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Numerous applications of machine learning involve representing probabilitydistributions over high-dimensional data. We propose autoregressive quantileflows, a flexible class of normalizing flow models trained using a novelobjective based on proper scoring rules. Our objective does not requirecalculating computationally expensive determinants of Jacobians during trainingand supports new types of neural architectures, such as neural autoregressiveflows from which it is easy to sample.  We leverage these models in quantile flow regression, an approach thatparameterizes predictive conditional distributions with flows, resulting inimproved probabilistic predictions on tasks such as time series forecasting andobject detection. Our novel objective functions and neural flowparameterizations also yield improvements on popular generation and densityestimation tasks, and represent a step beyond maximum likelihood learning offlows.

Autoregressive Quantile Flows for Predictive Uncertainty Estimation