Deep Generative Modeling for Images and Time Series
Abstract:
Unsupervised learning is a fundamental problem in machine learning. Generative models provide a principled framework for unsupervised learning of data through the lens of probability. Deep generative models (DGMs) -- generative models parameterized by deep neural networks -- have excelled at modeling high-dimensional data and have been successful at several tasks such as synthetic data generation, representation learning, and time-series analysis. However, constructing DGMs is an inherently difficult task that requires an understanding of the entire data distribution, including the various factors of variation in the data. Recent rapid advances in this field have engendered several research challenges. In this thesis, we propose new DGMs and methods -- primarily focusing on image and time series data -- that seek to address these challenges.
In the first part of the thesis, we delve into DGMs for images. We begin by offering a fresh perspective on the problem of learning in implicit generative models by formulating it as minimizing the distance between characteristic functions of real and generated data distributions. Specifically, we propose to use a weighted distance between characteristic functions to train generative adversarial networks (GANs). We show that the proposed distance enjoys desirable theoretical properties when used as the discrepancy measure in GANs. We demonstrate experimentally that our proposed optimized characteristic function GAN (OCF-GAN) outperforms baseline GAN variants on a variety of unsupervised image generation benchmarks.
Although GANs possess the ability to generate high fidelity samples, generation quality is generally inconsistent for any given model and can vary dramatically between samples. To address this problem, we introduce discriminator gradient flow (DGflow), a "plug-in" technique that improves generated samples via the gradient flow of entropy-regularized f-divergences between the real and the generated data distributions. The gradient flow can be easily simulated by using the density-ratio estimate provided by the GAN discriminator. By refining inferior samples, DGflow avoids wasteful sample rejection used by some previous methods. Compared to existing works that focus on specific GAN variants, we propose a simple technique that makes our refinement approach applicable to other generative models, beyond GANs. Empirical results on multiple datasets demonstrate that DGflow leads to significant improvement in the quality of generated samples for a variety of generative models, outperforming the state-of-the-art sample refinement methods.
In the second part of the thesis, we shift our focus to DGMs for time series. Many complex time series can be effectively subdivided into distinct regimes that exhibit persistent dynamics. Discovering the switching behavior and the statistical patterns in these regimes is important for understanding the underlying dynamical system. We propose the recurrent explicit duration switching dynamical system (RED-SDS), a flexible model that is capable of identifying both state- and time-dependent switching dynamics. State-dependent switching is enabled by a recurrent state-to-switch connection and explicit duration count variables are used to improve the time-dependent switching behavior. We demonstrate how to perform efficient inference using a hybrid algorithm that approximates the posterior of the continuous states via an inference network and performs exact inference for the discrete switches and counts. Empirical results on multiple datasets demonstrate that RED-SDS achieves considerable improvement in time series segmentation and competitive forecasting performance against the state of the art.