Ilias Diakonikolas wins 2026 Gödel Prize for breakthrough work in robust high-dimensional learning
University of Wisconsin–Madison Computer Sciences professor Ilias Diakonikolas has received the 2026 Gödel Prize, one of the highest honors in theoretical computer science, for transformational work in robust high-dimensional learning – the study of how algorithms can learn reliably from large, complex datasets even when some of the data has been corrupted.
The award recognizes the paper Robust Estimators in High Dimensions without the Computational Intractability, coauthored by Diakonikolas, Gautam Kamath, Daniel Kane, Jerry Li, Ankur Moitra, and Alistair Stewart. First presented at FOCS 2016 and later published in the SIAM Journal on Computing in 2019, the work showed for the first time that a broad class of high-dimensional statistical problems can be solved both efficiently and robustly, even when part of the data has been arbitrarily corrupted. The paper helped establish a new research area at the intersection of theoretical computer science, machine learning, and statistics.
The Gödel Prize is awarded annually by ACM SIGACT and the European Association for Theoretical Computer Science and is widely regarded as one of the field’s most prestigious honors.
“We are all thrilled to learn that our colleague Ilias Diakonikolas is a recipient of this year’s Gödel Prize,” said computer science professor Jin-Yi Cai, who received the Gödel Prize in 2021 and is the only other UW–Madison researcher to receive the honor. “Ilias has done tremendous work in designing computationally efficient algorithms for fundamental problems in statistics and machine learning, and his work is being recognized at the highest level — a great tribute to his groundbreaking contributions.”
A breakthrough in robust high-dimensional learning
At its core, the paper tackled a fundamental problem in statistics and machine learning: how to design algorithms that remain reliable even when some of the data they receive is corrupted.
For decades, researchers faced a basic tradeoff. In high-dimensional settings — where datasets may contain thousands or even millions of variables — algorithms could be computationally efficient, or they could be robust, but not both.
Imagine trying to calculate the average height of people in a city, but some of the data has been tampered with and includes impossible values — people are 500 feet tall, for example. In such low-dimensional settings (simple data), statisticians already had tools to manage this kind of corruption. But in modern high-dimensional datasets – such as medical, biological, or financial data — those approaches become computationally impossible to run in any reasonable time.
Diakonikolas and his coauthors showed that this tradeoff was not inevitable. Their paper introduced the first efficient algorithms with dimension-independent accuracy guarantees for several central robust estimation problems in high dimensions, along with a broader framework for detecting and filtering corrupted data. In practical terms, the work demonstrated that reliable learning from corrupted high-dimensional data could be both mathematically rigorous and computationally feasible.
“This work started from a very basic question,” Diakonikolas said. “Can we design algorithms that remain reliable even when part of the data is corrupted without paying an overwhelming computational price? For a long time, the prevailing view was that this should not be possible in high dimensions. What this paper showed is that it is.”
The implications reach far beyond a single theoretical problem. Real-world datasets often contain corrupted or unreliable entries, whether because of measurement errors, outliers, or deliberate manipulation. The paper laid the groundwork for learning reliably from corrupted high-dimensional data and later influenced research on machine learning systems that must remain robust in imperfect real-world environments.
Lasting impact on the field
The work helped launch what is now widely recognized as algorithmic high-dimensional robust statistics, a major research area at the intersection of theoretical computer science, machine learning, and statistics.
Over the past decade, its influence has extended well beyond the original problem, shaping later developments in latent variable models, high-dimensional statistics, differential privacy, optimization-based methods, and robust machine learning, including work on defenses against data poisoning attacks.
“What has been especially rewarding is seeing the work grow into a much broader field,” Diakonikolas said. “Ideas that began in one theoretical problem ended up influencing research in statistics, machine learning, privacy, and optimization.”
He later coauthored the graduate textbook Algorithmic High-Dimensional Robust Statistics, which helped consolidate the field and has become a widely used resource on the subject.
Diakonikolas joined UW–Madison in 2019. He is the Stephen C. Kleene Professor and Sheldon B. Lubar Professor in the Department of Computer Sciences, where his research focuses on the algorithmic foundations of machine learning and statistics.
The Gödel Prize adds to a series of recent honors recognizing his contributions to robust statistics and theoretical machine learning. In 2025, he received the 2024 Grace Murray Hopper Award, and earlier in 2026 he was named a Guggenheim Fellow.