Generative Max-Mahalanobis Classifiers for Image Classification, Generation and More

Joint Energy-based Model (JEM) of [11] shows that a standard softmax classifier can be reinterpreted as an energy-based model (EBM) for the joint distribution \(p(\boldsymbol{x}, y)\); resulting optimized to improve calibration, robustness and out-of-distribution detection, while generating samples rivaling quality recent GAN-based approaches. However, JEM exploits is inherently discriminative its latent feature space not well formulated probabilistic distributions, which may hinder potential image generation incur training instability. We hypothesize generative classifiers, such Linear Discriminant Analysis (LDA), might more suitable since classifiers data process explicitly. This paper therefore investigates LDA classification generation. In particular, Max-Mahalanobis Classifier (MMC) [30], special case LDA, fits our goal very well. show Generative MMC (GMMC) trained discriminatively, generatively or jointly Extensive experiments on multiple datasets GMMC achieves state-of-the-art performances, outperforming in adversarial detection by significant margin. Our source code available at https://github.com/sndnyang/GMMC.