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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Neural processing letters 4 (1996), S. 139-148 
    ISSN: 1573-773X
    Keywords: anti-Hebbian learning ; blind separation ; FIR filters ; lateral inhibition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A temporal variant of Foldiak's first model with lateral inhibitory synaptic weights is proposed. The usual symmetric scalar values of the lateral weights are replaced with data driven asymmetric memory based lateral weights, which take the form of Finite Impulse Response (FIR) coefficients. Linear anti-Hebbian learning, as defined by Foldiak (IEEE/INNS International Joint Conference on Neural Networks, 1989) and Matsuoka et al. (Neural Networks, Vol. 8, pp. 411–419, 1995), is employed in the self-organisation of the network weights. The temporal anti-Hebbian learning, when applied to the separation of convolved mixtures of signals, causes the network weights to converge to the truncated FIR filter coefficients of the unmixing transfer function and so recover the original signals. Simulation results are presented for separating two natural speech sources convolved and mixed by a priori unknown direct and cross-coupled transfer functions. We compare temporal anti-Hebbian learning with information maximisation learning when applied to the blind separation of convolved sources.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Neural processing letters 8 (1998), S. 27-39 
    ISSN: 1573-773X
    Keywords: data visualisation ; projection pursuit ; independent component analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This paper presents a generalisation of the nonlinear 'Infomax' algorithm based on the linear latent variable model of factor analysis. The algorithm is based on an information theoretic index for projection pursuit which defines linear projections of observed data onto subspaces of lower dimension. This is applied to the visualisation and interpretation of complex high dimensional data and is empirically compared with the recently developed Generative Topographic Mapping.
    Type of Medium: Electronic Resource
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  • 3
    Publication Date: 2021-10-28
    Description: This paper develops a class of meshless methods that are well-suited to statistical inverse problems involving partial differential equations (PDEs). The methods discussed in this paper view the forcing term in the PDE as a random field that induces a probability distribution over the residual error of a symmetric collocation method. This construction enables the solution of challenging inverse problems while accounting, in a rigorous way, for the impact of the discretisation of the forward problem. In particular, this confers robustness to failure of meshless methods, with statistical inferences driven to be more conservative in the presence of significant solver error. In addition, (i) a principled learning-theoretic approach to minimise the impact of solver error is developed, and (ii) the challenging setting of inverse problems with a non-linear forward model is considered. The method is applied to parameter inference problems in which non-negligible solver error must be accounted for in order to draw valid statistical conclusions.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 4
    Publication Date: 2021-10-28
    Description: It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that the decision-theoretic framework is neither appropriate nor sufficient. To this end, we consider an alternative optimality criterion from Bayesian experimental design and study its implied optimal information in the numerical context. This information is demonstrated to differ, in general, from the information that would be used in an average-case-optimal numerical method. The explicit connection to Bayesian experimental design suggests several distinct regimes in which optimal probabilistic numerical methods can be developed.
    Language: English
    Type: incollection , doc-type:Other
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  • 5
    Publication Date: 2021-10-28
    Description: Over forty years ago average-case error was proposed in the applied mathematics literature as an alternative criterion with which to assess numerical methods. In contrast to worst-case error, this criterion relies on the construction of a probability measure over candidate numerical tasks, and numerical methods are assessed based on their average performance over those tasks with respect to the measure. This paper goes further and establishes Bayesian probabilistic numerical methods as solutions to certain inverse problems based upon the numerical task within the Bayesian framework. This allows us to establish general conditions under which Bayesian probabilistic numerical methods are well defined, encompassing both the non-linear and non-Gaussian context. For general computation, a numerical approximation scheme is proposed and its asymptotic convergence established. The theoretical development is extended to pipelines of computation, wherein probabilistic numerical methods are composed to solve more challenging numerical tasks. The contribution highlights an important research frontier at the interface of numerical analysis and uncertainty quantification, and a challenging industrial application is presented.
    Language: English
    Type: article , doc-type:article
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  • 6
    Publication Date: 2021-10-28
    Description: This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem. In particular, this drives statistical inferences to be more conservative in the presence of significant solver error. Theoretical results are presented describing rates of convergence for the posteriors in both the forward and inverse problems. This method is tested on a challenging inverse problem with a nonlinear forward model
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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  • 7
    Publication Date: 2021-10-28
    Language: English
    Type: article , doc-type:article
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