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A Lightweight Generative Model for Interpretable Subject-level Prediction

Chiara Mauri, Stefano Cerri, Oula Puonti, Mark Mühlau, Koen Van Leemput

TL;DR

A simple technique for single-subject prediction that augments the generative models used in classical human brain mapping techniques, in which the underlying cause-effect relations can be encoded, with a multivariate noise model that captures dominant spatial correlations.

Abstract

Recent years have seen a growing interest in methods for predicting an unknown variable of interest, such as a subject's diagnosis, from medical images depicting its anatomical-functional effects. Methods based on discriminative modeling excel at making accurate predictions, but are challenged in their ability to explain their decisions in anatomically meaningful terms. In this paper, we propose a simple technique for single-subject prediction that is inherently interpretable. It augments the generative models used in classical human brain mapping techniques, in which the underlying cause-effect relations can be encoded, with a multivariate noise model that captures dominant spatial correlations. Experiments demonstrate that the resulting model can be efficiently inverted to make accurate subject-level predictions, while at the same time offering intuitive visual explanations of its inner workings. The method is easy to use: training is fast for typical training set sizes, and only a single hyperparameter needs to be set by the user. Our code is available at https://github.com/chiara-mauri/Interpretable-subject-level-prediction.

A Lightweight Generative Model for Interpretable Subject-level Prediction

TL;DR

A simple technique for single-subject prediction that augments the generative models used in classical human brain mapping techniques, in which the underlying cause-effect relations can be encoded, with a multivariate noise model that captures dominant spatial correlations.

Abstract

Recent years have seen a growing interest in methods for predicting an unknown variable of interest, such as a subject's diagnosis, from medical images depicting its anatomical-functional effects. Methods based on discriminative modeling excel at making accurate predictions, but are challenged in their ability to explain their decisions in anatomically meaningful terms. In this paper, we propose a simple technique for single-subject prediction that is inherently interpretable. It augments the generative models used in classical human brain mapping techniques, in which the underlying cause-effect relations can be encoded, with a multivariate noise model that captures dominant spatial correlations. Experiments demonstrate that the resulting model can be efficiently inverted to make accurate subject-level predictions, while at the same time offering intuitive visual explanations of its inner workings. The method is easy to use: training is fast for typical training set sizes, and only a single hyperparameter needs to be set by the user. Our code is available at https://github.com/chiara-mauri/Interpretable-subject-level-prediction.
Paper Structure (24 sections, 41 equations, 18 figures, 2 tables)

This paper contains 24 sections, 41 equations, 18 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Context and related work
  3. Problem statement
  4. Scenarios not considered
  5. Related work
  6. Basic Linear Version
  7. Generative model
  8. Making predictions
  9. Model training
  10. Practical implementation
  11. Experiments on Age and Gender Prediction
  12. Experimental set-up
  13. Implementation of the benchmark methods
  14. Prediction performance and training times
  15. Bias-variance trade-off
  16. ...and 9 more sections

Figures (18)

  • Figure 1: The causal diagrams of the models considered in this paper are illustrated in the top row: (a) basic model encoding how the unknown variable of interest $x$ generates an acquired brain scan $\mathbf{t}$; (b) the model with additional known covariates $\mathbf{y}$ included; and (c) the model where $\mathbf{y}$ are known confounders. The arrows indicate causal relationships, and variables in empty vs. shaded circles are unknown vs. observed, respectively. The bottom row illustrates two cases that are not considered in this paper: (d) a model with confounders that are not observed; and (e) a decoding model where the direction of causality is reversed.
  • Figure 2: Example of the forward model \ref{['eq:decomposition']}, applied to modeling the effect of age on brain morphology. Here $x$ denotes the difference between the age of the subject and the average age in a training set.
  • Figure 3: Illustration of how a subject's age is estimated by inverting the model shown in Fig. \ref{['fig:generativeModelWithRealImages']}.
  • Figure 4: The estimated template $\mathbf{m}$ (the average image in the training set) when the model is trained on $N=2,600$ subjects in an age prediction task.
  • Figure 5: Top: the generative map $\mathbf{w}_G$ -- expressing the effect of aging -- estimated from $N=2,600$ subjects, overlaid on the template of Fig. \ref{['fig:m']}. Voxels with zero weight are transparent. Bottom: the corresponding discriminative map $\mathbf{w}_D$ that is used for making age predictions. The discrepancy between these two maps is analyzed in Sec. \ref{['sec:interpretability']}.
  • ...and 13 more figures