Mandal, S. (2018) · 2018
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The neural tangent kernel in high dimensions: Triple descent and a multi-scale theory of generalization
Adlam, B. and Pennington, J. (2020) · 2020
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Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
Donoho, D. L. and Grimes, C. (2003) · 2003
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Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Spielman, D. A. and Teng, S.-H. (2004) · 2004
Cited alongside, same era.
Principal manifolds and nonlinear dimensionality reduction via tangent space alignment
Zhang, Z. and Zha, H. (2004) · 2004
Cited alongside, same era.
Absorption probabilities for gaussian polytopes and regular spherical simplices
Kabluchko, Z. and Zaporozhets, D. (2020) · 2020
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When does gradient descent with logistic loss find interpolating two-layer networks?
Chatterji, N. S., Long, P. M., and Bartlett, P. L. (2021) · 2021
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