36762: Algorithmic Robust Statistics

Course Information

Description
Outliers constitute a major challenge in any statistical estimation procedure: a tiny fraction of outliers in the training data could considerably change the algorithm’s output. As the dimensionality of the data increases, tackling outliers becomes increasingly more challenging. This course will be an introduction to the field of robust statistics, which aims to develop statistical methods that are robust to tiny contaminations in the data. Our primary focus will be on the statistical and computational challenges that arise when the dimensionality of the data increases. This course will be theory-oriented.

Logistics
Instructor: Ankit Pensia
Course number: 36762 (Mini course, Spring 2026)
Times: MW, 10 AM – 11:20 AM
Office hours: M 11:30 AM-12:30 PM (additional appointments are available by email request)
Link to Canvas


Schedule

Date Topic Reading
Jan 12 Introduction: Why robustness? [HR09, Ch. 1]
[DK23, Ch. 1]
Jan 14 Overview of classical robust statistics [HR09, Ch. 3]
[Hub64]
Jan 19 No class (Federal holiday)
Jan 21 Minimax rates - I [DK23, Ch. 1]
Jan 26 Minimax rates - II [DK23, Ch. 1]
Jan 28 Minimax rates - III [DK23, Ch. 1]
Feb 2 Efficient algorithms: Spectral certificates [DK23, Ch. 2]
Feb 4 Halving algorithm and stability [DK23, Ch. 2]
Feb 9 Stability and filtering algorithm [DK23, Ch. 2]
Feb 11 Universal filter and sample complexity [DK23, Ch. 3]
Feb 16 Linear regression, stochastic optimization, covariance estimation (in Frobenius norm) [DK23, Ch. 4 & 7]
Feb 18 Robust sparse estimation [DK23, Ch. 3]
Feb 23 SoS and robust covariance estimation (in operator norm) [DK23, Ch. 6]
Feb 26 Information-computation tradeoffs [DK23, Ch. 8]

References and Related Courses

  • [HR09] Book
    Peter Huber and Elevizio Ronchetti. Robust Statistics. 2009.
  • [DK23] Book
    Ilias Diakonikolas and Daniel M. Kane. Algorithmic High-Dimensional Robust Statistics. 2023. [Link]
  • [DK19] Survey
    Ilias Diakonikolas and Daniel M. Kane. Recent Advances in Algorithmic High-Dimensional Robust Statistics. 2019. [Link]
  • [Loh25] Survey
    Po-Ling Loh. A Theoretical Review of Modern Robust Statistics. 2025. [Link]
  • [Li25] Course
    Jerry Li. Algorithmic Robust Statistics. 2025. [Link]
  • [Loh24] Course
    Po-Ling Loh. Robust Statistics. 2024.
  • [Hub64] Paper
    Peter Huber. Robust Estimation of a Location Parameter. 1964. [Link]