Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Classification by minimum-message-length inference
ICCI'90 Proceedings of the international conference on Advances in computing and information
Keeping the neural networks simple by minimizing the description length of the weights
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Hierarchical non-linear factor analysis and topographic maps
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Variational learning in nonlinear Gaussian belief networks
Neural Computation
An introduction to variational methods for graphical models
Learning in graphical models
A view of the EM algorithm that justifies incremental, sparse, and other variants
Learning in graphical models
Learning in graphical models
Neural Computation
Learning nonlinear dynamical systems using an EM algorithm
Proceedings of the 1998 conference on Advances in neural information processing systems II
Kalman Filtering and Neural Networks
Kalman Filtering and Neural Networks
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
Self-Organizing Maps
Independent Component Analysis: Principles and Practice
Independent Component Analysis: Principles and Practice
Statistics and Computing
Mean-field approaches to independent component analysis
Neural Computation
Expectation Propagation for approximate Bayesian inference
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Accelerating Cyclic Update Algorithms for Parameter Estimation by Pattern Searches
Neural Processing Letters
Information Theory, Inference & Learning Algorithms
Information Theory, Inference & Learning Algorithms
Hierarchical models of variance sources
Signal Processing - Special issue on independent components analysis and beyond
Hierarchy, priors and wavelets: structure and signal modelling using ICA
Signal Processing - Special issue on independent components analysis and beyond
The Journal of Machine Learning Research
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Variational learning for rectified factor analysis
Signal Processing
Competition and multiple cause models
Neural Computation
Nonlinear relational markov networks with an application to the game of go
ICANN'05 Proceedings of the 15th international conference on Artificial neural networks: formal models and their applications - Volume Part II
A variational approximation for Bayesian networks with discrete and continuous latent variables
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
State inference in variational bayesian nonlinear state-space models
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Blind separation of instantaneous mixtures of nonstationary sources
IEEE Transactions on Signal Processing
Nonlinear dynamical factor analysis for state change detection
IEEE Transactions on Neural Networks
Variational learning and bits-back coding: an information-theoretic view to Bayesian learning
IEEE Transactions on Neural Networks
Blind separation of nonlinear mixtures by variational Bayesian learning
Digital Signal Processing
Principal Component Analysis for Large Scale Problems with Lots of Missing Values
ECML '07 Proceedings of the 18th European conference on Machine Learning
Practical Approaches to Principal Component Analysis in the Presence of Missing Values
The Journal of Machine Learning Research
Approximate Riemannian Conjugate Gradient Learning for Fixed-Form Variational Bayes
The Journal of Machine Learning Research
Active learning for online bayesian matrix factorization
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
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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 nonlinear and variance models, which are lacking from most existing variational systems. The introduced blocks are designed to fit together and to yield efficient 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 experimental results on several structures, including a new hierarchical nonlinear model for variances and means. The test results demonstrate the good performance and usefulness of the introduced method.