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Tutorial: VAE as an inference paradigm for neuroimaging

C. Vázquez-García, F. J. Martínez-Murcia, F. Segovia Román, Juan M. Górriz Sáez

TL;DR

The paper addresses modeling high-dimensional neuroimaging data using VAEs as an inference paradigm. It presents the theoretical foundations of VAEs, including the encoder/decoder structure and the ELBO objective for approximate inference. It discusses practical challenges in neuroimaging applications—such as convergence, overfitting, and information preservation—and surveys strategies like the reparameterization trick and Info-VAE. It also highlights the interpretability advantages of latent representations for downstream analyses, including cross-modal fusion and longitudinal clinical patterns related to neurodegenerative processes.

Abstract

In this tutorial, we explore Variational Autoencoders (VAEs), an essential framework for unsupervised learning, particularly suited for high-dimensional datasets such as neuroimaging. By integrating deep learning with Bayesian inference, VAEs enable the generation of interpretable latent representations. This tutorial outlines the theoretical foundations of VAEs, addresses practical challenges such as convergence issues and over-fitting, and discusses strategies like the reparameterization trick and hyperparameter optimization. We also highlight key applications of VAEs in neuroimaging, demonstrating their potential to uncover meaningful patterns, including those associated with neurodegenerative processes, and their broader implications for analyzing complex brain data.

Tutorial: VAE as an inference paradigm for neuroimaging

TL;DR

The paper addresses modeling high-dimensional neuroimaging data using VAEs as an inference paradigm. It presents the theoretical foundations of VAEs, including the encoder/decoder structure and the ELBO objective for approximate inference. It discusses practical challenges in neuroimaging applications—such as convergence, overfitting, and information preservation—and surveys strategies like the reparameterization trick and Info-VAE. It also highlights the interpretability advantages of latent representations for downstream analyses, including cross-modal fusion and longitudinal clinical patterns related to neurodegenerative processes.

Abstract

In this tutorial, we explore Variational Autoencoders (VAEs), an essential framework for unsupervised learning, particularly suited for high-dimensional datasets such as neuroimaging. By integrating deep learning with Bayesian inference, VAEs enable the generation of interpretable latent representations. This tutorial outlines the theoretical foundations of VAEs, addresses practical challenges such as convergence issues and over-fitting, and discusses strategies like the reparameterization trick and hyperparameter optimization. We also highlight key applications of VAEs in neuroimaging, demonstrating their potential to uncover meaningful patterns, including those associated with neurodegenerative processes, and their broader implications for analyzing complex brain data.
Paper Structure (8 sections, 22 equations, 2 figures)

This paper contains 8 sections, 22 equations, 2 figures.

Table of Contents

  1. Introduction
  2. An opportunity: latent generative models
  3. The variational autoencoder as a latent generator paradigm
  4. The theory of the Variational Autoencoder
  5. The practical implementation of the Variational Autoencoder and its complications
  6. The gradient problem and the reparameterization trick
  7. The information preference problem and the hyperparameter space
  8. Latent representations as a benchmark for analysis in neuroimaging

Figures (2)

  • Figure 1: Conceptual scheme of the VAE. A neural network codifies the information into a lower dimensional manifold characterized by a probability distribution $p(z|x)$ which can be sampled to analyze the latent data. A neural network is also trained to decode the latent information back to the data space
  • Figure 2: On top: Input volume slices from the neuroimaging database. On bottom: reconstructed images from random subjects using a variational autoencoder using the volumes on top as input. In the figure we see that the reconstruction of each subject is the same. This happens because the model is stuck at the mean local minimum, and thus it is not able to capture the inter-subject variability.