Variational autoencoder for distributional learning via quantile function estimation

Area of Science:

• Machine Learning
• Statistical Modeling
• Data Privacy

Background:

• Gaussian Variational AutoEncoders (VAEs) offer computational efficiency for probability distribution estimation.
• However, Gaussian VAEs struggle with approximating non-smooth densities.
• Accurate distributional learning is crucial for various data analysis tasks.

Purpose of the Study:

• To develop a VAE-based approach for distributional learning that handles both smooth and non-smooth densities.
• To extend VAEs for accurate quantile function estimation.
• To enable privacy-preserving synthetic data generation using VAEs.

Main Methods:

• Utilized the continuous ranked probability score (CRPS) as the reconstruction loss.
• Framed the method as a nonparametric M-estimator for quantile functions.
• Established a theoretical link between the VAE model and quantile estimation.

Main Results:

• The proposed method effectively estimates quantile functions for diverse data densities.
• The reconstruction loss is shown to be a lower bound for an infinite mixture of asymmetric Laplace distributions.
• Synthetic data generation mechanism inherently supports differential privacy.

Conclusions:

• The novel VAE approach overcomes limitations of Gaussian VAEs for non-smooth densities.
• The method provides a robust framework for distributional learning and quantile estimation.
• The approach facilitates adjustable differential privacy for synthetic data generation.