title: TraDE: A Simple Self-Attention-Based Density Estimator
abstract: We present TraDE, a self-attention-based architecture for auto-regressive density estimation with continuous and discrete valued  data. Our model is trained using a penalized maximum likelihood objective, which  ensures that samples from the density estimate resemble the training data distribution. The use of self-attention means that the model need not retain conditional sufficient statistics during the auto-regressive process beyond what is needed for each covariate. On standard tabular and image data  benchmarks, TraDE produces significantly better density estimates than existing approaches such as normalizing flow estimators and recurrent auto-regressive models. However log-likelihood on held-out data only partially reflects how useful these estimates are in real-world applications. In order to systematically evaluate density estimators, we present a suite of tasks such as regression using generated samples, out-of-distribution detection, and robustness to noise in the training data and demonstrate that TraDE works well in these scenarios. 
authors: Rasool Fakoor Pratik Anil Chaudhari Jonas Mueller Alex Smola
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