Computing ML Degrees with Euler Characteristics

The maximum likelihood degree (ML degree) of a statistical model counts the number of critical points of the likelihood function restricted to the model’s Zariski closure, thereby measuring the difficulty of maximum likelihood estimation.  The ML degree can be determined by solving a structured polynomial system called likelihood equations. On the other hand, the ML degree can also be computed using topological methods.  In this talk, we discuss computing ML degrees of rank 2 matrices using Euler characteristics. Using ML duality we are able to determine the ML degrees of determinants.