Temporal Modeling of EEG Signals using Block Sparse Variational Bayes Framework

Some Comments on Variational Bayes Block Sparse Modeling with Correlated Entries

Abstract: We present some details of Bayesian block sparse modeling using hierarchical prior having deterministic and random parameters when entries within the blocks are correlated. In particular, the effect of the threshold to prune out variance parameters of algorithms corresponding to several choices of marginals, viz. multivariate Jeffery prior, multivariate Laplace distribution and multivariate Student’s t distribution, is discussed. We also provide details of experiments with Electroencephalograph (EEG) data which shed some light on the possible applicability of the proposed Sparse Variational Bayes framework.

Fundamentals of statistical signal processing: estimation theory

Abstract: (1995). Fundamentals of Statistical Signal Processing: Estimation Theory. Technometrics: Vol. 37, No. 4, pp. 465-466.

Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information

Abstract: This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal f/spl isin/C/sup N/ and a randomly chosen set of frequencies /spl Omega/. Is it possible to reconstruct f from the partial knowledge of its Fourier coefficients on the set /spl Omega/? A typical result of this paper is as follows. Suppose that f is a superposition of |T| spikes f(t)=/spl sigma//sub /spl tau//spl isin/T/f(/spl tau/)/spl delta/(t-/spl tau/) obeying |T|/spl les/C/sub M//spl middot/(log N)/sup -1/ /spl middot/ |/spl Omega/| for some constant C/sub M/>0. We do not know the locations of the spikes nor their amplitudes. Then with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the /spl lscr//sub 1/ minimization problem. In short, exact recovery may be obtained by solving a convex optimization problem. We give numerical values for C/sub M/ which depend on the desired probability of success. Our result may be interpreted as a novel kind of nonlinear sampling theorem. In effect, it says that any signal made out of |T| spikes may be recovered by convex programming from almost every set of frequencies of size O(|T|/spl middot/logN). Moreover, this is nearly optimal in the sense that any method succeeding with probability 1-O(N/sup -M/) would in general require a number of frequency samples at least proportional to |T|/spl middot/logN. The methodology extends to a variety of other situations and higher dimensions. For example, we show how one can reconstruct a piecewise constant (one- or two-dimensional) object from incomplete frequency samples - provided that the number of jumps (discontinuities) obeys the condition above - by minimizing other convex functionals such as the total variation of f.

Pattern Recognition and Machine Learning (Information Science and Statistics)

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Information Theory, Inference and Learning Algorithms

Abstract: Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.

Information theory, inference, and learning algorithms

Abstract: Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.