Embedded-model flows: Combining the inductive biases of model-free deep learning and explicit probabilistic modeling

Gianluigi Silvestri, Emily Fertig, Dave Moore, Luca Ambrogioni

Keywords: Normalizing Flows, Probabilistic model, Probabilistic programming, Generative modeling, Variational Inference

Abstract: Normalizing flows have shown great success as general-purpose density estimators. However, many real world applications require the use of domain-specific knowledge, which normalizing flows cannot readily incorporate. We propose embedded-model flows (EMF), which alternate general-purpose transformations with structured layers that embed domain-specific inductive biases. These layers are automatically constructed by converting user-specified differentiable probabilistic models into equivalent bijective transformations. We also introduce gated structured layers, which allow bypassing the parts of the models that fail to capture the statistics of the data. We demonstrate that EMFs can be used to induce desirable properties such as multimodality and continuity. Furthermore, we show that EMFs enable a high performance form of variational inference where the structure of the prior model is embedded in the variational architecture. In our experiments, we show that this approach outperforms a large number of alternative methods in common structured inference problems.

One-sentence Summary: We introduce bijective transformations that embed domain-specific inductive biases in Normalizing Flow architectures.