π VAE: a stochastic process prior for Bayesian deep learning with MCMC.

Area of Science:

• Machine Learning
• Stochastic Processes
• Bayesian Inference

Background:

• Stochastic processes model complex data but face inference challenges with large datasets.
• Efficiently handling high-dimensional input spaces in stochastic processes is difficult.

Purpose of the Study:

• Introduce a novel variational autoencoder (VAE) named prior encoding variational autoencoder (π VAE).
• Develop a continuous stochastic process for efficient function class embedding and Bayesian inference.

Main Methods:

• Utilize a trainable feature mapping combined with a VAE to create the π VAE.
• Apply π VAE for learning low-dimensional function embeddings and properties like integrals.
• Demonstrate Bayesian inference for stochastic processes within probabilistic programming languages.

Main Results:

• π VAE accurately learns expressive function classes, including Gaussian processes.
• Achieved state-of-the-art performance in spatial interpolation regarding accuracy and computational efficiency.
• Showcased scalable Bayesian inference for stochastic processes.

Conclusions:

• π VAE offers an efficient and scalable solution for inference in stochastic processes.
• The framework enables accurate learning of function properties and Bayesian inference.
• π VAE integrates seamlessly with probabilistic programming languages like Stan.