Stochastic Gradient Annealed Importance Sampling for Efficient Online Marginal Likelihood Estimation

We consider estimating the marginal likelihood in settings with independent and identically distributed (i.i.d.) data. We propose estimating the predictive distributions in a sequential factorization of the marginal likelihood in such settings by using stochastic gradient Markov Chain Monte Carlo techniques. This approach is far more efficient than traditional marginal likelihood estimation techniques such as nested sampling and annealed importance sampling due to its use of mini-batches to approximate the likelihood. Stability of the estimates is provided by an adaptive annealing schedule. The resulting stochastic gradient annealed importance sampling (SGAIS) technique, which is the key contribution of our paper, enables us to estimate the marginal likelihood of a number of models considerably faster than traditional approaches, with no noticeable loss of accuracy. An important benefit of our approach is that the marginal likelihood is calculated in an online fashion as data becomes available, allowing the estimates to be used for applications such as online weighted model combination

Building Proteins in a Day: Efficient 3D Molecular Reconstruction

Discovering the 3D atomic structure of molecules such as proteins and viruses is a fundamental research problem in biology and medicine. Electron Cryomicroscopy (Cryo-EM) is a promising vision-based technique for structure estimation which attempts to reconstruct 3D structures from 2D images. This paper addresses the challenging problem of 3D reconstruction from 2D Cryo-EM images. A new framework for estimation is introduced which relies on modern stochastic optimization techniques to scale to large datasets. We also introduce a novel technique which reduces the cost of evaluating the objective function during optimization by over five orders or magnitude. The net result is an approach capable of estimating 3D molecular structure from large scale datasets in about a day on a single workstation.Comment: To be presented at IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 201