Exact Solutions in Log-Concave Maximum Likelihood Estimation

Our paper with Alexandros Grosdos, Alexander Heaton, Olga Kuznetsova, Georgy Scholten, and Miruna-Stefana Sorea is now published in Advances in Applied Mathematics. The log-concave maximum likelihood estimate is known to be the exponential of a tent function with the tentpoles being the data points. The tent function induces a subdivision of the convex hull of the data points. It turns out that even determining the optimal subdivision can be challenging! We study the transcendentality of the solutions, give a closed form solution in the simplest case and explore how to certify the solutions.