Latent Variable Models

Latent variable models represent observed data as arising from unobserved factors, classes, states, or embeddings, helping explain structure when measurements are incomplete, noisy, or high-dimensional. Common approaches include factor analysis and matrix factorization, finite mixtures and topic models, probabilistic graphical models, and deep generative models such as variational autoencoders; they are fit with EM, Bayesian or variational inference, and spectral or gradient-based methods. Applications range from clustering, recommendation, and multimodal integration to causal discovery, time-series forecasting, and personalized clinical prediction. A central challenge is identifiability: different hidden representations can explain the same observations, so work seeks assumptions and diagnostics that make latent structure recoverable while balancing flexibility, interpretability, computation, and calibrated uncertainty.