High Dimensional Inference with Random Maximum A-Posteriori Perturbations
Technion - Israel Institute of Technology（以色列理工学院）；Stony Brook University（纽约州立大学石溪分校）；Yahoo Labs（雅虎实验室）；Rutgers, The State University of New Jersey（罗格斯大学）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；Massachusetts Institute of Technology（麻省理工学院）
Tamir Hazan, Francesco Orabona, Anand D. Sarwate, Subhransu Maji, Tommi Jaakkola
This paper presents a new approach, called perturb-max, for high-dimensional statistical inference that is based on applying random perturbations followed by optimization. This framework injects randomness to maximum a-posteriori (MAP) predictors by randomly perturbing the potential function for the input. A classic result from extreme value statistics asserts that perturb-max operations generate unbiased samples from the Gibbs distribution using high-dimensional perturbations. Unfortunately, the computational cost of generating so many high-dimensional random variables can be prohibitive. However, when the perturbations are of low dimension, sampling the perturb-max prediction is as efficient as MAP optimization. This paper shows that the expected value of perturb-max inference with low dimensional perturbations can be used sequentially to generate unbiased samples from the Gibbs distribution. Furthermore the expected value of the maximal perturbations is a natural bound on the entropy of such perturb-max models. A measure concentration result for perturb-max values shows that the deviation of their sampled average from its expectation decays exponentially in the number of samples, allowing effective approximation of the expectation.
X2CT-FLOW: Maximum a posteriori reconstruction using a progressive flow-based deep generative model for ultra sparse-view computed tomography in ultra low-dose protocols
The University of Tokyo Hospital（东京大学医学部附属医院）；Center for Frontier Medical Engineering, Chiba University（千叶大学前沿医疗工程中心）；Division of Radiology and Biomedical Engineering, Graduate School of Medicine, The University of Tokyo（东京大学医学研究生院放射科与生物医学工程学系）
