Sublinear time algorithms for earth mover's distance
We study the problem of estimating the Earth Mover’s Distance (EMD) between probability distributions when given access only to samples of the distributions. We give closeness testers and additive-error estimators over domains in [0, 1][superscript d], with sample complexities independent of domai...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Springer New York
2012
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| Online Access: | http://hdl.handle.net/1721.1/71576 https://orcid.org/0000-0002-4353-7639 |
| Summary: | We study the problem of estimating the Earth Mover’s Distance (EMD) between probability distributions
when given access only to samples of the distributions. We give closeness testers and additive-error
estimators over domains in [0, 1][superscript d], with sample complexities independent of domain size – permitting
the testability even of continuous distributions over infinite domains. Instead, our algorithms depend on
other parameters, such as the diameter of the domain space, which may be significantly smaller. We also
prove lower bounds showing the dependencies on these parameters to be essentially optimal. Additionally,
we consider whether natural classes of distributions exist for which there are algorithms with better
dependence on the dimension, and show that for highly clusterable data, this is indeed the case. Lastly,
we consider a variant of the EMD, defined over tree metrics instead of the usual l 1 metric, and give tight
upper and lower bounds. |
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