Masked Autoregressive Flow for Density Estimation

Autoregressive models are among the best performing neural density estimators. We describe an approach for increasing the flexibility of an autoregressive model, based on modelling the random numbers that the model uses internally when generating data. By constructing a stack of autoregressive models, each modelling the random numbers of the next model in the stack, we obtain a type of normalizing flow suitable for density estimation, which we call Masked Autoregressive Flow. This type of flow is closely related to Inverse Autoregressive Flow and is a generalization of Real NVP. Masked Autoregressive Flow achieves state-of-the-art performance in a range of general-purpose density estimation tasks.

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Results from the Paper


Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Density Estimation BSDS300 MADE MoG Log-likelihood 153.71 # 2
Density Estimation CIFAR-10 MAF Log-likelihood 3049 # 1
Density Estimation CIFAR-10 (Conditional) MAF Log-likelihood 3058 # 1
Density Estimation MNIST MADE MoG Log-likelihood -1038.5 # 1
Density Estimation MNIST (Conditional) MADE MoG Log-likelihood -1030.3 # 1
Density Estimation UCI HEPMASS MADE MoG Log-likelihood -15.15 # 1
Density Estimation UCI MINIBOONE MADE MoG Log-likelihood -12.27 # 1
Density Estimation UCI POWER MADE MoG Log-likelihood 0.4 # 5

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