5 research outputs found
Graphical LASSO Based Model Selection for Time Series
We propose a novel graphical model selection (GMS) scheme for
high-dimensional stationary time series or discrete time process. The method is
based on a natural generalization of the graphical LASSO (gLASSO), introduced
originally for GMS based on i.i.d. samples, and estimates the conditional
independence graph (CIG) of a time series from a finite length observation. The
gLASSO for time series is defined as the solution of an l1-regularized maximum
(approximate) likelihood problem. We solve this optimization problem using the
alternating direction method of multipliers (ADMM). Our approach is
nonparametric as we do not assume a finite dimensional (e.g., an
autoregressive) parametric model for the observed process. Instead, we require
the process to be sufficiently smooth in the spectral domain. For Gaussian
processes, we characterize the performance of our method theoretically by
deriving an upper bound on the probability that our algorithm fails to
correctly identify the CIG. Numerical experiments demonstrate the ability of
our method to recover the correct CIG from a limited amount of samples
Performance analysis of approximate message passing for distributed compressed sensing
Bayesian approximate message passing (BAMP) is an efficient method in
compressed sensing that is nearly optimal in the minimum mean squared error
(MMSE) sense. Bayesian approximate message passing (BAMP) performs joint
recovery of multiple vectors with identical support and accounts for
correlations in the signal of interest and in the noise. In this paper, we show
how to reduce the complexity of vector BAMP via a simple joint decorrelation
diagonalization) transform of the signal and noise vectors, which also
facilitates the subsequent performance analysis. We prove that BAMP and the
corresponding state evolution (SE) are equivariant with respect to the joint
decorrelation transform and preserve diagonality of the residual noise
covariance for the Bernoulli-Gauss (BG) prior. We use these results to analyze
the dynamics and the mean squared error (MSE) performance of BAMP via the
replica method, and thereby understand the impact of signal correlation and
number of jointly sparse signals