Training Normalizing Flows with the Information Bottleneck for Competitive Generative Classification
This work addresses the problem of improving generative classifiers for researchers and practitioners in machine learning by offering a novel method to enhance uncertainty quantification without sacrificing accuracy, though it is incremental as it builds on existing IB and normalizing flow frameworks.
The authors tackled the challenge of applying the Information Bottleneck (IB) objective to train normalizing flows, which are inherently information-preserving, by developing IB-INNs that introduce controlled information loss to balance generative capabilities and classification accuracy. They found that this approach improves uncertainty quantification and out-of-distribution detection while achieving accuracy close to standard classifiers, with empirical results showing favorable uncertainty estimates compared to conventional methods.
The Information Bottleneck (IB) objective uses information theory to formulate a task-performance versus robustness trade-off. It has been successfully applied in the standard discriminative classification setting. We pose the question whether the IB can also be used to train generative likelihood models such as normalizing flows. Since normalizing flows use invertible network architectures (INNs), they are information-preserving by construction. This seems contradictory to the idea of a bottleneck. In this work, firstly, we develop the theory and methodology of IB-INNs, a class of conditional normalizing flows where INNs are trained using the IB objective: Introducing a small amount of {\em controlled} information loss allows for an asymptotically exact formulation of the IB, while keeping the INN's generative capabilities intact. Secondly, we investigate the properties of these models experimentally, specifically used as generative classifiers. This model class offers advantages such as improved uncertainty quantification and out-of-distribution detection, but traditional generative classifier solutions suffer considerably in classification accuracy. We find the trade-off parameter in the IB controls a mix of generative capabilities and accuracy close to standard classifiers. Empirically, our uncertainty estimates in this mixed regime compare favourably to conventional generative and discriminative classifiers.