Modelling longitudinal data is an important yet challenging task. These datasets can be high-dimensional, contain non-linear effects and time-varying covariates. Gaussian process (GP) prior-based variational autoencoders (VAEs) have emerged as a promising approach due to their ability to model time-series data. However, they are costly to train and struggle to fully exploit the rich covariates characteristic of longitudinal data, making them difficult for practitioners to use effectively. In this work, we leverage linear mixed models (LMMs) and amortized variational inference to provide conditional priors for VAEs, and propose LMM-VAE, a scalable, interpretable and identifiable model. We highlight theoretical connections between it and GP-based techniques, providing a unified framework for this class of methods. Our proposal performs competitively compared to existing approaches across simulated and real-world datasets.

本研究解决了高维纵向数据建模中的挑战，特别是非线性效应和时间变化协变量的问题。通过结合线性混合模型和变分推断，提出了可扩展的LMM-VAE模型，提供了一种新的条件先验。该方法在模拟和真实数据集上的表现优于现有技术，具有重要的应用潜力。

高维纵向数据的潜在混合效应模型