Unsupervised state-learning for multivariate time series data: a survey and practical guidelines

Abstract Unsupervised state-learning aims to infer latent variables or representations from multivariate time series that can serve as predictive summaries of a system evolution. Depending on the modelling assumptions, these summaries may appear as discrete regimes, posterior belief states, continuous latent trajectories or learnt embeddings that are subsequently interpreted or regularised as states. State-learning enables segmentation, anomaly detection, predictive maintenance and clinical monitoring, but the literature is fragmented across probabilistic regime-switching models, clustering and change-point methods, as well as modern representation learning. This survey unifies these strands and provides a synthesis aimed at practical method selection. We formalise the notion of state and introduce a taxonomy that makes modelling choices explicit along key dimensions: discrete versus continuous states, observable versus latent representations, output formats (hard assignments, posteriors, embeddings) and fixed versus adaptive state cardinality. We then review three major methodological families: probabilistic models, clustering/segmentation approaches, as well as self-supervised or generative representation learning. We highlight core assumptions, computational trade-offs and failure modes under missingness, irregular sampling, non-stationarity, as well as scarce evaluation labels. Building on this synthesis, we present a method-selection framework and implementation-oriented workflows that summarise recurring patterns in the literature and our practical reading of them, covering preprocessing, model fitting, diagnostics and uncertainty handling. Furthermore, we propose an evaluation and reporting protocol tailored to state-learning, emphasising leakage-free temporal splits, temporal coherence, interpretability, complexity control and uncertainty calibration. Finally, we summarise widely used benchmark testbeds that provide evaluation-only labels.