Deep Discriminative to Kernel Generative Networks for Calibrated Inference

The fight between discriminative versus generative goes deep, in both the study of artificial and natural intelligence. In our view, both camps have complementary values. So, we sought to synergistically combine them. Here, we propose a methodology to convert deep discriminative networks to kernel generative networks. We leveraged the fact that deep models, including both random forests and deep networks, learn internal representations which are unions of polytopes with affine activation functions to conceptualize them both as generalized partitioning rules. We replace the affine function in each polytope populated by the training data with Gaussian kernel that results in a generative model. Theoretically, we derive the conditions under which our generative models are a consistent estimator of the corresponding class conditional density. Moreover, our proposed models obtain well calibrated posteriors for in-distribution, and extrapolate beyond the training data to handle out-of-distribution inputs reasonably. We believe this approach may be an important step in unifying the thinking and the approaches across the discriminative and the generative divide.