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Quick Black Box Variational Inference Using Gaussian Cubature Integration Rules

A novel variant of black box variational inference, which employs Gaussian cubature integration rules, is proposed. The method is applicable to small and medium scale problems and is particularly well fitted for real-time applications such as radar. The application of the cubature rule results in noise-free estimates of the evidence lower bound and its gradient. This feature allows one to employ quasi-Newton optimization methods, which converge considerably faster than stochastic gradient methods used in classical black box variational inference. The improvement in convergence speed is demonstrated using the direction of arrival estimation as an example.