Approximating L1-distances between mixture distributions using random projections

dc.creatorMahalanabis, Satyaki
dc.creatorStefankovic, Daniel
dc.date2008-04-08
dc.date.accessioned2026-07-07T09:30:59Z
dc.date.available2026-07-07T09:30:59Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/0804.1170
dc.identifierhttp://arxiv.org/abs/0804.1170
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158306
dc.subjectData Structures and Algorithms
dc.titleApproximating L1-distances between mixture distributions using random projections
dc.typetext

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