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A Bayesian ensemble learning method is introduced for unsupervised extraction of dynamic processes from noisy data. The data are assumed to be generated by an unknown nonlinear mapping from unknown factors. The dynamics of the factors are modeled using a nonlinear state-space model. The nonlinear mappings in the model are represented using multilayer(More)
We combine supervised learning with unsupervised learning in deep neural networks. The proposed model is trained to simultaneously minimize the sum of supervised and unsupervised cost functions by backpropagation, avoiding the need for layer-wise pre-training. Our work builds on top of the Ladder network proposed by Valpola [1] which we extend by combining(More)
We show that the choice of posterior approximation of sources affects the solution found in Bayesian varia-tional learning of linear independent component analysis models. Assuming the sources to be independent a posteriori favours a solution which has an orthogonal mixing matrix. A linear dynamic model which uses second-order statistics is considered but(More)
We transform the outputs of each hidden neuron in a multi-layer perceptron network to have zero output and zero slope on average , and use separate shortcut connections to model the linear dependencies instead. This transformation aims at separating the problems of learning the linear and nonlin-ear parts of the whole input-output mapping, which has many(More)
In many models, variances are assumed to be constant although this assumption is known to be unrealistic. Joint modelling of means and variances can lead to infinite probability densities which makes it a difficult problem for many learning algorithms. We show that a Bayesian variational technique which is sensitive to probability mass instead of density is(More)
We introduce building blocks from which a large variety of latent variable models can be built. The blocks include continuous and discrete variables, summation, addition, non-linearity and switching. Ensemble learning provides a cost function which can be used for updating the variables as well as optimising the model structure. The blocks are designed to(More)
SUMMARY Blind separation of sources from their linear mixtures is a well understood problem. However, if the mixtures are nonlinear, this problem becomes generally very difficult. This is because both the nonlinear mapping and the underlying sources must be learned from the data in a blind manner, and the problem is highly ill-posed without a suitable(More)