Learning the Morphology of Brain Signals Using Alpha-Stable Convolutional Sparse Coding

Mainak Jas (1) , Tom Dupré La Tour (1) , Umut Şimşekli (1) , Alexandre Gramfort (2, 1)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 PARIETAL - Modelling brain structure, function and variability based on high-field MRI data

Neural time-series data contain a wide variety of prototypical signal waveforms (atoms) that are of significant importance in clinical and cognitive research. One of the goals for analyzing such data is hence to extract such 'shift-invariant' atoms. Even though some success has been reported with existing algorithms, they are limited in applicability due to their heuristic nature. Moreover, they are often vulnerable to artifacts and impulsive noise, which are typically present in raw neural recordings. In this study, we address these issues and propose a novel probabilistic convolutional sparse coding (CSC) model for learning shift-invariant atoms from raw neural signals containing potentially severe artifacts. In the core of our model, which we call αCSC, lies a family of heavy-tailed distributions called α-stable distributions. We develop a novel, computationally efficient Monte Carlo expectation-maximization algorithm for inference. The maximization step boils down to a weighted CSC problem, for which we develop a computationally efficient optimization algorithm. Our results show that the proposed algorithm achieves state-of-the-art convergence speeds. Besides, αCSC is significantly more robust to artifacts when compared to three competing algorithms: it can extract spike bursts, oscillations, and even reveal more subtle phenomena such as cross-frequency coupling when applied to noisy neural time series.

Mots clés: Convolutional sparse coding; Dictionary learning; Alpha stable probability distribution; Heavy tailed distributions; Local field potentials

Domaines: Machine Learning [stat.ML]; Neurosciences [q-bio.NC]

Mainak Jas, Tom Dupré La Tour, Umut Şimşekli, Alexandre Gramfort. Learning the Morphology of Brain Signals Using Alpha-Stable Convolutional Sparse Coding. Advances in neural information processing systems, Dec 2017, Long Beach, United States. ⟨hal-01590988⟩