KNIFE: Kernelized-Neural Differential Entropy Estimation

Mutual Information (MI) has been widely used as a loss regularizer for training neural networks. This has been particularly effective when learn disentangled or compressed representations of high dimensional data. However, differential entropy (DE), another fundamental measure of information, has not found widespread use in neural network training. Although DE offers a potentially wider range of applications than MI, off-the-shelf DE estimators are either non differentiable, computationally intractable or fail to adapt to changes in the underlying distribution. These drawbacks prevent them from being used as regularizers in neural networks training. To address shortcomings in previously proposed estimators for DE, here we introduce KNIFE, a fully parameterized, differentiable kernel-based estimator of DE. The flexibility of our approach also allows us to construct KNIFE-based estimators for conditional (on either discrete or continuous variables) DE, as well as MI. We empirically validate our method on high-dimensional synthetic data and further apply it to guide the training of neural networks for real-world tasks. Our experiments on a large variety of tasks, including visual domain adaptation, textual fair classification, and textual fine-tuning demonstrate the effectiveness of KNIFE-based estimation. Code can be found at https://github.com/g-pichler/knife.