Events
Department of Mathematics and Statistics
Texas Tech University
 | Monday
Oct. 23
|
| Algebra and Number Theory
No Seminar
|
Estimation of the optimal treatment regime is an important problem with applications in various fields including precision medicine, finance, engineering, and policy learning. The majority of the literature has focused on a mean-optimal treatment regime, which optimizes the average outcome of interest in the potential population. However, the mean-optimal treatment regime is not reliable when the outcome distribution is not symmetric. The quantile-optimal treatment regime, which optimizes some desired quantile of the potential outcome instead of the mean, may occasionally be of interest. For the estimation of quantile-optimal treatment regimes, we propose a flexible penalized single-index model that uses polynomial splines for the estimation of link functions and a nonconvex penalty for selecting the important variables from high-dimensional baseline covariates. We discuss the asymptotic properties of the proposed estimators. Because spline estimators often lack an asymptotic distribution, we consider a spline-backfitted kernel estimator for which the asymptotic distribution can be obtained. As a result, we may use simultaneous confidence bands to quantify the variability associated with the estimated quantile optimal treatment regime. We demonstrate the usefulness of the proposed methodology using simulations and real data analysis. This is a joint work with Indrabati Bhattacharya (FSU)
Please attend this week's Statistics seminar at 4 PM (UT-5) Monday via this Zoom link.
Meeting ID: 917 1422 3687
Passcode: 690937
In this session, we finish making the connections between matrix cocycles, and learning theory -- the two independent topics that have been covered in the past talks. The theory of matrix cocycles provides a foundation for random matrix theory in Ergodic theory - the measure theoretic study of deterministic dynamical systems. The foundational works in this field establish the existence of Lyapunov exponents and stable / unstable splittings, for general matrix cocycles. Matrix cocycles appear naturally in a wide variety of physical phenomenon. The performance of a learning technique can be modelled using a cocycle, and we demonstrate the application of this theory in establishing the limits of learning.
The Virasoro groups are a family of central extensions of ${\rm Diff}^+(S^1)$ by the circle group $\bf T$. In this talk I will discuss recent work, joint with Yu Leon Liu and Christoph Weis, constructing these groups by beginning with a lift of the first Pontrjagin class to “off-diagonal” differential cohomology, then transgressing it to obtain a central extension. Along the way, I will discuss what the Virasoro extensions are and how to recognize them; a brief introduction to differential cohomology; and lifts of characteristic classes to differential cohomology.
We review a form of the Gauss-Bonnet theorem on a four-manifold with corners for which the curvatures have nice conformal transformation properties. A natural question of Escobar-Yamabe type is: can one make a conformal change so that all of the Gauss-Bonnet integrands vanish except on the corner, and are there constant? We answer this in the affirmative for the half-ball in four-space. This is joint work with several authors.
Abstract. Semi-Lagrangian (SL) schemes are known as a major numerical tool for solving transport equations with many advantages and have been widely deployed in the fields of computational fluid dynamics, plasma physics modeling, numerical weather prediction, among others. In this work, we develop a novel machine learning-assisted approach to accelerate the conventional SL finite volume (FV) schemes. The proposed scheme avoids the expensive tracking of upstream cells but attempts to learn the SL discretization from the data by incorporating specific inductive biases in the neural network, significantly simplifying the algorithm implementation, and leading to improved efficiency. In addition, the method delivers sharp shock transitions and a level of accuracy that would typically require a much finer grid with traditional transport solvers. Furthermore, we present a multi-fidelity version of the method which is designed for scenarios where there is an abundance of low-fidelity data and a limited amount of high-fidelity data. Numerical tests demonstrate the effectiveness and efficiency of the proposed method.
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
 | Wednesday
Oct. 25
7 PM
MA 108
|
| Mathematics Education
Math Circle
Álvaro Pámpano
Department of Mathematics and Statistics, Texas Tech University
|
Math Circle Fall Poster
abstract noon CDT (UT-5)