Error analyses of deep generative models

Deep generative models have emerged as contemporary nonparametric statistical tools that effectively addresses the “curse of dimensionality” problem, which refers to the exponential increase in sample complexity associated with the growth of the data dimension, for learning high-dimensional data distributions. Instead of directly learning the functional form of the probability density functions, deep generative models learn how to generate samples from the complex target data distributions. They have become widely used for high-dimensional machine learning tasks, such as the generation of images, speech, and other complex data. Despite their remarkable empirical successes, the theoretical foundations of deep generative models are not yet fully established. This dissertation aims to bridge this gap by exploring the statistical properties and function approximation of deep neural networks in deep generative models.