Functional Mixed Model using Autoencoder Representations

Music City Center 

Latent feature representations (e.g., PCA) are widely used for dimensionality reduction and statistical modeling of high-dimensional functional and multivariate data. Traditional functional regression models typically rely on linear basis expansions (e.g., PCA, B-splines, wavelets), but modern non-linear machine learning methods (e.g., autoencoders, GANs) offer more flexible alternatives.
In this work, we present two main contributions:
1. We propose CLaRe (Compact near-Lossless Latent Representations), a flexible evaluation framework for selecting among linear and non-linear latent feature representations in high-dimensional functional and multivariate data. CLaRe provides a principled set of criteria to assess methods based on their dimensionality reduction (compactness) and the information they preserve (near-losslessness).
2. We demonstrate how, when non-linear methods such as autoencoders are selected, they can be embedded within the Functional Mixed Model (FMM) framework of Morris and Carroll (2006). This integration enables flexible modeling of complex functional structures while retaining the interpretability and inference capabilities of FMMs. We illustrate the utility of this approach on multidimensional functional imaging data.