Variational Optimization for Scalable Unsupervised and Semi-supervised Probabilistic Learning

As data availability increases while labels remain scarce, semi-supervised and unsupervised learning have become central to modern machine learning. Yet, scaling these methods to large, high-dimensional datasets remains computationally challenging. This work develops and investigates highly efficient algorithms for optimizing probabilistic generative models with discrete latent variables. Novel truncated variational posterior approximations are derived and combined with mixtures of factor analyzers (MFAs). The proposed approach exhibits sublinear scaling w.r.t. data and model size and enables training of Gaussian mixture models and MFAs at previously not reported scales on a single compute node. Furthermore, this work combines the variational optimization techniques with graph-based semi-supervised learning and investigates the application of variationally optimized generative models to the task of blind zero-shot denoising of macroscopic and microscopy images.