Nonparametric Conditional Density Estimation in a HighDimensional Regression Setting
Abstract
In some applications (e.g., in cosmology and economics), the regression E[Zx] is not adequate to represent the association between a predictor x and a response Z because of multimodality and asymmetry of f(zx); using the full density instead of a singlepoint estimate can then lead to less bias in subsequent analysis. As of now, there are no effective ways of estimating f(zx) when x represents highdimensional, complex data. In this paper, we propose a new nonparametric estimator of f(zx) that adapts to sparse (lowdimensional) structure in x. By directly expanding f(zx) in the eigenfunctions of a kernelbased operator, we avoid tensor products in high dimensions as well as ratios of estimated densities. Our basis functions are orthogonal with respect to the underlying data distribution, allowing fast implementation and tuning of parameters. We derive rates of convergence and show that the method adapts to the intrinsic dimension of the data. We also demonstrate the effectiveness of the series method on images, spectra, and an application to photometric redshift estimation of galaxies.
 Publication:

arXiv eprints
 Pub Date:
 April 2016
 DOI:
 10.48550/arXiv.1604.00540
 arXiv:
 arXiv:1604.00540
 Bibcode:
 2016arXiv160400540I
 Keywords:

 Statistics  Methodology
 EPrint:
 doi:10.1080/10618600.2015.1094393