I have begun life as a postdoc. This semester, I am planning to focus on using optimization and linear algebra strategies to design new algorithms. These (ideally efficient) algorithms would be for various statistical inference tasks under different constraints. In the cases where efficient algorithms cannot be obtained, can we prove computational lower bounds? Are there computational-statistical gaps for certain statistical problems?

Also, we are working on the Summer 2023 syllabus for http://naijacoder.org, which might incorporate some of the aforementioned topics.

Some References

[1] Otto Bretscher. Linear Algebra with Applications (4th Edition). 2009.

[2] Stephen Boyd and Lieven Vandenberghe. Convex Optimization. Cambridge University Press, 2004.

[3] Noah Fleming, Pravesh Kothari, Toniann Pitassi. Semialgebraic Proofs and Efficient Algorithm Design. In Foundations and Trends in Theoretical Computer Science, Volume 14, Issue 1-2, 2019.

[4] Daniel Hsu. Computational Linear Algebra. https://www.cs.columbia.edu/~djhsu/coms3251-f22/

[5] Salil P. Vadhan. Pseudorandomness. In Foundations and Trends in Theoretical Computer Science, Volume 7, Issue 1-3, 2011.