Minimax optimal density estimation using a shallow generative model with a one-dimensional latent variable

2023/05/11 by Hyeok Kyu Kwon, Kwon, Hyeok Kyu, Minwoo Chae +1
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Markov Chains and Monte Carlo Methods #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2305.06755

openalex publication_date 2023/05/11 · openalex created_date 2023/05/13 · openalex updated_date 2026/07/28

Abstract

A deep generative model yields an implicit estimator for the unknown distribution or density function of the observation. This paper investigates some statistical properties of the implicit density estimator pursued by VAE-type methods from a nonparametric density estimation framework. More specifically, we obtain convergence rates of the VAE-type density estimator under the assumption that the underlying true density function belongs to a locally Hölder class. Remarkably, a near minimax optimal rate with respect to the Hellinger metric can be achieved by the simplest network architecture, a shallow generative model with a one-dimensional latent variable.

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