Learn about the connections between invariant theory and maximum likelihood estimation in this 41-minute workshop lecture from Harvard CMSA's Workshop on Nonlinear Algebra and Combinatorics from Physics. Explore how norm minimization over a torus orbit relates to maximum likelihood estimation in log-linear models, with detailed explanations of polytopes and scaling algorithms. Delve into topics including independence models, log-linear models, null cone analysis, and practical methods for finding Maximum Likelihood Estimation (MLE). Follow along as Anna Seigal presents collaborative research conducted with Carlos Améndola, Kathlén Kohn, and Philipp Reichenbach, bridging the mathematical foundations of invariant theory with statistical applications.