Srikantan S. Nagarajan

Kensuke Sekihara, Hagai Attias, Julia P. Owen et al.

This paper examines the effectiveness of a sparse Bayesian algorithm to estimate multivariate autoregressive coefficients when a large amount of background interference exists. This paper employs computer experiments to compare two methods in the source-space causality analysis: the conventional least-squares method and a sparse Bayesian method. Results of our computer experiments show that the interference affects the least-squares method in a very severe manner. It produces large false-positive results, unless the signal-to-interference ratio is very high. On the other hand, the sparse Bayesian method is relatively insensitive to the existence of interference. However, this robustness of the sparse Bayesian method is attained on the scarifies of the detectability of true causal relationship. Our experiments also show that the surrogate data bootstrapping method tends to give a statistical threshold that are too low for the sparse method. The permutation-test-based method gives a higher (more conservative) threshold and it should be used with the sparse Bayesian method whenever the control period is available.

Ali Hashemi, Yijing Gao, Chang Cai et al.

Several problems in neuroimaging and beyond require inference on the parameters of multi-task sparse hierarchical regression models. Examples include M/EEG inverse problems, neural encoding models for task-based fMRI analyses, and climate science. In these domains, both the model parameters to be inferred and the measurement noise may exhibit a complex spatio-temporal structure. Existing work either neglects the temporal structure or leads to computationally demanding inference schemes. Overcoming these limitations, we devise a novel flexible hierarchical Bayesian framework within which the spatio-temporal dynamics of model parameters and noise are modeled to have Kronecker product covariance structure. Inference in our framework is based on majorization-minimization optimization and has guaranteed convergence properties. Our highly efficient algorithms exploit the intrinsic Riemannian geometry of temporal autocovariance matrices. For stationary dynamics described by Toeplitz matrices, the theory of circulant embeddings is employed. We prove convex bounding properties and derive update rules of the resulting algorithms. On both synthetic and real neural data from M/EEG, we demonstrate that our methods lead to improved performance.