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Linear-time Learning on Distributions with Approximate Kernel Embeddings | | Dougal J. Sutherland
; Junier B. Oliva
; Barnabás Póczos
; Jeff Schneider
; | | Date: |
25 Sep 2015 | | Abstract: | Many interesting machine learning problems are best posed by considering
instances that are distributions, or sample sets drawn from distributions.
Previous work devoted to machine learning tasks with distributional inputs has
done so through pairwise kernel evaluations between pdfs (or sample sets).
While such an approach is fine for smaller datasets, the computation of an $N
imes N$ Gram matrix is prohibitive in large datasets. Recent scalable
estimators that work over pdfs have done so only with kernels that use
Euclidean metrics, like the $L_2$ distance. However, there are a myriad of
other useful metrics available, such as total variation, Hellinger distance,
and the Jensen-Shannon divergence. This work develops the first random features
for pdfs whose dot product approximates kernels using these non-Euclidean
metrics, allowing estimators using such kernels to scale to large datasets by
working in a primal space, without computing large Gram matrices. We provide an
analysis of the approximation error in using our proposed random features and
show empirically the quality of our approximation both in estimating a Gram
matrix and in solving learning tasks in real-world and synthetic data. | | Source: | arXiv, 1509.7553 | | Services: | Forum | Review | PDF | Favorites | |
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