GAT–GMM: Generative Adversarial Training for Gaussian Mixture Models

Generative adversarial networks (GANs) learn the distribution of observed samples through a zero-sum game between two machine players, generator and discriminator. While GANs achieve great success in learning complex image, sound, text data, they perform suboptimally multimodal distribution-learning benchmarks such as Gaussian mixture models (GMMs). In this paper, we propose Adversarial Training for Mixture Models (GAT-GMM), minimax GAN framework GMMs. Motivated by optimal transport theory, design GAT-GMM using random linear softmax-based quadratic discriminator architecture, which leads to nonconvex concave optimization problem. We show that gradient descent ascent (GDA) method converges an approximate stationary point benchmark case symmetric, well-separated Gaussians, further recovers true parameters underlying GMM. discuss application proposed GMMs distributed federated setting, where widely used expectation-maximization (EM) algorithm can incur computational communication costs. On other hand, provides scalable approach GDA still solve problem without incurring extra computation numerically support our theoretical results performing experiments is successful centralized tasks outperform standard EM-type algorithms setting.