Maximum likelihood thresholds of generic linear concentration models

The maximum likelihood threshold of a statistical model is the minimum number of datapoints required to fit the model via maximum likelihood estimation. In this paper we determine the maximum likelihood thresholds of generic linear concentration models. This turns out to be the number one would expect from a naive dimension count, which is surprising and nontrivial to prove given that the maximum likelihood threshold is a semi-algebraic concept. We also describe geometrically how a linear concentration model can fail to exhibit this generic behavior and briefly discuss connections to rigidity theory.