The Dual Information Bottleneck (2006.04641v1)

Abstract: The Information Bottleneck (IB) framework is a general characterization of optimal representations obtained using a principled approach for balancing accuracy and complexity. Here we present a new framework, the Dual Information Bottleneck (dualIB), which resolves some of the known drawbacks of the IB. We provide a theoretical analysis of the dualIB framework; (i) solving for the structure of its solutions (ii) unraveling its superiority in optimizing the mean prediction error exponent and (iii) demonstrating its ability to preserve exponential forms of the original distribution. To approach large scale problems, we present a novel variational formulation of the dualIB for Deep Neural Networks. In experiments on several data-sets, we compare it to a variational form of the IB. This exposes superior Information Plane properties of the dualIB and its potential in improvement of the error.

• The paper introduces the dualIB framework that reformulates the traditional Information Bottleneck to improve prediction accuracy.
• It modifies the KL-divergence order and leverages exponential family properties to create a robust, parametric representation model.
• Empirical tests confirm that dualIB achieves more compressed and informative representations than classical IB on standard datasets.

The Dual Information Bottleneck

The paper "The Dual Information Bottleneck" introduces a novel framework for optimal representation learning, termed the Dual Information Bottleneck (dualIB). The dualIB addresses and resolves several limitations inherent in the traditional Information Bottleneck (IB) framework, most notably its non-parametric nature and disregard for observed features of data in prediction tasks.

Context and Motivation

The IB method, extensively utilized in various domains such as vision, neuroscience, and natural language processing, is a cornerstone for learning representations that efficiently encode relevant information about outputs while discarding unnecessary input features. However, the IB approach often neglects the underlying parametric structure of data and assumes comprehensive access to joint probability distributions, which can complicate its application to unseen data or scaled tasks. The dualIB framework considers these nuances by shifting the focus during problem definition and incorporating prediction optimization over unseen examples.

Core Contributions

1. DualIB Formulation: The dualIB reformulates the IB problem from a prediction perspective, introducing changes that revolve around the dual distortion problem. It modifies the KL-divergence order in the distortion measure, incorporating a geometric mean that allows it to better target prediction accuracy over unseen data.
2. Theoretical Insights: Theoretical analysis of the dualIB framework leads to a set of self-consistent equations similar to those of the original IB but distinct in encoder updates. These developments uncover theoretical advantages of the dualIB in terms of optimizing mean prediction error exponents and preserving sufficient statistics under exponential family distributions.
3. Exponential Family Solutions: For data exhibiting exponential family structures, the dualIB naturally recognizes and retains these structural parameters in the learned representations. This is an enhancement over the IB, which otherwise treats all inputs in a non-parametric fashion, ignoring parametric configurations where pertinent.
4. Variational Formulation: To enable practical application, especially for high-dimensional datasets, a novel variational form of dualIB is introduced, allowing its implementation using Deep Neural Networks (DNNs). This form facilitates experiments comparing variants of dualIB to the classical IB when applied to real-world datasets.

Empirical Evaluation

Experiments conducted using the proposed variational dualIB framework on standard datasets, such as FashionMNIST and CIFAR10, confirm the theoretical expectations. They illustrate that models trained with dualIB achieve more robust and compressed representations, offering more informative performance in the prediction phase compared to traditional IB-trained models. The results on CIFAR10, however, suggest that the noise model selection for dualIB could significantly influence its performance relative to the VIB, indicating challenges for implementation accuracy in more complex datasets like CIFAR100.

Implications and Future Directions

The dualIB's theoretical and empirical advantages suggest a significant potential for enhancing representation learning, with especially promising applications in domains where prediction accuracy and data-specific features are crucial. The framework also implies a broader effort towards unifying representation learning with predictive modeling by utilizing data features more explicitly. Future exploration could involve extending dualIB to diverse datasets and refining noise models, as well as integrating it with other machine learning paradigms where prediction reliability over unseen samples is critical.

In conclusion, the dual Information Bottleneck presents a step forward in balancing accuracy and complexity within representation learning, offering a robust alternative to the IB framework with promising implications for future AI models and applications.