Duality of I Projections and Maximum Likelihood Estimation for Log-Linear Models Under Cone Constraints
锥约束对数线性模型中 I 投影与最大似然估计的对偶性
Important order restrictions and general log-linear models for multinomial experiments can often be expressed by requiring that the vector composed of the logs of the probabilities fall within a closed convex cone. Here we exhibit a duality relationship (by way of a Fenchel duality theorem) between these types of problems and projections in I-divergence geometry. We show that many cone-constrained maximum likelihood estimation problems are exactly equivalent to an I…