Connectionist multivariate density-estimation and its application to speech synthesis

Autoregressive models factorize a multivariate joint probability distribution into a product of one-dimensional conditional distributions. The variables are assigned an ordering, and the conditional distribution of each variable modelled using all variables preceding it in that ordering as predictors. Calculating normalized probabilities and sampling has polynomial computational complexity under autoregressive models. Moreover, binary autoregressive models based on neural networks obtain statistical performances similar to that of some intractable models, like restricted Boltzmann machines, on several datasets. The use of autoregressive probability density estimators based on neural networks to model real-valued data, while proposed before, has never been properly investigated and reported. In this thesis we extend the formulation of neural autoregressive distribution estimators (NADE) to real-valued data; a model we call the real-valued neural autoregressive density estimator (RNADE). Its statistical performance on several datasets, including visual and auditory data, is reported and compared to that of other models. RNADE obtained higher test likelihoods than other tractable models, while retaining all the attractive computational properties of autoregressive models. However, autoregressive models are limited by the ordering of the variables inherent to their formulation. Marginalization and imputation tasks can only be solved analytically if the missing variables are at the end of the ordering. We present a new training technique that obtains a set of parameters that can be used for any ordering of the variables. By choosing a model with a convenient ordering of the dimensions at test time, it is possible to solve any marginalization and imputation tasks analytically. The same training procedure also makes it practical to train NADEs and RNADEs with several hidden layers. The resulting deep and tractable models display higher test likelihoods than the equivalent one-hidden-layer models for all the datasets tested. Ensembles of NADEs or RNADEs can be created inexpensively by combining models that share their parameters but differ in the ordering of the variables. These ensembles of autoregressive models obtain state-of-the-art statistical performances for several datasets. Finally, we demonstrate the application of RNADE to speech synthesis, and confirm that capturing the phone-conditional dependencies of acoustic features improves the quality of synthetic speech. Our model generates synthetic speech that was judged by naive listeners as being of higher quality than that generated by mixture density networks, which are considered a state-of-the-art synthesis techniqu

Deep Architectures for Articulatory Inversion

We implement two deep architectures for the acousticarticulatory inversion mapping problem: a deep neural network and a deep trajectory mixture density network. We find that in both cases, deep architectures produce more accurate predictions than shallow architectures and that this is due to the higher expressive capability of a deep model and not a consequence of adding more adjustable parameters. We also find that a deep trajectory mixture density network is able to obtain better inversion accuracies than smoothing the results of a deep neural network. Our best model obtained an average root mean square error of 0.885 mm on the MNGU0 test dataset. Index Terms: Articulatory inversion, deep neural network, deep belief network, deep regression network, pretrainin

A Deep and Tractable Density Estimator

The Neural Autoregressive Distribution Estimator (NADE) and its real-valued version RNADE are competitive density models of multidimensional data across a variety of domains. These models use a fixed, arbitrary ordering of the data dimen-sions. One can easily condition on variables at the beginning of the ordering, and marginalize out variables at the end of the ordering, however other inference tasks require approximate infer-ence. In this work we introduce an efficient pro-cedure to simultaneously train a NADE model for each possible ordering of the variables, by shar-ing parameters across all these models. We can thus use the most convenient model for each infer-ence task at hand, and ensembles of such models with different orderings are immediately available. Moreover, unlike the original NADE, our train-ing procedure scales to deep models. Empirically, ensembles of Deep NADE models obtain state of the art density estimation performance. 1

RNADE: The real-valued neural autoregressive density-estimator

We introduce RNADE, a new model for joint density estimation of real-valued vectors. Our model calculates the density of a datapoint as the product of one-dimensional conditionals modeled using mixture density networks with shared parameters. RNADE learns a distributed representation of the data, while having a tractable expression for the calculation of densities. A tractable likelihood allows direct comparison with other methods and training by standard gradient-based optimizers. We compare the performance of RNADE on several datasets of heterogeneous and perceptual data, finding it outperforms mixture models in all but one case.

Modelling acoustic feature dependencies with artificial neural networks: Trajectory-RNADE

Given a transcription, sampling from a good model of acous-tic feature trajectories should result in plausible realizations of an utterance. However, samples from current probabilis-tic speech synthesis systems result in low quality synthetic speech. Henter et al. have demonstrated the need to capture the dependencies between acoustic features conditioned on the phonetic labels in order to obtain high quality synthetic speech. These dependencies are often ignored in neural network based acoustic models. We tackle this deficiency by introducing a probabilistic neural network model of acoustic trajectories, trajectory RNADE, able to capture these dependencies. Index Terms — Speech synthesis, artificial neural net-works, acoustic modelling, RNADE, trajectory mode

Neural Autoregressive Distribution Estimation

We present Neural Autoregressive Distribution Estimation (NADE) models, which are neural network architectures applied to the problem of unsupervised distribution and density estimation. They leverage the probability product rule and a weight sharing scheme inspired from restricted Boltzmann machines, to yield an estimator that is both tractable and has good generalization performance. We discuss how they achieve competitive performance in modeling both binary and real-valued observations. We also present how deep NADE models can be trained to be agnostic to the ordering of input dimensions used by the autoregressive product rule decomposition. Finally, we also show how to exploit the topological structure of pixels in images using a deep convolutional architecture for NADE