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Approximating L 1-distances between mixture distributions using random projections
| Content Provider | Semantic Scholar |
|---|---|
| Author | Mahalanabis, Satyaki Stefankovic, Daniel |
| Copyright Year | 2008 |
| Abstract | We consider the problem of computing L1-distances between every pair of probability densities from a given family. We point out that the technique of Cauchy random projections [Ind06] in this context turns into stochastic integrals with respect to Cauchy motion. For piecewise-linear densities these integrals can be sampled from if one can sample from the stochastic integral of the function x 7→ (1, x). We give an explicit density function for this stochastic integral and present an efficient (exact) sampling algorithm. As a consequence we obtain an efficient algorithm to approximate the L1-distances with a small relative error. For piecewise-polynomial densities we show how to approximately sample from the distributions resulting from the stochastic integrals. This also results in an efficient algorithm to approximate the L1-distances, although our inability to get exact samples worsens the dependence on the parameters. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.cs.rochester.edu/~stefanko/Publications/cauchy.pdf |
| Alternate Webpage(s) | http://www.cs.rochester.edu/users/faculty/stefanko/Publications/cauchy.pdf |
| Alternate Webpage(s) | http://ftp.cs.rochester.edu/~stefanko/Publications/cauchy.pdf |
| Alternate Webpage(s) | http://ftp.cs.rochester.edu/u/stefanko/Publications/cauchy.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/0804.1170v1.pdf |
| Alternate Webpage(s) | http://www.cs.rochester.edu/u/stefanko/Publications/cauchy.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
