Embedded-model flows: Combining the inductive biases of model-free deep learning and explicit probabilistic modeling
This addresses the need for combining model-free deep learning with explicit probabilistic modeling in real-world applications, offering a novel hybrid approach for researchers and practitioners in machine learning.
The paper tackles the problem of incorporating domain-specific knowledge into normalizing flows, which are general-purpose density estimators, by proposing embedded-model flows (EMF) that alternate general transformations with structured layers derived from probabilistic models. The result is a method that outperforms state-of-the-art approaches in structured inference tasks, enabling properties like multimodality and hierarchical coupling.
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, hierarchical coupling 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 state-of-the-art methods in common structured inference problems.