Doctoral Thesis: Simulating Dynamical Systems from Data
The ever-increasing availability of data from dynamical systems offers an opportunity for automated data-driven decision-making in various domains. However, a significant barrier to realizing this potential is the issues inherent to these datasets: high-dimensionality, noise, sparsity, and confounding. In this thesis, we propose methods to exploit the richness in the structure of such datasets to overcome the above-mentioned problems while undertaking various inference tasks.
Central to these methods is a key factorization characterizing the function governing the dynamics. Specifically, we harness trajectories from different, yet related, dynamical systems. We posit that the function governing the dynamics of each individual system can be factorized into a linear combination of latent separable functions of the state and action. Crucially, these latent functions are shared across the different dynamical systems. This principled factorization structure provides guidance on how to devise theoretically sound methods that perform well empirically across a variety of tasks. These tasks include time series imputation and forecasting, change point detection, reinforcement learning, and trace-driven simulation in networked systems.
Exploiting the principled factorization structure has paved the way for the contributions we make in different tasks. First, we propose and analyze algorithms for mean and variance estimation and forecasting of time series with varying noise models, data missingness patterns, and assumptions on the factorization structure. These algorithms employ variants of the classical multivariate singular spectrum analysis (mSSA) algorithm and strengthen the link between time series analysis and Matrix/Tensor Completion. Second, we develop and analyze an algorithm for change point detection inspired by the factorization structure and based on the cumulative sum (CUSUM) statistic. This work extends the analysis of CUSUM statistics traditionally done for the setting of independent observations. Finally, we explore the potential gains of considering the factorization structure in simulating Markov Decision Processes (MDPs). We then build upon this approach to accommodate partially observed MDPs and more specifically trace-driven simulation in networked systems.
Thesis Supervisor: Prof. Devavrat Shah
- Date: Wednesday, November 8
- Time: 3:30 pm - 5:00 pm
- Category: Thesis Defense
- Location: E18-304