|
Abstract:
|
We introduce a geometric approach for estimating a probability density function (pdf) given its samples. The procedure involves obtaining an initial estimate of the pdf and then transforming it via a warping function to reach the final estimate. The initial estimate is intended to be computationally fast, albeit suboptimal, but its warping creates a larger, flexible class of density functions, resulting in substantially improved estimation. The warping is accomplished by mapping diffeomorphic functions to the tangent space of a Hilbert sphere, a vector space whose elements can be expressed using an orthogonal basis. This framework is introduced for univariate, unconditional pdf estimation and then extended to conditional pdf estimation. The approach avoids many of the computational pitfalls associated with current methods without losing on estimation performance. In presence of irrelevant predictors, the approach achieves both statistical and computational efficiency. We derive asymptotic convergence rates of the density estimator and demonstrate this approach using synthetic datasets, and a case study to understand association of a toxic metabolite on preterm birth.
|
