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