Hyperparameter selection generally relies on running multiple full training trials, with selection based on validation set performance. We propose a gradient-based approach for locally adjusting hyperparameters during training of the model. Hyperparameters are adjusted so as to make the model parameter gradients, and hence updates, more advantageous for the validation cost. We explore the approach for tuning regularization hyperparameters and find that in experiments on MNIST, SVHN and CIFAR-10, the resulting regularization levels are within the optimal regions. The additional computational cost depends on how frequently the hyperparameters are trained, but the tested scheme adds only 30% computational overhead regardless of the model size. Since the method is significantly less computationally demanding compared to similar gradient-based approaches to hyperparameter optimization, and consistently finds good hyperparameter values, it can be a useful tool for training neural network models.

Writing rap lyrics requires both creativity to construct a meaningful, interesting story and lyrical skills to produce complex rhyme patterns, which form the cornerstone of good flow. We present a rap lyrics generation method that captures both of these aspects. First, we develop a prediction model to identify the next line of existing lyrics from a set of candidate next lines. This model is based on two machine-learning techniques: the RankSVM algorithm and a deep neural network model with a novel structure. Results show that the prediction model can identify the true next line among 299 randomly selected lines with an accuracy of 17%, i.e., over 50 times more likely than by random. Second, we employ the prediction model to combine lines from existing songs, producing lyrics with rhyme and a meaning. An evaluation of the produced lyrics shows that in terms of quantitative rhyme density, the method outperforms the best human rappers by 21%. The rap lyrics generator has been deployed as an online tool called DeepBeat, and the performance of the tool has been assessed by analyzing its usage logs. This analysis shows that machine-learned rankings correlate with user preferences.

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.

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 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.

A missing data mask estimation method based on Gaussian-Bernoulli restricted Boltzmann machine (GRBM) trained on cross-correlation representation of the audio signal is presented in the study. The automatically learned features by the GRBM are utilized in dividing the time-frequency units of the spectrographic mask into noise and speech dominant. The system is evaluated against two baseline mask estimation methods in a reverberant multisource environment speech recognition task. The proposed system is shown to provide a performance improvement in the speech recognition accuracy over the previous multifeature approaches.

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 improvements of the learning algorithm for GDBM include parallel tempering, enhanced gradient, adaptive learning rate and layer-wise pretraining. We empirically show that they help avoid some of the common difficulties found in training deep Boltzmann machines such as divergence of learning, the difficulty in choosing right learning rate scheduling, and the existence of meaningless higher layers.

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 sensitive to specific data representation. An equivalent RBM can be obtained by flipping some bits and changing the weights and biases accordingly, but traditional learning rules are not invariant to such transformations. Without careful tuning of these training settings, traditional algorithms can easily get stuck or even diverge. In this letter, we present an enhanced gradient that is derived to be invariant to bit-flipping transformations. We experimentally show that the enhanced gradient yields more stable training of RBMs both when used with a fixed learning rate and an adaptive one.

Abstract—We study a novel type of a semi-supervised anomaly detection problem where the anomalies occur collectively among a background of normal data. Such problem arises in experimental high energy physics when one is trying to discover deviations from known Standard Model physics. We solve the problem by first fitting a mixture of Gaussians to a labeled background sample. We then fit a mixture of this background model and a number of additional Gaussians to an unlabeled sample containing both background and anomalies. This way we not only detect but also perform pattern recognition of anomalies. Such mixture model allows us to perform classification of anomalies vs. background, estimate the proportion of anomalies in the sample and study the statistical significance of the anomalous contribution. We first verify the performance of the method using artificial data and then demonstrate its real-life applicability using a data set related to the search of the Higgs boson at the Tevatron collider. Index Terms—Anomaly detection, semi-supervised learning, EM algorithm, Gaussian mixture models, high energy physics

Missing-feature reconstruction can improve speech recognition performance in unknown noisy environments. In this work, we examine using a nonlinear state-space model (NSSM) for missing-feature reconstruction and propose estimation with observed bounds to improve the NSSM performance. Evaluated in large-vocabulary continuous speech recognition task with babble and impulsive noise, using observed bounds in NSSM state estimation significantly improved the method performance.

A new interest towards restricted Boltzmann machines (RBMs) has risen due to their usefulness in greedy learning of deep neural networks. While contrastive divergence learning has been considered an efficient way to learn an RBM, it has a drawback due to a biased approximation in the learning gradient. We propose to use an advanced Monte Carlo method called parallel tempering instead, and show experimentally that it works efficiently.

We introduce a probabilistic version of the self-organizing map (SOM) where we model the uncertainty of both the model vectors and the data. While uncertainty information about the data is often not available, this property becomes very useful when the method is combined in a hierarchical manner with probabilistic principal component analysis (PCA), where we do estimate uncertainty of the principal components and the weights. We apply the hierarchical model to the domain of collaborative filtering, where probabilistic PCA is a popular approach due to its robustness for tackling many missing values in the data. The main focus in this paper is for recommendation systems about movies, where the movie rating data matrix of size people times movies is available, but contains lots of missing values. The matrix is first decomposed into a matrix product of people times features and features times movies by PCA. Then we apply the probabilistic SOM to both of those matrices separately. The uncertainty is large when a person (or a movie) has only a few ratings. The experiments with Movielens and Netflix data show an improvement over traditional SOM.

While variational Bayesian (VB) inference is typically done with the so called VB EM algorithm, there are models where it cannot be applied because either the E-step or the M-step cannot be solved analytically. In 2007, Honkela et al. introduced a recipe for a gradient-based algorithm for VB inference that does not have such a restriction. In this paper, we derive the algorithm in the case of the mixture of Gaussians model. For the first time, the algorithm is experimentally compared to VB EM and its variant with both artificial and real data. We conclude that the algorithms are approximately as fast depending on the problem.

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.

Logical hidden Markov models (LOHMMs) upgrade traditional hidden Markov models to deal with sequences of structured symbols in the form of logical atoms, rather than flat characters. This note formally introduces LOHMMs and presents solutions to the three central inference problems for LOHMMs: evaluation, most likely hidden state sequence and parameter estimation. The resulting representation and algorithms are experimentally evaluated on problems from the domain of bioinformatics.

This paper studies the learning of nonlinear state-space models for a control task. This has some advantages over traditional methods. Variational Bayesian learning provides a framework where uncertainty is explicitly taken into account and system identification can be combined with model-predictive control. Three different control schemes are used. One of them, optimistic inference control, is a novel method based directly on the probabilistic modelling. Simulations with a cart-pole swing-up task confirm that the latent state space provides a representation that is easier to predict and control than the original observation space.

It is common to have both observed and missing values in data. This paper concentrates on the case where a value can be somewhere between those two ends, partially observed and partially missing. To achieve that, a method of using evidence nodes in a Bayesian network is studied. Different ways of handling inaccuracies are discussed in examples and the proposed approach is justified in the experiments with real image data. Also, a justification is given for the standard preprocessing step of adding a tiny amount of noise to the data, when a continuous valued model is used for discrete-valued data.