Name
Abstract | ||
|---|---|---|
We consider the problem of computing L1-distances between every pair ofcprobability densities from a given family. We point out that the technique of Cauchy random projections (Indyk'06) 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->(1,x). We give an explicit density function for this stochastic integral and present an efficient 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. |
Year | Venue | Keywords |
|---|---|---|
2009 | ANALCO | piecewise linear,data structure,mixture distribution,relative error |
DocType | Volume | Citations |
Conference | abs/0804.1170 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Satyaki Mahalanabis | 1 | 7 | 2.28 |
| Daniel Stefankovic | 2 | 243 | 28.65 |