Dual Decomposition for Joint Discrete-Continuous Optimization
Christopher Zach · 2013
We analyse convex formulations for com-bined discrete-continuous MAP inference us-ing the dual decomposition method. As a consquence we can provide a more intuitive derivation for the resulting convex relaxation than presented in the literature. Further, we show how to strengthen the relaxation by reparametrizing the potentials, hence convex relaxations for discrete-continuous inference does not share an important feature of LP relaxations for discrete labeling problems: in-corporating unary potentials into higher or-der ones affects the quality of the relaxation. We argue that the convex model for discrete-continuous inference is very general and can be used as alternative for alternation-based methods often employed for such joint infer-ence tasks. 1