arXiv subjects

Gabor Hannak

Publications and source records attributed to Gabor Hannak.

4 recordsLinked to original sources

arXiv2018

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.

cs.IT↗

arXiv2015

An Approach to Complex Bayesian-optimal Approximate Message Passing

In this work we aim to solve the compressed sensing problem for the case of a complex unknown vector by utilizing the Bayesian-optimal structured signal approximate message passing (BOSSAMP) algorithm on the jointly sparse real and imaginary parts of the unknown. By introducing a latent activity variable, BOSSAMP separates the tasks of activity detection and value estimation to overcome the problem of detecting different supports in the real and imaginary parts. We complement the recovery algorithm by two novel support detection schemes that utilize the updated auxiliary variables of BOSSAMP. Simulations show the superiority of our proposed method against approximate message passing (AMP) and its Bayesian-optimal sibling (BAMP), both in mean squared error and support detection performance.

cs.IT↗

arXiv2014

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.

stat.ML↗

arXiv2014

On the Information-theoretic Limits of Graphical Model Selection for Gaussian Time Series

We consider the problem of inferring the conditional independence graph (CIG) of a multivariate stationary dicrete-time Gaussian random process based on a finite length observation. Using information-theoretic methods, we derive a lower bound on the error probability of any learning scheme for the underlying process CIG. This bound, in turn, yields a minimum required sample-size which is necessary for any algorithm regardless of its computational complexity, to reliably select the true underlying CIG. Furthermore, by analysis of a simple selection scheme, we show that the information-theoretic limits can be achieved for a subclass of processes having sparse CIG. We do not assume a parametric model for the observed process, but require it to have a sufficiently smooth spectral density matrix (SDM).

math.ST↗