Factor-Assisted Density Estimation: When Ambient Dimension Enables Oracle Rates
Abstract
We study density estimation in the high-dimensional factor model, whose fixed-dimensional latent factors have an unknown smooth density. We propose factor-assisted density estimation (FADE), a non-iterative procedure that applies kernel density estimation to spectral estimates of the latent scores. The score proxies are dependent and do not follow the latent density, so standard kernel-density arguments do not apply. A refined rowwise expansion separates error into a conditionally centered Gaussian perturbation and a uniformly controlled remainder. We show that FADE achieves the oracle rate in sufficiently high ambient dimension and prove a minimax lower bound separating ordinary nonparametric difficulty from a Gaussian deconvolution obstruction. Together, the upper and lower bounds establish rate optimality of FADE in specified high-dimensional regimes. We also derive L1 upper and lower bounds for the induced observation density, distinguishing latent-distribution uncertainty from the cost of estimating a growing number of parameters. These results formalize a blessing of ambient dimension: sufficiently many observed coordinates can make a simple spectral reduction statistically lossless even for the nonparametric task of recovering an unobserved low-dimensional density.
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BibTeX
@misc{chakraborty2026factorassisted,
title = {{Factor-Assisted Density Estimation: When Ambient Dimension Enables Oracle Rates}},
author = {Sunrit Chakraborty and David Dunson},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20944},
eprint = {2610.20944},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20944},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Factor-Assisted Density Estimation: When Ambient Dimension Enables Oracle Rates
AU - Sunrit Chakraborty
AU - David Dunson
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20944
UR - https://arxiv.org/abs/2610.20944
AB - We study density estimation in the high-dimensional factor model, whose fixed-dimensional latent factors have an unknown smooth density. We propose factor-assisted density estimation (FADE), a non-iterative procedure that applies kernel density estimation to spectral estimates of the latent scores. The score proxies are dependent and do not follow the latent density, so standard kernel-density arguments do not apply. A refined rowwise expansion separates error into a conditionally centered Gaussian perturbation and a uniformly controlled remainder. We show that FADE achieves the oracle rate in sufficiently high ambient dimension and prove a minimax lower bound separating ordinary nonparametric difficulty from a Gaussian deconvolution obstruction. Together, the upper and lower bounds establish rate optimality of FADE in specified high-dimensional regimes. We also derive L^1 upper and lower bounds for the induced observation density, distinguishing latent-distribution uncertainty from the cost of estimating a growing number of parameters. These results formalize a blessing of ambient dimension: sufficiently many observed coordinates can make a simple spectral reduction statistically lossless even for the nonparametric task of recovering an unobserved low-dimensional density.
ER -