Conference Paper

Fast adaptive variational sparse Bayesian learning with automatic relevance determination.

DOI: 10.1109/ICASSP.2011.5946760 Conference: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011, May 22-27, 2011, Prague Congress Center, Prague, Czech Republic
Source: DBLP

ABSTRACT In this work a new adaptive fast variational sparse Bayesian learning (V-SBL) algorithm is proposed that is a variational counterpart of the fast marginal likelihood maximization approach to SBL. It allows one to adaptively construct a sparse regression or classification function as a linear combination of a few basis functions by minimizing the variational free energy. In the case of non-informative hyperpriors, also referred to as automatic relevance determination, the minimization of the free energy can be efficiently realized by computing the fixed points of the update expressions for the variational distribution of the sparsity parameters. The criteria that establish convergence to these fixed points, termed pruning conditions, allow an efficient addition or removal of basis functions; they also have a simple and intuitive interpretation in terms of a component’s signal-to-noise ratio. It has been demonstrated that this interpretation allows a simple empirical adjustment of the pruning conditions, which in turn improves sparsity of SBL and drastically accelerates the convergence rate of the algorithm. The experimental evidence collected with synthetic data demonstrates the effectiveness of the proposed learning scheme.

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Available from: Dmitriy Shutin, Aug 19, 2015
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    • "This can be seen by substitutingˆα l = ∞ into (5) and (6) which leads to a zero variance and mean for the lth model weight and removes the influence of the corresponding basis function. The terms ς l and ρ 2 l in (10) can be efficiently computed without explicitly computing the matrix inversion in (9) for each l, which is given in [7]. "
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    ABSTRACT: In this work a new online learning algorithm that uses automatic relevance determination (ARD) is proposed for fast adaptive non linear filtering. A sequential decision rule for inclusion or deletion of basis functions is obtained by applying a recently proposed fast variational sparse Bayesian learning (SBL) method. The proposed scheme uses a sliding window estimator to process the data in an online fashion. The noise variance can be implicitly estimated by the algorithm. It is shown that the described method has better mean square error (MSE) performance than a state of the art kernel re cursive least squares (Kernel-RLS) algorithm when using the same number of basis functions.
    Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on; 06/2011
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    • "depend exclusively on the measurement t and the matrixˆS that essentially determines how well a basis function " aligns " or correlates with the other basis functions in the active dictionary. Notice that the ratio ω 2 l /ς l can be interpreted as an estimate of the component signal-to-noise ratio 3 SNR l = ω 2 l /ς l [10]. Thus, SBL prunes a component if its estimated SNR is below 0dB. "
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    ABSTRACT: In this work a new adaptive fast variational sparse Bayesian learning (V-SBL) algorithm is proposed that is a variational counterpart of the fast marginal likelihood maximization approach to SBL. It allows one to adaptively construct a sparse regression or classification function as a linear combination of a few basis functions by minimizing the variational free energy. In the case of non-informative hyperpriors, also referred to as automatic relevance determination, the minimization of the free energy can be efficiently realized by computing the fixed points of the update expressions for the variational distribution of the sparsity parameters. The criteria that establish convergence to these fixed points, termed pruning conditions, allow an efficient addition or removal of basis functions; they also have a simple and intuitive interpretation in terms of a component’s signal-to-noise ratio. It has been demonstrated that this interpretation allows a simple empirical adjustment of the pruning conditions, which in turn improves sparsity of SBL and drastically accelerates the convergence rate of the algorithm. The experimental evidence collected with synthetic data demonstrates the effectiveness of the proposed learning scheme.
    Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011, May 22-27, 2011, Prague Congress Center, Prague, Czech Republic; 01/2011
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    ABSTRACT: In this paper we provide an algorithm allowing to solve the variational Bayesian issue as a functional optimization problem. The main contribution of this paper is to transpose a classical iterative algorithm of optimization in the metric space of probability densities involved in the Bayesian methodology. The main advantage of this methodology is that it allows to address large dimensional inverse problems by unsupervised algorithms. The interest of our algorithm is enhanced by its application to large dimensional linear inverse problems involving sparse objects. Finally, we provide simulation results. First we show the good numerical performances of our method by comparing it with classical ones on a small tomographic problem. On a second time we treat a large dimensional dictionary learning problem and compare our method with a wavelet based one. keywords: ill-posed inverse problems, variational bayesian methodol-ogy, sparse signal reconstruction, infinite dimensional convex optimization 1. Introduction. The recent development of information technologies has in-creased the expansion of inverse problems for very large dimensional datasets. Indeed whereas the 90's decade have seen the introduction of image reconstruction problems, the current main interest is on 3D sequences (3D + T), thus on large dimensional sets of data. There is therefore a significant growth in the number of measurements in the involved problems. One has frequently to treat the reconstruction of more than one million data. At the same time, the signal processing techniques have helped to over-come the limitations of measuring instruments as they supplied the design of systems involving indirect measures. These new equipments introduced in exchange novel sig-nal processing challenges, such as super resolution deconvolution, source separation or tomographic reconstruction. All these problems are ill posed, the only information contained in the data and in the model of acquisition are not sufficient to obtain a good estimation of the unknown objects.
    SIAM Journal on Imaging Sciences 10/2014; 7(4). DOI:10.1137/140966575 · 2.87 Impact Factor
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