Training of the neural autoregressive density estimator (NADE) can be viewed as doing one step of probabilistic inference on missing values in data. We propose a new model that extends this inference scheme to multiple steps, arguing that it is easier to learn to improve a reconstruction in $k$ steps rather than to learn to reconstruct in a single inference step. The proposed model is an unsupervised building block for deep learning that combines the desirable properties of NADE and multi-predictive training: (1) Its test likelihood can be computed analytically, (2) it is easy to generate independent samples from it, and (3) it uses an inference engine that is a superset of variational inference for Boltzmann machines. The proposed NADE-k is competitive with the state-of-the-art in density estimation on the two datasets tested. Papers published at the Neural Information Processing Systems Conference.

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 distribution by a data dependent approximate likelihood in a process resembling the recently proposed Ladder Network. We show that this model provides state of the art predictive log-likelihood and tighter log-likelihood lower bound compared to the purely bottom-up inference in layered Variational Autoencoders and other generative models. We provide a detailed analysis of the learned hierarchical latent representation and show that our new inference model is qualitatively different and utilizes a deeper more distributed hierarchy of latent variables. Finally, we observe that batch-normalization and deterministic warm-up (gradually turning on the KL-term) are crucial for training variational models with many stochastic layers.

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 distribution by a data dependent approximate likelihood in a process resembling the recently proposed Ladder Network. We show that this model provides state of the art predictive log-likelihood and tighter log-likelihood lower bound compared to the purely bottom-up inference in layered Variational Autoencoders and other generative models. We provide a detailed analysis of the learned hierarchical latent representation and show that our new inference model is qualitatively different and utilizes a deeper more distributed hierarchy of latent variables. Finally, we observe that batch normalization and deterministic warm-up (gradually turning on the KL-term) are crucial for training variational models with many stochastic layers.

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 (2015) which we extend by combining the model with supervision. We show that the resulting model reaches state-of-the-art performance in semi-supervised MNIST and CIFAR-10 classification in addition to permutation-invariant MNIST classification with all labels.

Bidirectional recurrent neural networks (RNN) are trained to predict both in the positive and negative time directions simultaneously. They have not been used commonly in unsupervised tasks, because a probabilistic interpretation of the model has been difficult. Recently, two different frameworks, GSN and NADE, provide a connection between reconstruction and probabilistic modeling, which makes the interpretation possible. As far as we know, neither GSN or NADE have been studied in the context of time series before.As an example of an unsupervised task, we study the problem of filling in gaps in high-dimensional time series with complex dynamics. Although unidirectional RNNs have recently been trained successfully to model such time series, inference in the negative time direction is non-trivial. We propose two probabilistic interpretations of bidirectional RNNs that can be used to reconstruct missing gaps efficiently. Our experiments on text data show that both proposed methods are much more accurate than unidirectional reconstructions, although a bit less accurate than a computationally complex bidirectional Bayesian inference on the unidirectional RNN. We also provide results on music data for which the Bayesian inference is computationally infeasible, demonstrating the scalability of the proposed methods.

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 model with supervision. We show that the resulting model reaches state-of-the-art performance in semi-supervised MNIST and CIFAR-10 classification, in addition to permutation-invariant MNIST classification with all labels.

We show how a deep denoising autoencoder with lateral connections can be used as an auxiliary unsupervised learning task to support supervised learning. The proposed model is trained to minimize simultaneously the sum of supervised and unsupervised cost functions by back-propagation, avoiding the need for layer-wise pretraining. It improves the state of the art significantly in the permutation-invariant MNIST classification task.

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 structured prediction problems, where modeling the internal structure of the output is important. (3) Stochasticity has been shown to be an excellent regularizer, which makes generalization performance potentially better in general. However, training stochastic networks is considerably more difficult. We study training using M samples of hidden activations per input. We show that the case M=1 leads to a fundamentally different behavior where the network tries to avoid stochasticity. We propose two new estimators for the training gradient and propose benchmark tests for comparing training algorithms. Our experiments confirm that training stochastic networks is difficult and show that the proposed two estimators perform favorably among all the five known estimators.

Suitable lateral connections between encoder and decoder are shown to allow higher layers of a denoising autoencoder (dAE) to focus on invariant representations. In regular autoencoders, detailed information needs to be carried through the highest layers but lateral connections from encoder to decoder relieve this pressure. It is shown that abstract invariant features can be translated to detailed reconstructions when invariant features are allowed to modulate the strength of the lateral connection. Three dAE structures with modulated and additive lateral connections, and without lateral connections were compared in experiments using real-world images. The experiments verify that adding modulated lateral connections to the model 1) improves the accuracy of the probability model for inputs, as measured by denoising performance; 2) results in representations whose degree of invariance grows faster towards the higher layers; and 3) supports the formation of diverse invariant poolings.

Training of the neural autoregressive density estimator (NADE) can be viewed as doing one step of probabilistic inference on missing values in data. We propose a new model that extends this inference scheme to multiple steps, arguing that it is easier to learn to improve a reconstruction in $k$ steps rather than to learn to reconstruct in a single inference step. The proposed model is an unsupervised building block for deep learning that combines the desirable properties of NADE and multi-predictive training: (1) Its test likelihood can be computed analytically, (2) it is easy to generate independent samples from it, and (3) it uses an inference engine that is a superset of variational inference for Boltzmann machines. The proposed NADE-k is competitive with the state-of-the-art in density estimation on the two datasets tested.