Efficient Inference of Continuous Markov Random Fields with Polynomial Potentials

@inproceedings{Wang2014EfficientIO,
title={Efficient Inference of Continuous Markov Random Fields with Polynomial Potentials},
author={Shenlong Wang and Alexander G. Schwing and Raquel Urtasun},
booktitle={NIPS},
year={2014}
}

In this paper, we prove that every multivariate polynomial with even degree can be decomposed into a sum of convex and concave polynomials. Motivated by this property, we exploit the concave-convex procedure to perform inference on continuous Markov random fields with polynomial potentials. In particular, we show that the concave-convex decomposition of polynomials can be expressed as a sum-of-squares optimization, which can be efficiently solved via semidefinite programing. We demonstrate the… CONTINUE READING