Gaussian process latent variable models (GPLVMs) are a versatile family of unsupervised learning models commonly used for dimensionality reduction. However, common challenges in modeling data with GPLVMs include inadequate kernel flexibility and improper selection of the projection noise, leading to a type of model collapse characterized by vague latent representations that do not reflect the underlying data structure. This paper addresses these issues by, first, theoretically examining the impact of projection variance on model collapse through the lens of a linear GPLVM. Second, we tackle model collapse due to inadequate kernel flexibility by integrating the spectral mixture (SM) kernel and a differentiable random Fourier feature (RFF) kernel approximation, which ensures computational scalability and efficiency through off-the-shelf automatic differentiation tools for learning the kernel hyperparameters, projection variance, and latent representations within the variational inference framework. The proposed GPLVM, named advisedRFLVM, is evaluated across diverse datasets and consistently outperforms various salient competing models, including state-of-the-art variational autoencoders (VAEs) and other GPLVM variants, in terms of informative latent representations and missing data imputation.

翻译：高斯过程隐变量模型（GPLVMs）是一个通用的无监督学习模型族，常用于降维。然而，使用GPLVMs建模数据时常见的挑战包括核函数灵活性不足以及投影噪声选择不当，这会导致一种模型坍塌现象，其特征是产生模糊的隐表示，无法反映底层数据结构。本文通过以下方式解决这些问题：首先，从线性GPLVM的角度理论分析了投影方差对模型坍塌的影响。其次，我们通过集成谱混合（SM）核和可微随机傅里叶特征（RFF）核近似，解决了因核函数灵活性不足导致的模型坍塌问题。该方法通过现成的自动微分工具学习核超参数、投影方差和变分推断框架内的隐表示，确保了计算的可扩展性和效率。所提出的GPLVM模型命名为advisedRFLVM，在多个数据集上进行了评估。在信息丰富的隐表示和缺失数据插补方面，其性能始终优于各种突出的竞争模型，包括最先进的变分自编码器（VAEs）和其他GPLVM变体。