Events
Department of Mathematics and Statistics
Texas Tech University
Stochastic optimization has become a cornerstone of modern data analysis, powering large-scale statistical estimation and machine learning. While computational efficiency has been extensively studied, statistical inference, such as quantifying uncertainty in estimates obtained from stochastic algorithms, remains less explored. In this talk, I will present two related projects that integrate statistical inference into batch-based stochastic optimization algorithms. The first project considers the classical setting where data are independent and identically distributed (i.i.d.). We establish a Central Limit Theorem for batched stochastic gradient descent (SGD) algorithms, which enables the construction of valid confidence intervals. The second project extends these ideas to dependent data, such as time series and reinforcement learning trajectories. A key contribution is to show that in the presence of dependence, batch SGD is essential for valid statistical inference, in contrast to vanilla SGD. Together, these projects establish a unified framework for scalable stochastic optimization with statistical guarantees and advance both the theoretical foundations and practical applications of big data analytics.
Mathematical models provide valuable insight into how and why things change. If we build models in terms of observed behaviors, we can analyze how these behaviors impact overall outcomes. If we incorporate factors that we expect to change or vary, we can explore theoretical scenarios under novel conditions. In this presentation, I will focus on how we apply such modelling principles in mathematical biology, with an emphasis on ecological interactions and insect populations. Insects are highly prevalent and directly impact people in a variety of ways; they can be beneficial (providing services like pollination or biological control) or detrimental (spreading diseases or acting as pests). In either case, mathematical models provide valuable information about what drives those impacts and how we might expect them to change with management choices or weather patterns. I will also briefly discuss my teaching and service experience in the department.