View PDF HTML (experimental)

Abstract:In latent variables models, two important goals are denoising and deconvolution: denoising aims to estimate the latent variables, whereas deconvolution aims to estimate the distribution of the latent variables. As has been recognized in the literature over the last century, these two goals are fundamentally in tension, since denoising yields a poor estimate of the distribution of the latent variables due to shrinkage, and deconvolution yields a distribution-valued estimate that carries no unit-specific information. In this paper, we provide a systematic study of denoisers, and empirical Bayes approximations thereof, which attain optimal denoising error subject to the constraint that the distribution of the denoised data matches, in some sense, the distribution of the latent variables. Our insight is that optimal transport allows practitioners to navigate the tension between denoising and deconvolution. More precisely, we propose a modular methodology that combines any suitable unconstrained empirical Bayes denoiser (arising, e.g., via $F$-modeling, $G$-modeling, conjugate-parametric models) with any suitable information about the distribution of the latent variables (e.g., its moments, support, or an approximation of the entire distribution via deconvolution) into a single denoised data set. We prove explicit rates of convergence for our proposed methodologies, and we apply the resulting methods in applications in astronomy, baseball analytics, and marketing.

Submission history

From: Adam Quinn Jaffe [view email]
[v1] Wed, 11 Jun 2025 17:57:17 UTC (539 KB)
[v2] Fri, 27 Jun 2025 23:10:19 UTC (585 KB)
[v3] Wed, 9 Sep 2026 16:04:33 UTC (633 KB)