Adventures in PCA for Heterogeneous Data: Optimal Weights and Rank Estimation

Abstract: PCA is a textbook method for discovering underlying low-rank signals in noisy high-dimensional data and is ubiquitous throughout machine learning, data science, and engineering. But what happens to this workhorse technique when the data are heterogeneous? This talk presents recent progress on understanding (and improving) PCA for settings where the data are high-dimensional and of heterogeneous quality, i.e., some samples are noisier than others (the noise is samplewise heteroscedastic). Data with heterogeneous quality are common in modern data analysis (e.g., in genomics, medical imaging, astronomy, and RADAR to name just a few). We will see some surprising discoveries (inverse noise variance weighting is suboptimal!) as well as some new PCA methods that rigorously account for the noise heterogeneity.

Short Bio: David Hong is an Assistant Professor in the Department of Electrical and Computer Engineering at the University of Delaware, where he is also a Resident Faculty of the Data Science Institute. Previously, he was an NSF Postdoctoral Research Fellow in the Department of Statistics and Data Science at the University of Pennsylvania. He completed his PhD in the Department of Electrical Engineering and Computer Science at the University of Michigan, where he was an NSF Graduate Research Fellow. He also spent a summer as a Data Science Graduate Intern at Sandia National Labs.

*** The event will take place in a hybrid format. The location for in-person attendance will be room 3427 EECS. Attendance will also be available via Zoom.

Join Zoom Meeting: https://umich.zoom.us/j/93679028340

Meeting ID: 936 7902 8340

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Zoom Passcode information is available upon request to Kristi Rieger ([email protected]).