An explainable framework for the relationship between dementia and glucose metabolism patterns

High-dimensional neuroimaging data presents challenges for assessing neurodegenerative diseases due to complex non-linear relationships. Variational Autoencoders (VAEs) can encode scans into lower-dimensional latent spaces capturing disease-relevant features. We propose a semi-supervised VAE framework with a flexible similarity regularization term that aligns selected latent variables with clinical or biomarker measures of dementia progression. This allows adapting the similarity metric and supervised variables to specific goals or available data. We demonstrate the approach using PET scans from the Alzheimer's Disease Neuroimaging Initiative (ADNI), guiding the first latent dimension to align with a cognitive score. Using this supervised latent variable, we generate average reconstructions across levels of cognitive impairment. Voxel-wise GLM analysis reveals reduced metabolism in key regions, mainly the hippocampus, and within major Resting State Networks, particularly the Default Mode and Central Executive Networks. The remaining latent variables encode affine transformations and intensity variations, capturing confounds such as inter-subject variability and site effects. Our framework effectively extracts disease-related patterns aligned with established Alzheimer's biomarkers, offering an interpretable and adaptable tool for studying neurodegenerative progression.

Statistical Agnostic Regression: a machine learning method to validate regression models

Regression analysis is a central topic in statistical modeling, aiming to estimate the relationships between a dependent variable, commonly referred to as the response variable, and one or more independent variables, i.e., explanatory variables. Linear regression is by far the most popular method for performing this task in several fields of research, such as prediction, forecasting, or causal inference. Beyond various classical methods to solve linear regression problems, such as Ordinary Least Squares, Ridge, or Lasso regressions - which are often the foundation for more advanced machine learning (ML) techniques - the latter have been successfully applied in this scenario without a formal definition of statistical significance. At most, permutation or classical analyses based on empirical measures (e.g., residuals or accuracy) have been conducted to reflect the greater ability of ML estimations for detection. In this paper, we introduce a method, named Statistical Agnostic Regression (SAR), for evaluating the statistical significance of an ML-based linear regression based on concentration inequalities of the actual risk using the analysis of the worst case. To achieve this goal, similar to the classification problem, we define a threshold to establish that there is sufficient evidence with a probability of at least 1-eta to conclude that there is a linear relationship in the population between the explanatory (feature) and the response (label) variables. Simulations in only two dimensions demonstrate the ability of the proposed agnostic test to provide a similar analysis of variance given by the classical $F$ test for the slope parameter.

Revealing Patterns of Symptomatology in Parkinson's Disease: A Latent Space Analysis with 3D Convolutional Autoencoders

This work proposes the use of 3D convolutional variational autoencoders (CVAEs) to trace the changes and symptomatology produced by neurodegeneration in Parkinson's disease (PD). In this work, we present a novel approach to detect and quantify changes in dopamine transporter (DaT) concentration and its spatial patterns using 3D CVAEs on Ioflupane (FPCIT) imaging. Our approach leverages the power of deep learning to learn a low-dimensional representation of the brain imaging data, which then is linked to different symptom categories using regression algorithms. We demonstrate the effectiveness of our approach on a dataset of PD patients and healthy controls, and show that general symptomatology (UPDRS) is linked to a d-dimensional decomposition via the CVAE with R2>0.25. Our work shows the potential of representation learning not only in early diagnosis but in understanding neurodegeneration processes and symptomatology.