A Deep and Tractable Density Estimator
This work addresses the inference flexibility problem in density estimation for researchers and practitioners in machine learning, representing an incremental improvement over existing NADE models.
The paper tackles the limitation of fixed ordering in Neural Autoregressive Distribution Estimators (NADE) by introducing a method to train models for all possible orderings with shared parameters, enabling flexible inference and ensembles. This approach achieves state-of-the-art performance in density estimation, as demonstrated empirically.
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.