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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)
Principal component analysis (PCA) is a classical data analysis technique that finds linear transformations of data that retain the maximal amount of variance. We study a case where some of the data values are missing, and show that this problem has many features which are usually associated with nonlinear models, such as overfitting and bad locally optimal(More)
Restricted Boltzmann machines (RBMs) are often used as building blocks in greedy learning of deep networks. However, training this simple model can be laborious. Traditional learning algorithms often converge only with the right choice of metaparameters that specify, for example, learning rate scheduling and the scale of the initial weights. They are also(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 the Ladder network proposed by Valpola (2015), which we extend by combining the(More)
Boltzmann machines are often used as building blocks in greedy learning of deep networks. However, training even a simplified model, known as restricted Boltzmann machine (RBM), can be extremely laborious: Traditional learning algorithms often converge only with the right choice of the learning rate scheduling and the scale of the initial weights. They are(More)
Stochastic binary hidden units in a multi-layer perceptron (MLP) network give at least three potential benefits when compared to deterministic MLP networks. (1) They allow to learn one-to-many type of mappings. (2) They can be used in struc-tured prediction problems, where modeling the internal structure of the output is important. (3) Stochasticity has(More)
Variational autoencoders are a powerful framework for unsupervised learning. However, previous work has been restricted to shallow models with one or two layers of fully factorized stochastic latent variables, limiting the flexibility of the latent representation. We propose three advances in training algorithms of variational au-toencoders, for the first(More)
Variational Bayesian (VB) methods are typically only applied to models in the conjugate-exponential family using the variational Bayesian expectation maximisation (VB EM) algorithm or one of its variants. In this paper we present an efficient algorithm for applying VB to more general models. The method is based on specifying the functional form of the(More)
In this paper, we study a model that we call Gaussian-Bernoulli deep Boltzmann machine (GDBM) and discuss potential improvements in training the model. GDBM is designed to be applicable to continuous data and it is constructed from Gaussian-Bernoulli restricted Boltzmann machine (GRBM) by adding multiple layers of binary hidden neurons. The studied(More)
Variational autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive models. We propose a new inference model, the Ladder Variational Autoencoder, that recursively corrects the generative(More)