Gabor Hannak

Graphical LASSO based Model Selection for Time Series

We propose a novel graphical model selection scheme for high-dimensional stationary time series or discrete time processes. The method is based on a natural generalization of the graphical LASSO algorithm, introduced originally for the case of i.i.d. samples, and estimates the conditional independence graph of a time series from a finite length observation. The graphical LASSO 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. Our approach is nonparametric as we do not assume a finite dimensional parametric model, but only 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. Numerical experiments demonstrate the ability of our method to recover the correct conditional independence graph from a limited amount of samples.

Joint channel estimation and activity detection for multiuser communication systems

We consider overloaded (non-orthogonal) code division multiple access multiuser wireless communication systems with many transmitting users and one central aggregation node, a typical scenario in e.g. machine-to-machine communications. The task of the central node is to detect the set of active devices and separate their data streams, whose number at any time instance is relatively small compared to the total number of devices in the system. We introduce a novel two-step detection procedure: the first step involves the simultaneous transmission of a pilot sequence used for identification of the active devices and the estimation of their respective channel coefficients. In the second step the payload is transmitted by all active devices and received synchronously at the central node. The first step reduces to a compressed sensing (CS) problem due to the relatively small number of simultaneously active devices. Using an efficient CS recovery scheme (approximate message passing), joint activity detection and channel estimation with high reliability is possible, even for extremely large-scale systems. This, in turn, reduces the data detection task to a simple overdetermined system of linear equations that is then solved by classical methods in the second step.

Scalable graph signal recovery for big data over networks

We formulate the recovery of a graph signal from noisy samples taken on a subset of graph nodes as a convex optimization problem that balances the empirical error for explaining the observed values and a complexity term quantifying the smoothness of the graph signal. To solve this optimization problem, we propose to combine the alternating direction method of multipliers with a novel denoising method that minimizes total variation. Our algorithm can be efficiently implemented in a distributed manner using message passing and thus is attractive for big data problems over networks.

Efficient graph signal recovery over big networks

We consider the problem of recovering a smooth graph signal from noisy samples taken at a small number of graph nodes. The recovery problem is formulated as a convex optimization problem which minimizes the total variation (accounting for the smoothness of the graph signal) while controlling the empirical error. We solve this total variation minimization problem efficiently by applying a recent algorithm proposed by Nesterov for non-smooth optimization problems. Furthermore, we develop a distributed implementation of our algorithm and verify the performance of our scheme on a large-scale real-world dataset.

Graph Signal Recovery via Primal-Dual Algorithms for Total Variation Minimization

We consider the problem of recovering a smooth graph signal from noisy samples taken on a subset of graph nodes. The smoothness of the graph signal is quantified in terms of total variation. We formulate the signal recovery task as a convex optimization problem that minimizes the total variation of the graph signal while controlling its global or node-wise empirical error. We propose a first-order primal-dual algorithm to solve these total variation minimization problems. A distributed implementation of the algorithm is devised to handle large-dimensional applications efficiently. We use synthetic and real-world data to extensively compare the performance of our approach with state-of-the-art methods.

On the convergence of average consensus with generalized metropolis-hasting weights

Average consensus is a well-studied method for distributed averaging. The convergence properties of average consensus depend on the averaging weights. Examples for commonly used weight designs are Metropolis-Hastings (MH) weights and constant weights. In this paper, we provide a complete convergence analysis for a generalized MH weight design that encompasses conventional MH as special case. More specifically, we formulate sufficient and necessary conditions for convergence. A main conclusion is that AC with MH weights is guaranteed to converge unless the underlying network is a regular bipartite graph.

Exploiting joint sparsity in compressed sensing-based RFID

We propose a novel scheme to improve compressed sensing (CS)-based radio frequency identification (RFID) by exploiting multiple measurement vectors. Multiple measurement vectors are obtained by employing multiple receive antennas at the reader or by separation into real and imaginary parts. Our problem formulation renders the corresponding signal vectors jointly sparse, which in turn enables the utilization of CS. Moreover, the joint sparsity is exploited by an appropriate algorithm.We formulate the multiple measurement vector problem in CS-based RFID and demonstrate how a joint recovery of the signal vectors strongly improves the identification speed and noise robustness. The key insight is as follows: Multiple measurement vectors allow to shorten the CS measurement phase, which translates to shortened tag responses in RFID. Furthermore, the new approach enables robust signal support estimation and no longer requires prior knowledge of the number of activated tags.

Bayesian QAM demodulation and activity detection for multiuser communication systems

We consider overloaded (non-orthogonal) multiple access multiuser wireless communication systems with many transmitting devices and one central aggregation node, a typical scenario in e.g. machine-to-machine communications. The task of the central node is to detect the set of active devices and to separate and detect their data streams, whose number at any time instance is small compared to the total number of devices in the system. The payload bits are mapped to a quadrature amplitude modulation (QAM) symbol alphabet, transmitted by the active devices and received synchronously at the central node. The data detection can be cast as a compressed sensing (CS) problem due to the sparsity granted by the sporadic transmission of the typically low-complexity nodes. Separation of the real and imaginary parts of the measurement matrix, the unknown QAM symbols, and the received signal yields a group-sparsity problem. We utilize an efficient iterative Bayesian CS recovery scheme which, instead of separately solving for the real and imaginary parts, uses the Turbo principle to exchange and update parameters between the two solvers and thus comes to consensus regarding the sparsity structure. By tailoring this algorithm to QAM detection, joint activity detection, demodulation and data detection with high reliability is possible, even for very large-scale systems.

Generalized approximate message passing for one-bit compressed sensing with AWGN

Compressed sensing recovery techniques allow for reconstruction of an unknown sparse vector from an underde-termined system of linear equations. Recently, a lot of attention was drawn to the problem of recovering the sparse vector from quantized CS measurements. Especially interesting is the case, when extreme quantization is enforced that captures only the sign of the measurements. The problem becomes even more difficult if the measurements are corrupted by noise. In this paper we consider additive white Gaussian noise (AWGN). To solve this problem, we employ the highly efficient generalized approximate message passing (GAMP) algorithm and provide closed-form expressions for the nonlinear steps. We demonstrate superiority of this approach in terms of the mean squared error (MSE)-performance compared to a similar state-of-the-art algorithm from the literature.