Events
Department of Mathematics and Statistics
Texas Tech University
 | Monday
Sep. 11
|
| Algebra and Number Theory
No Seminar
|
Abstract: Stochastic gradient descent (SGD) is a scalable and memory-efficient optimization algorithm for large datasets and stream data, which has drawn a great deal of attention and popularity. The applications of SGD-based estimators to statistical inference such as interval estimation have also achieved great success. However, most of the related works are based on i.i.d. observations or Markov chains. When the observations come from a mixing time series, how to conduct valid statistical inference remains unexplored. As a matter of fact, the general correlation among observations imposes a challenge on interval estimation. Most existing methods may ignore this correlation and lead to invalid confidence intervals. In this paper, we propose a mini-batch SGD estimator for statistical inference when the data is $\phi$-mixing. The confidence intervals are constructed using an associated mini-batch bootstrap SGD procedure. Using "independent block'' trick from Yu (1994), we show that the proposed estimator is asymptotically normal, and its limiting distribution can be effectively approximated by the bootstrap procedure. The proposed method is memory-efficient and easy to implement in practice. Simulation studies on synthetic data and an application to a real-world dataset confirm our theory.
Please attend this week's Statistics seminar at 4 PM (UT-5) Monday via this Zoom link.
Meeting ID: 996 3242 1033
Passcode: 091601
This talk is focused on the behavior near the extinction time of solutions of systems of ordinary differential equations with a sublinear dissipation term. Suppose the dissipation term is a product of a linear operator $A$ and a positively homogeneous scalar function $H$ of a negative degree $-\alpha$. Then any solution with an extinction time $T_*$ behaves like $(T_*-t)^{1/\alpha}\xi_*$ as time $t\to T_*^-$, where $\xi_*$ is an eigenvector of $A$. The proof first establishes the asymptotic behaviors of the "Dirichlet" quotient and the normalized solution. They are then combined with a perturbation technique that requires the function $H$ to satisfy some pointwise H\"older-like condition. The result allows the higher order terms to be general and the nonlinear function $H$ to take very complicated forms.
Abstract. Based on ideas due to Scovel-Weinstein, I present a general framework for constructing fluid moment closures of the Vlasov-Poisson system that exactly preserve that system's Hamiltonian structure. Notably, the technique applies in any space dimension and produces closures involving arbitrarily-large finite collections of moments. After selecting a desired collection of moments, the Poisson bracket for the closure is uniquely determined. Therefore data-driven fluid closures can be constructed by adjusting the closure Hamiltonian for compatibility with kinetic simulations. The talk is based on a longer discussion in: arXiv:2308.02733.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room MATH 011 (basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
- Choice #2: join meeting using this link
Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 968 6501 7586
* Passcode: Applied