SDS Seminar Series – Dr. Purna Sarkar

Mar

2024

2:00 pm – 3:00 pm

Cost: Free

In Person (view details)

Some New Results for Streaming Principal Component Analysis

Description

The Spring 2024 SDS Seminar Series continues on March 29th from 2:00 p.m. to 3:00 p.m. with Dr. Purna Sarkar (Statistics and Data Sciences, University of Texas at Austin). This event is in-person.

Title: Some New Results for Streaming Principal Component Analysis

Abstract: Streaming PCA, also known as Oja's algorithm, with roots going back to 1949, has attracted much attention in Statistics and Computer Science in the last decade. In this talk, I will discuss two of our works that consider this problem under slight departures from the setup considered widely in the literature.

Our first work looks at data streams generated from a Markov chain. While streaming PCA is typically analyzed under the IID data model, in many applications like distributed optimization, data points are sampled from a Markov chain and, therefore, are dependent. The naive approach of dropping data leads to a suboptimal rate. We use a novel linearization argument to remove the logarithmic dependence on the number of samples n.

Typically, the analysis of Oja's algorithm assumes that the effective rank of the covariance matrix is much smaller than n. Our second work examines online sparse PCA, where the effective rank is comparable to n. This differs from previously studied settings because the Oja vector does not concentrate on the true population eigenvector. Here, we show that a simple thresholding yields a consistent estimate of the population eigenvector. Both are joint works with Syamantak Kumar.