Bayesian Nonparametric Identification of Frequency-Selective Neural Oscillatory States

Identifying neural oscillations is essential for linking fast brain dynamics to underlying cognitive processes. However, this is challenging because oscillatory events can be brief, embedded in 1/f-like background activity, and may comprise an unknown number of spectrally distinct states. Conventional approaches often apply narrowband band-pass filters to one or a few predefined frequency bands and then use amplitude thresholding to identify oscillatory events, but detection outcomes can be highly sensitive to these choices. Although recent unsupervised alternatives based on hidden Markov models (HMMs) address these limitations, they still require the number of states to be specified in advance and can underfit or overfit when this number is misspecified. We propose a Bayesian nonparametric method that identifies distinct oscillatory states while inferring an appropriate number of states directly from the data. This method combines time-delay embedding (TDE) with the Dirichlet-process Gaussian mixture model (DP-GMM). TDE augments the signal with time-shifted copies, enabling the DP-GMM to capture frequency-specific local autocovariance structures, while the Dirichlet-process prior adapts model complexity by pruning inactive components. We benchmarked the approach against a filter-based thresholding method and the time-delay embedded HMM using single-channel synthetic data designed to mimic neural time series (e.g., EEG, MEG, and local field potentials), with multiple frequency components masked by 1/f-like noise. In this setting, the proposed model reliably recovered multiple distinct frequency components under noisy conditions while also inferring the number of oscillatory states. Applied to a resting-state motor-cortex MEG dataset, the model identified multiple frequency-selective, short-lived oscillatory states alongside distinct aperiodic states with different spectral profiles. These states exhibited substantial inter-individual heterogeneity in peak frequency, occurrence rate, and power. Overall, this provides an unsupervised framework for discovering frequency-selective oscillatory states without predefining frequency bands or fixing the number of states.