NIPS 2015 Workshop (Duvenaud) 15644 Probabilistic Integration

Integration is the central numerical operation required for Bayesian machine learning (in the form of marginalization and conditioning). Sampling algorithms still abound in this area, although it has long been known that Monte Carlo methods are fundamentally sub-optimal. The challenges for the development of better performing integration methods are mostly algorithmic. Moreover, recent algorithms have begun to outperform MCMC and its siblings, in wall-clock time, on realistic problems from machine learning. A community website for probabilistic numerics can be found at http://probabilistic-numerics.org.