Density estimation using deep generative neural networks

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Density estimation is among the most fundamental problems in statistics. It is notoriously difficult to estimate the density of high-dimensional data due to the “curse of dimensionality.” Here, we introduce a new general-purpose density estimator based on deep generative neural networks. By modeling data normally distributed around a manifold of reduced dimension, we show how the power of bidirectional generative neural networks (e.g., cycleGAN) can be exploited for explicit evaluation of the data density. Simulation and real data experiments suggest that our method is effective in a wide range of problems. This approach should be helpful in many applications where an accurate density estimator is needed.