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Latent 3D Brain MRI Counterfactual

Wei Peng, Tian Xia, Fabio De Sousa Ribeiro, Tomas Bosschieter, Ehsan Adeli, Qingyu Zhao, Ben Glocker, Kilian M. Pohl

TL;DR

This work proposes a two-stage method that constructs a Structural Causal Model (SCM) within the latent space and executes a three-step counterfactual procedure using a closed-form Generalized Linear Model (GLM).

Abstract

The number of samples in structural brain MRI studies is often too small to properly train deep learning models. Generative models show promise in addressing this issue by effectively learning the data distribution and generating high-fidelity MRI. However, they struggle to produce diverse, high-quality data outside the distribution defined by the training data. One way to address the issue is using causal models developed for 3D volume counterfactuals. However, accurately modeling causality in high-dimensional spaces is a challenge so that these models generally generate 3D brain MRIS of lower quality. To address these challenges, we propose a two-stage method that constructs a Structural Causal Model (SCM) within the latent space. In the first stage, we employ a VQ-VAE to learn a compact embedding of the MRI volume. Subsequently, we integrate our causal model into this latent space and execute a three-step counterfactual procedure using a closed-form Generalized Linear Model (GLM). Our experiments conducted on real-world high-resolution MRI data (1mm) demonstrate that our method can generate high-quality 3D MRI counterfactuals.

Latent 3D Brain MRI Counterfactual

TL;DR

This work proposes a two-stage method that constructs a Structural Causal Model (SCM) within the latent space and executes a three-step counterfactual procedure using a closed-form Generalized Linear Model (GLM).

Abstract

The number of samples in structural brain MRI studies is often too small to properly train deep learning models. Generative models show promise in addressing this issue by effectively learning the data distribution and generating high-fidelity MRI. However, they struggle to produce diverse, high-quality data outside the distribution defined by the training data. One way to address the issue is using causal models developed for 3D volume counterfactuals. However, accurately modeling causality in high-dimensional spaces is a challenge so that these models generally generate 3D brain MRIS of lower quality. To address these challenges, we propose a two-stage method that constructs a Structural Causal Model (SCM) within the latent space. In the first stage, we employ a VQ-VAE to learn a compact embedding of the MRI volume. Subsequently, we integrate our causal model into this latent space and execute a three-step counterfactual procedure using a closed-form Generalized Linear Model (GLM). Our experiments conducted on real-world high-resolution MRI data (1mm) demonstrate that our method can generate high-quality 3D MRI counterfactuals.
Paper Structure (12 sections, 4 equations, 3 figures, 1 table)

This paper contains 12 sections, 4 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Deep Structural Causal Models
  4. Latent SCM for 3D Counterfactual MRIs
  5. Computing latent feature $\mathbf{z}$.
  6. Estimate latent counterfactual $\mathbf{\widehat{z}}$ and $\mathbf{\widehat{x}}$.
  7. Experiments
  8. Counterfactual Generation
  9. Counterfactual Evaluation
  10. Discussion
  11. Conclusion
  12. Acknowledgement

Figures (3)

  • Figure 1: Architecture of the LSCM for image: Stage I (black box) consists of a VQ-VAE to encode the real 3D MRI to a quantized vector representation. Based on this, in stage II (blue boxes), a Latent SCM is constructed. The three-step procedure of counterfactual inference is achieved by a efficient GLM.
  • Figure 2: Counterfactual cases. Left: the counterfactual, the differences with original input, and the uncertainty for each intervention. Right: The assumed causal graph is based on sullivan2018role. Variables in the graph are: age $(a)$, diagnosis $(d)$, Parietal $(p)$, Frontal $(f)$, Insula $(i)$, and latent features of MRI $(\mathbf{z})$.
  • Figure 3: Show cases. 2 views of real MRI vs synthetic MRIs generated by 4 models. Our model can produce visually similar MRI to others but we can do counterfactual generation.