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Concave Gaussian variational approximations for inference in large-scale Bayesian linear models

<13>A bottleneck in the application of probability to large-scale problems is that the computational complexity prohibits an exact implementation. It was long believed that the standard Kullback-Leibler method resulting in a non-convex optimisation problem and would not scale to large problems. This paper overturns a decade of misconception by showing that in fact the KL method results in a convex problem and is scalable. This is important in understanding the properties of approximation approaches spanning computer science and statistics. This resulted in invited talks at Microsoft Research and the Royal Statistical Society. The software has been downloaded over 500 times.