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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 ..."
Abstract

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
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
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 ..."
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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.
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"... 0.1 Bayesian modeling and variational learning: introduction Unsupervised learning methods are often based on a generative approach where the goal is to find a model which explains how the observations were generated. It is assumed that there exist certain source signals (also called factors, latent ..."
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0.1 Bayesian modeling and variational learning: introduction Unsupervised learning methods are often based on a generative approach where the goal is to find a model which explains how the observations were generated. It is assumed that there exist certain source signals (also called factors, latent or hidden variables, or hidden causes) which have generated the observed data through an unknown mapping. The goal of generative learning is to identify both the source signals and the unknown generative mapping. The success of a specific model depends on how well it captures the structure of the phenomena underlying the observations. Various linear models have been popular, because their mathematical treatment is fairly easy. However, in many realistic cases the observations have been generated by a nonlinear process. Unsupervised learning of a nonlinear model is a challenging task, because it is typically computationally much more demanding than for linear models, and flexible models require strong regularization. In Bayesian data analysis and estimation methods, all the uncertain quantities are modeled in terms of their joint probability distribution. The key principle is to construct
Chapter 4 Variational Bayesian learning of generative models
"... 80 Variational Bayesian learning of generative models 4.1 Bayesian modeling and variational learning: introduction Unsupervised learning methods are often based on a generative approach where the goal is to find a model which explains how the observations were generated. It is assumed that there exi ..."
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80 Variational Bayesian learning of generative models 4.1 Bayesian modeling and variational learning: introduction Unsupervised learning methods are often based on a generative approach where the goal is to find a model which explains how the observations were generated. It is assumed that there exist certain source signals (also called factors, latent or hidden variables, or hidden causes) which have generated the observed data through an unknown mapping. The goal of generative learning is to identify both the source signals and the unknown generative mapping. The success of a specific model depends on how well it captures the structure of the phenomena underlying the observations. Various linear models have been popular, because their mathematical treatment is fairly easy. However, in many realistic cases the observations have been generated by a nonlinear process. Unsupervised learning of a nonlinear model is a challenging task, because it is typically computationally much more demanding than for linear models, and flexible models require strong regularization. In Bayesian data analysis and estimation methods, all the uncertain quantities are