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Building Blocks For Variational Bayesian Learning Of Latent Variable Models
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2006
"... We introduce standardised building blocks designed to be used with variational Bayesian learning. The blocks include Gaussian variables, summation, multiplication, nonlinearity, and delay. A large variety of latent variable models can be constructed from these blocks, including variance models a ..."
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Cited by 11 (8 self)
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We introduce standardised building blocks designed to be used with variational Bayesian learning. The blocks include Gaussian variables, summation, multiplication, nonlinearity, and delay. A large variety of latent variable models can be constructed from these blocks, including variance models and nonlinear modelling, which are lacking from most existing variational systems. The introduced blocks are designed to fit together and to yield e#cient update rules. Practical implementation of various models is easy thanks to an associated software package which derives the learning formulas automatically once a specific model structure has been fixed. Variational Bayesian learning provides a cost function which is used both for updating the variables of the model and for optimising the model structure. All the computations can be carried out locally, resulting in linear computational complexity. We present
Partially observed values, in
 Proc. Int. Joint Conf. on Neural Networks (IJCNN 2004
, 2004
"... It is common to have both observed and missing values in data. This paper concentrates on the case where a value can be somewhere between those two ends, partially observed and partially missing. To achieve that, a method of using evidence nodes in a Bayesian network is studied. Different ways of ha ..."
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Cited by 7 (4 self)
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It is common to have both observed and missing values in data. This paper concentrates on the case where a value can be somewhere between those two ends, partially observed and partially missing. To achieve that, a method of using evidence nodes in a Bayesian network is studied. Different ways of handling inaccuracies are discussed in examples and the proposed approach is justified in the experiments with real image data.
Bayes Blocks: An implementation of the variational Bayesian building blocks framework
 In Proceedings of the 21st Conference on Uncertainty in Artificial Intelligence, UAI 2005
, 2005
"... A software library for constructing and learning probabilistic models is presented. The library offers a set of building blocks from which a large variety of static and dynamic models can be built. These include hierarchical models for variances of other variables and many nonlinear models. The unde ..."
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Cited by 7 (5 self)
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A software library for constructing and learning probabilistic models is presented. The library offers a set of building blocks from which a large variety of static and dynamic models can be built. These include hierarchical models for variances of other variables and many nonlinear models. The underlying variational Bayesian machinery, providing for fast and robust estimation but being mathematically rather involved, is almost completely hidden from the user thus making it very easy to use the library. The building blocks include Gaussian, rectified Gaussian and mixtureofGaussians variables and computational nodes which can be combined rather freely. 1
An Information Theoretic Approach to Machine Learning
, 2005
"... In this thesis, theory and applications of machine learning systems based on information theoretic criteria as performance measures are studied. A new clustering algorithm based on maximizing the CauchySchwarz (CS) divergence measure between probability density functions (pdfs) is proposed. The CS ..."
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Cited by 7 (2 self)
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In this thesis, theory and applications of machine learning systems based on information theoretic criteria as performance measures are studied. A new clustering algorithm based on maximizing the CauchySchwarz (CS) divergence measure between probability density functions (pdfs) is proposed. The CS divergence is estimated nonparametrically using the Parzen window technique for density estimation. The problem domain is transformed from discrete 0/1 cluster membership values to continuous membership values. A constrained gradient descent maximization algorithm is implemented. The gradients are stochastically approximated to reduce computational complexity, making the algorithm more practical. Parzen window annealing is incorporated into the algorithm to help avoid convergence to a local maximum. The clustering results obtained on synthetic and real data are encouraging. The Parzen windowbased estimator for the CS divergence is shown to have a dual expression as a measure of the cosine of the angle between cluster mean vectors in a feature space determined by the eigenspectrum of a Mercer kernel matrix. A spectral clustering
A variational Bayesian method for rectified factor analysis
 In Proc. 2005 IEEE Int. Joint Conf. on Neural Networks (IJCNN 2005
, 2005
"... Abstract — Linear factor models with nonnegativity constraints have received a great deal of interest in a number of problem domains. In existing approaches, positivity has often been associated with sparsity. In this paper we argue that sparsity of the factors is not always a desirable option, but ..."
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Cited by 5 (4 self)
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Abstract — Linear factor models with nonnegativity constraints have received a great deal of interest in a number of problem domains. In existing approaches, positivity has often been associated with sparsity. In this paper we argue that sparsity of the factors is not always a desirable option, but certainly a technical limitation of the currently existing solutions. We then reformulate the problem in order to relax the sparsity constraint while retaining positivity. A variational inference procedure is derived and this is contrasted to existing related approaches. Both i.i.d. and firstorder AR variants of the proposed model are provided and these are experimentally demonstrated in a realworld astrophysical application. I.
Compact modeling of data using independent variable group analysis
 IEEE Transactions on Neural Networks
, 2007
"... Abstract—We introduce a modeling approach called independent variable group analysis (IVGA) which can be used for finding an efficient structural representation for a given data set. The basic idea is to determine such a grouping for the variables of the data set that mutually dependent variables ar ..."
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Cited by 4 (2 self)
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Abstract—We introduce a modeling approach called independent variable group analysis (IVGA) which can be used for finding an efficient structural representation for a given data set. The basic idea is to determine such a grouping for the variables of the data set that mutually dependent variables are grouped together whereas mutually independent or weakly dependent variables end up in separate groups. Computation of an IVGA model requires a combinatorial algorithm for grouping of the variables and a modeling algorithm for the groups. In order to be able to compare different groupings, a cost function which reflects the quality of a grouping is also required. Such a cost function can be derived, for example, using the variational Bayesian approach, which is employed in our study. This approach is also shown to be approximately equivalent to minimizing the mutual information between the groups. The modeling task is computationally demanding. We describe an efficient heuristic grouping algorithm for the variables and derive a computationally light nonlinear mixture model for modeling of the dependencies within the groups. Finally, we carry out a set of experiments which indicate that IVGA may turn out to be beneficial in many different applications. Index Terms—compact modeling, independent variable group analysis, mutual information, variable grouping, variational Bayesian learning I.
and A Kabán, Variational Learning for Rectified Factor Analysis
 Signal Processing
, 2007
"... Linear factor models with nonnegativity constraints have received a great deal of interest in a number of problem domains. In existing approaches, positivity has often been associated with sparsity. In this paper we argue that sparsity of the factors is not always a desirable option, but certainly ..."
Abstract

Cited by 2 (1 self)
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Linear factor models with nonnegativity constraints have received a great deal of interest in a number of problem domains. In existing approaches, positivity has often been associated with sparsity. In this paper we argue that sparsity of the factors is not always a desirable option, but certainly a technical limitation of the currently existing solutions. We then reformulate the problem in order to relax the sparsity constraint while retaining positivity. This is achieved by employing a rectification nonlinearity rather than a positively supported prior directly on the latent space. A variational learning procedure is derived for the proposed model and this is contrasted to existing related approaches. Both i.i.d. and firstorder AR variants of the proposed model are provided and they are experimentally demonstrated with artificial data. Application to the analysis of galaxy spectra show the benefits of the method in a real world astrophysical problem, where the existing approach is not a viable alternative.
SPARSE MEG INVERSE SOLUTIONS VIA HIERARCHICAL BAYESIAN MODELING: EVALUATION WITH A PARALLEL fMRI STUDY
, 2007
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Variational learning for Generalized Associative Functional Networks in modeling
"... journal homepage: www.elsevier.com/locate/ecolinf ..."