
2:00 pm
Purnamrita Sarkar  UT Austin
Some new results for streaming principal component analysis
HDSI Building, room 123
AbstractWhile streaming PCA (also known as Oja’s algorithm) was proposed about four decades ago and has roots going back to 1949, theoretical resolution in terms of obtaining optimal convergence rates has been obtained only in the last decade. However, we are not aware of any available distributional guarantees, which can help provide confidence intervals on the quality of the solution. In this talk, I will present the problem of quantifying uncertainty for the estimation error of the leading eigenvector using Oja's algorithm for streaming PCA, where the data are generated IID from some unknown distribution. Combining classical tools from the Ustatistics literature with recent results on highdimensional central limit theorems for quadratic forms of random vectors and concentration of matrix products, we establish a distributional approximation result for the error between the population eigenvector and the output of Oja's algorithm. We also propose an online multiplier bootstrap algorithm and establish conditions under which the bootstrap distribution is close to the corresponding sampling distribution with high probability. While there are optimal rates for the streaming PCA problem, they typically apply to the IID setting, whereas in many applications like distributed optimization, the data is generated from a Markov chain and the goal is to infer parameters of the limiting stationary distribution. If time permits, I will also present our nearoptimal finite sample guarantees which remove the logarithmic dependence on the sample size in previous work, where Markovian data is downsampled to get a nearly independent data stream.
Note: The speaker will also give an overview of her latest research.

10:00 am
Amanda Wilkens  University of Texas, Austin
TBA
Math 211B  Group Actions Seminar
AP&M 7321 and Zoom ID 967 4109 3409
Password: dynamics

11:00 am

3:30 pm
Karthik Ganapathy  University of Michigan
Equivariant commutative algebra in positive characteristic
Math 208: Seminar in Algebraic Geometry
APM 7321
AbstractIn the presence of a large group action, even nonnoetherian rings sometimes behave like noetherian rings. For example, Cohen proved that every symmetric ideal in the infinite variable polynomial ring is generated by finitely many polynomials (and their orbits under the infinite symmetric group). In this talk, I will give a brief introduction to equivariant commutative algebra where we systematically study such noetherian phenomena in infinite variable polynomial rings, and explain my work over fields of positive characteristic.

10:00 am
Koichi Oyakawa  Vanderbilt University
TBA
Math 211B  Group Actions Seminar
AP&M 7321 and Zoom ID 967 4109 3409
Password: dynamics

11:00 am

10:00 am
Christopher Shriver  University of Texas, Austin
TBA
Math 211B  Group Actions Seminar
APM 7321 and Zoom ID 967 4109 3409
Password: dynamics

10:00 am
Prof. Ferrán Valdez  National Autonomous University of Mexico, Morelia
TBA
Math 211B  Group Actions Seminar
AP&M 7321 and Zoom ID 967 4109 3409
Password: dynamics