We introduce a two versions of a new sketch for approximately embedding the Gaussian kernel into Euclidean inner product space. These work by truncating infinite expansions of the Gaussian inner product , and carefully invoking the TensorSketch. ] After providing concentration and approximation properties of these sketches, we demonstrate them to approximate the kernel distance between points sets. These sketches yield almost (1+\varepsilon)-relative error, but with a small additive \alpha term. In the first variants the dependence on 1/\alpha is logarithmic , but has a separate exponential dependence on the original dimension d. In the second variant, the dependence on 1/\alpha is still sub-polynomial , but the dependence on d is linear.
We introduce two versions of a new sketch for approximately embedding the Gaussian kernel into Euclidean inner product space. These work by truncating infinite expansions of the Gaussian kernel , and carefully invoking the RecursiveTensorSketch Ahle et al. SODA 2020]. After providing concentration and approximation properties of these sketches, we use them to approximate the kernel distance between points sets. These sketches yield almost (1+\varepsilon)-relative error, but with a small additive \alpha term. In the first variants the dependence on 1/\alpha is poly-logarithmic , but has higher degree of polynomial dependence on the original dimension d. In the second variant, the dependence on 1/\alpha is still poly-logarithmic , but the dependence on d is linear.
D
a
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inner product
kernel
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TensorSketch.
RecursiveTensorSketch
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Ahle et al. SODA 2020
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.
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demonstrate
use
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logarithmic
poly-logarithmic
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a separate exponential
higher degree of polynomial
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sub-polynomial
poly-logarithmic