Bayesian Nonparametric Identification of Frequency-Selective Neural Oscillatory States

AO_SCPLOWBSTRACTC_SCPLOWIdentifying neural oscillations is essential for linking fast brain dynamics to underlying cognitive states. 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, followed by fixed power- or amplitude-thresholding to identify oscillatory events. Although recent unsupervised alternatives based on Hidden Markov models (HMM) address these limitations, they still require a priori specification of the number of states and can underfit or overfit when the number of states 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 embedded in 1/f-like noise. In this setting, the proposed model reliably recovered multiple distinct frequency components under noisy conditions while also inferring the correct number of oscillatory states. Applied to a resting-state motor-cortex MEG dataset, the model identified multiple frequency-selective, short-lived oscillatory states that exhibited substantial inter-individual heterogeneity in peak frequency, occurrence rate, and power. Overall, this provides a fully unsupervised route to discovering frequency-selective oscillatory states without predefining frequency bands or selecting the number of states in advance.