Nonparametric Conditional Density Estimation in a High-Dimensional Regression Setting
By Rafael Izbicki, Ann B. Lee. 2016
73 citations recorded by the source corpus.
In some applications (e.g., in cosmology and economics), the regression is not adequate to represent the association between a predictor x and a response Z because of multi-modality and asymmetry of f(z|x); using the full density instead of a single-point estimate can then lead to less bias in subsequent analysis. As of now, there are no effective ways of estimating f(z|x) when x represents high-dimensional, complex data. In this article, we propose a new nonparametric estimator of f(z|x) that adapts to sparse (low-dimensional) structure in x. By directly expanding f(z|x) in the eigenfunctions of a kernel-based 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. Supplementary materials for this article are available online.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/7084fbc8252bc7e5abbd74c5bfe78cce749cf839
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In Artificial Intelligence
In Statistics and Probability
Citations in the corpus
- Converting High-Dimensional Regression to High-Dimensional Conditional Density Estimation (2017, methodology): “The latter result is consistent with our previous findings that spectral series adapt to the intrinsic dimension of the data [29, 28, 36].”