Information for Prospective Theory Students

I am interested in machine learning theory, economics and computation, and questions at the intersection of these fields. If you have little or no prior experience with theoretical research, I strongly recommend first taking one of my courses to build the necessary background. I typically teach a graduate-level learning theory course in the fall and an undergraduate algorithmic game theory course in the spring. Both undergraduate and graduate students are welcome to take my learning theory course (CMSC848P) in Fall 2026.

Email Guidelines

You are welcome to email me about possible research opportunities. But because of the volume of email I receive, I may not be able to respond to every inquiry. To help me understand your background and question, please:

1. Provide relevant background. Briefly describe your coursework or research experience in theoretical computer science, machine learning theory, algorithms, probability, or related areas of mathematics. Because my work is primarily theoretical, a list of programming languages or software skills alone is generally not informative.
2. State clearly what you are asking. For example, indicate whether you are asking about taking a course, joining a research project, or discussing a specific open problem.
3. Build the necessary background first. If you are interested in machine learning theory research but have not yet studied its foundations, my usual recommendation will be to take a learning theory course or learn comparable material independently. A shared foundation is necessary for a productive conversation about research.

Below, I list several open questions that I find interesting. If you have made concrete progress on any of them or have a specific idea for approaching one, please feel free to contact me.

Open Questions: Precision and Recall Learning

For my precision and recall learning paper (with Lee Cohen, Yishay Mansour, and Shay Moran, NeurIPS 2025), there are a few interesting open questions:

1. Finite input space: Note that the negative result in this paper relies on the assumption that the input space X is infinite and each input has been observed at most once in the training data. If the input space X is finite, what will the results look like? Then the sample complexity will depend on the size of |X|. Or other assumptions such that for some x I can observe the same input more than once and thus get two different answers/labels for this same input.
2. Non-uniform label distribution: What if the label in the training data is not sampled from a uniform distribution, i.e., v_i is not from Unif(g*(x_i))?
3. Pairwise comparison data: If we get pairwise-comparison-type data for post-training, can we learn precision and recall simultaneously?

The first question is more concrete, while the other two require some additional modeling.

Related Papers

1. Density estimation
   This paper is technically related to density estimation.
2. Pairwise comparison data
   For pairwise-comparison-type of data, it has been discussed in this paper.
3. Non-uniform distribution
   For non-uniform distribution, there is one slightly related paper.

Machine Learning Theory Basics

For the basics of machine learning theory, I usually teach a learning theory course in the fall. But I only have handwritten notes. You can refer to lecture notes by Nika Haghtalab or the textbook by Shai and Shai.