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Register a new userGridless Line Spectral Estimation with Multiple Measurement Vector via Variational Bayesian Inference
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Added by
Jiang Zhu
Publication date
2018
fields
Electronic Engineering
and research's language is
English
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Line spectral estimation (LSE) from multi snapshot samples is studied utilizing the variational Bayesian methods. Motivated by the recently proposed variational line spectral estimation (VALSE) method for a single snapshot, we develop the multisnapshot VALSE (MVALSE) for multi snapshot scenarios, which is important for array processing. The MVALSE shares the advantages of the VALSE method, such as automatically estimating the model order, noise variance and weight variance, closed-form updates of the posterior probability density function (PDF) of the frequencies. By using multiple snapshots, MVALSE improves the recovery performance and it encodes the prior distribution naturally. Finally, numerical results demonstrate the competitive performance of the MVALSE compared to state-of-the-art methods.
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Gridless methods show great superiority in line spectral estimation. These methods need to solve an atomic $l_0$ norm (i.e., the continuous analog of $l_0$ norm) minimization problem to estimate frequencies and model order. Since this problem is NP-hard to compute, relaxations of atomic $l_0$ norm, such as nuclear norm and reweighted atomic norm, have been employed for promoting sparsity. However, the relaxations give rise to a resolution limit, subsequently leading to biased model order and convergence error. To overcome the above shortcomings of relaxation, we propose a novel idea of simultaneously estimating the frequencies and model order by means of the atomic $l_0$ norm. To accomplish this idea, we build a multiobjective optimization model. The measurment error and the atomic $l_0$ norm are taken as the two optimization objectives. The proposed model directly exploits the model order via the atomic $l_0$ norm, thus breaking the resolution limit. We further design a variable-length evolutionary algorithm to solve the proposed model, which includes two innovations. One is a variable-length coding and search strategy. It flexibly codes and interactively searches diverse solutions with different model orders. These solutions act as steppingstones that help fully exploring the variable and open-ended frequency search space and provide extensive potentials towards the optima. Another innovation is a model order pruning mechanism, which heuristically prunes less contributive frequencies within the solutions, thus significantly enhancing convergence and diversity. Simulation results confirm the superiority of our approach in both frequency estimation and model order selection.
Variational Bayes (VB) has been used to facilitate the calculation of the posterior distribution in the context of Bayesian inference of the parameters of nonlinear models from data. Previously an analytical formulation of VB has been derived for nonlinear model inference on data with additive gaussian noise as an alternative to nonlinear least squares. Here a stochastic solution is derived that avoids some of the approximations required of the analytical formulation, offering a solution that can be more flexibly deployed for nonlinear model inference problems. The stochastic VB solution was used for inference on a biexponential toy case and the algorithmic parameter space explored, before being deployed on real data from a magnetic resonance imaging study of perfusion. The new method was found to achieve comparable parameter recovery to the analytic solution and be competitive in terms of computational speed despite being reliant on sampling.
Recently, particle-based variational inference (ParVI) methods have gained interest because they can avoid arbitrary parametric assumptions that are common in variational inference. However, many ParVI approaches do not allow arbitrary sampling from the posterior, and the few that do allow such sampling suffer from suboptimality. This work proposes a new method for learning to approximately sample from the posterior distribution. We construct a neural sampler that is trained with the functional gradient of the KL-divergence between the empirical sampling distribution and the target distribution, assuming the gradient resides within a reproducing kernel Hilbert space. Our generative ParVI (GPVI) approach maintains the asymptotic performance of ParVI methods while offering the flexibility of a generative sampler. Through carefully constructed experiments, we show that GPVI outperforms previous generative ParVI methods such as amortized SVGD, and is competitive with ParVI as well as gold-standard approaches like Hamiltonian Monte Carlo for fitting both exactly known and intractable target distributions.
Since transmission lines are crucial links in the power system, one line outage event may bring about interruption or even cascading failure of the power system. If a quick and accurate line outage detection and localization can be achieved, the system operator can take necessary actions in time to mitigate the negative impact. Therefore, the objective of this paper is to study a method for line outage detection and localization via synchrophasor measurements. The density of deployed phasor measurement units (PMUs) is increasing recently, which greatly improves the visibility of the power grid. Taking advantage of the high-resolution synchrophasor data, the proposed method utilizes frequency measurement for line outage detection and power change for localization. The procedure of the proposed method is given. Compared with conventional methods, it does not require the pre-knowledge on the system. Simulation study validates the effectiveness of the proposed method.
Probabilistic approaches for tensor factorization aim to extract meaningful structure from incomplete data by postulating low rank constraints. Recently, variational Bayesian (VB) inference techniques have successfully been applied to large scale models. This paper presents full Bayesian inference via VB on both single and coupled tensor factorization models. Our method can be run even for very large models and is easily implemented. It exhibits better prediction performance than existing approaches based on maximum likelihood on several real-world datasets for missing link prediction problem.
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