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 dimensions. 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 inference. In this work we introduce an efficient procedure to simultaneously train a NADE model for each possible ordering of the variables, by sharing parameters across all these models. We can thus use the most convenient model for each inference task at hand, and ensembles of such models with different orderings are immediately available. Moreover, unlike the original NADE, our training procedure scales to deep models. Empirically, ensembles of Deep NADE models obtain state of the art density estimation performance.
Our algorithm also bears similarity with denoising autoencoders @cite_5 trained using so-called masking noise''. There are two crucial differences however. The first is that our procedure corresponds to training on the average reconstruction of only the inputs that are missing from the input layer. The second is that, unlike denoising autoencoders, the NADE models that we train can be used as tractable density estimators.
@cite_5
2025768430
Previous work has shown that the difficulties in learning deep generative or discriminative models can be overcome by an initial unsupervised learning step that maps inputs to useful intermediate representations. We introduce and motivate a new training principle for unsupervised learning of a representation based on the idea of making the learned representations robust to partial corruption of the input pattern. This approach can be used to train autoencoders, and these denoising autoencoders can be stacked to initialize deep architectures. The algorithm can be motivated from a manifold learning and information theoretic perspective or from a generative model perspective. Comparative experiments clearly show the surprising advantage of corrupting the input of autoencoders on a pattern classification benchmark suite.