Progressive VAE Training on Highly Sparse and Imbalanced Data

In this paper, we present a novel approach for training a Variational Autoencoder (VAE) on a highly imbalanced data set. The proposed training of a high-resolution VAE model begins with the training of a low-resolution core model, which can be successfully trained on imbalanced data set. In subsequent training steps, new convolutional, upsampling, deconvolutional, and downsampling layers are iteratively attached to the model. In each iteration, the additional layers are trained based on the intermediate pretrained model - a result of previous training iterations. Thus, the resolution of the model is progressively increased up to the required resolution level. In this paper, the progressive VAE training is exploited for learning a latent representation with imbalanced, highly sparse data sets and, consequently, generating routes in a constrained 2D space. Routing problems (e.g., vehicle routing problem, travelling salesman problem, and arc routing) are of special significance in many modern applications (e.g., route planning, network maintenance, developing high-performance nanoelectronic systems, and others) and typically associated with sparse imbalanced data. In this paper, the critical problem of routing billions of components in nanoelectronic devices is considered. The proposed approach exhibits a significant training speedup as compared with state-of-the-art existing VAE training methods, while generating expected image outputs from unseen input data. Furthermore, the final progressive VAE models exhibit much more precise output representation, than the Generative Adversarial Network (GAN) models trained with comparable training time. The proposed method is expected to be applicable to a wide range of applications, including but not limited image impainting, sentence interpolation, and semi-supervised learning.