Events
Department of Mathematics and Statistics
Texas Tech University
With the availability of information in the big data era, the training data and testing data could come from different sources, and their distributions are not necessarily identical. We consider the scenario that the training data consists of observations from multiple distributions, and we aim to train a classifier that can be applied to the classification task under the target distribution. The contribution of this work is twofold. First, we discover a phase phenomenon of the minimax optimal convergence rate of the classification problem, which depends on the smoothness of the distributions of the training and testing data. Second, we propose a computationally efficient and data-driven nearest neighbor classifier that can achieve the optimal rate (up to a logarithm factor). Simulation studies on synthetic data and application to automobile market data confirm our theory.We will first introduce some basic facts about the energy of a condenser $(D,K)$ in $\mathbb{R}^{n}$. Then we will consider a variation of $D$ described via a family of smooth domains $D_{t}$, $t\in(0,1)$, whose boundaries $\partial D_{t}$ are level sets of a $C^{2}$ function $V$. We will show that, if $V$ is subharmonic, then the energy of the condenser $(D_{t},K)$ is a concave function of $t$, and we will characterize the cases where this function is affine.We show that the following five categories are equivalent: (1) the opposite category of commutative von Neumann algebras; (2) compact strictly localizable enhanced measurable spaces; (3) measurable locales; (4) hyperstonean locales; (5) hyperstonean spaces. This result can be seen as a measure-theoretic counterpart of the Gelfand duality between commutative unital C*-algebras and compact Hausdorff topological spaces.  | Wednesday
Nov. 4
3:00 PM
Online
|
| Algebra and Number Theory
No Seminar
|
Using the singular cohesion one can formulate orbifold geometry, internal to infinity-toposes. In this talk our goal is to define basis notions related to this construction and discuss their properties. We introduce a (2,1)-category that is better suited for globally equivariant homotopy theory, “the global indexing category”, which consists of delooping groupoids of compact Lie groups. Its full subcategory of finite, connected, 1-truncated objects captures singular quotients, and homotopy sheaves on this subcategory valued in a smooth infinity-topos are naturally equipped with a cohesion that reveals various perspectives on singularities.Watch online at 2 PM Friday the 6th via this Zoom link. Passcode 486269