Latent variable models are widely used in social and behavioural sciences, including education, psychology, and political science. With the increasing availability of large and complex datasets, high-dimensional latent variable models have become more common. However, estimating such models via marginal maximum likelihood is computationally challenging because it requires evaluating a large number of high-dimensional integrals. Stochastic optimisation, which combines stochastic approximation and sampling techniques, has been shown to be effective. It iterates between sampling latent variables from their posterior distribution under current parameter estimates and updating the model parameters using an approximate stochastic gradient constructed from the latent variable samples. In this paper, we investigate strategies to improve the performance of stochastic optimisation for high-dimensional latent variable models. The improvement is achieved through two strategies: a Metropolis-adjusted Langevin sampler that uses the gradient of the negative complete-data log-likelihood to sample latent variables efficiently, and a minibatch gradient technique that uses only a subset of observations when sampling latent variables and constructing stochastic gradients. Our simulation studies show that combining these strategies yields the best overall performance among competitors. An application to a personality test with 30 latent dimensions further demonstrates that the proposed algorithm scales effectively to high-dimensional settings.

翻译：潜变量模型广泛应用于社会与行为科学领域，包括教育、心理学和政治学。随着大规模复杂数据集的日益普及，高维潜变量模型变得越来越常见。然而，通过边际最大似然估计这类模型在计算上具有挑战性，因为它需要评估大量高维积分。随机优化结合了随机逼近和采样技术，已被证明是有效的。该方法在当前参数估计下从后验分布中采样潜变量，并利用基于潜变量样本构建的近似随机梯度更新模型参数，进行迭代优化。本文研究了提升高维潜变量模型随机优化性能的策略。改进通过两种策略实现：一是采用Metropolis-adjusted Langevin采样器，利用负完全数据对数似然的梯度高效采样潜变量；二是采用小批量梯度技术，在采样潜变量和构建随机梯度时仅使用观测数据的子集。我们的模拟研究表明，结合这些策略在同类方法中取得了最佳整体性能。在一个包含30个潜维度的个性测试应用中，进一步证明了所提算法能够有效扩展到高维场景。