Mon, Oct 2 2023
  • 2:00 pm
    Purnamrita Sarkar - UT Austin
    Some new results for streaming principal component analysis

    HDSI Building, room 123

     

    While 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 U-statistics literature with recent results on high-dimensional 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 near-optimal 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.

Tue, Oct 3 2023
  • 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

Tue, Oct 10 2023
Fri, Oct 13 2023
  • 3:30 pm
    Karthik Ganapathy - University of Michigan
    Equivariant commutative algebra in positive characteristic

    Math 208: Seminar in Algebraic Geometry

    APM 7321

     

    In the presence of a large group action, even non-noetherian 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.

Thu, Oct 19 2023
  • 10:00 am
    Koichi Oyakawa - Vanderbilt University
    TBA

    Math 211B - Group Actions Seminar

    AP&M 7321 and Zoom ID 967 4109 3409
    Password: dynamics

Tue, Oct 24 2023
Thu, Oct 26 2023
  • 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

Thu, Nov 30 2023
  • 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