# CAREER: Statistical Inference in the Presence of Group Actions: Theory, Method, and Application

> **NSF 01002728DB NSF RESEARCH & RELATED ACTIVIT** · University of Pennsylvania (PA) · $450,000

## Abstract

In the rapidly expanding field of data science, the ability to understand group actions in data analysis is pivotal for a broad spectrum of scientific tasks. In mathematical terms, a “group” is a collection of elements combined with an operation that links any two elements to form a third, adhering to closure, associativity, identity, and invertibility principles. A “group action” involves applying elements of a group to another set’s elements, transforming them in structured ways, such as through rotations or reflections. These transformations are crucial in many data processing applications, including cryo-electron microscopy (cryo-EM), image registration, and multi-reference alignment. Each observation in these problems involves a common, unknown signal and an unknown group element, with the primary goal being to infer both the signal and the group elements accurately. This project aims to significantly advance statistical understanding and develop effective methodologies for handling data influenced by group actions. The wide existence of such data ensures that the progress we make towards our objectives will have a great impact not only on the statistics and machine learning community but also on a much broader scientific community, including fields such as structural biology, computer vision, and signal processing. This project will have educational outcomes that result in curriculum development, teaching, and outreach activities, including activities to K-12 students t

## Key facts

- **NSF award ID:** 2440180
- **Awardee organization:** University of Pennsylvania (PA)
- **SAM.gov UEI:** GM1XX56LEP58
- **PI:** Ye Zhang
- **Primary program:** 01002728DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** CAREER-Faculty Erly Career Dev
- **Estimated total:** $450,000
- **Funds obligated:** $90,000
- **Transaction type:** Continuing Grant
- **Period:** 07/01/2025 → 06/30/2030

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2440180

## Citation

> US National Science Foundation, Award 2440180, CAREER: Statistical Inference in the Presence of Group Actions: Theory, Method, and Application. Retrieved via AI Analytics 2026-06-06 from https://api.ai-analytics.org/grant/nsf/2440180. Licensed CC0.

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