Learning Feature–State Dependence with Sparse Variational Mixtures

High-dimensional anomaly detection is often jointly affected by latent multimodality, variable dependence, and heavy-tailed contamination, making a single global distribution inadequate for characterizing the complex probabilistic structure of normal data. Mixture models can represent latent heterogeneous states through multiple local components, but existing methods typically overlook that variables may depend on the latent mixture state to different degrees, leading to parameter redundancy and unstable estimation in high-dimensional, finite-sample settings. To address this issue, we propose the Sparse Variational Student-$t$ Mixture Factor Model (SVStMFM). The method uses Bernoulli structural variables to adaptively learn component-dependent and component-invariant parameters, while a low-rank Student-$t$ factor structure captures both high-dimensional correlations and heavy-tailed behavior. We further develop structured variational Bayesian inference to jointly learn latent states, factor representations, local scales, and variable structures, and construct a locally adaptive anomaly score through a marginal–conditional decomposition of the Student-$t$ distribution. Experiments on the Tennessee Eastman process and real industrial data show that SVStMFM consistently improves anomaly-detection performance while reducing model parameters by 83.1%. These results demonstrate that learning feature–state dependence provides a compact and robust solution for high-dimensional, multimodal, and heavy-tailed data.