# Black-Box Alpha Divergence Minimization

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Jose Hernandez-Lobato,
Yingzhen Li,
Mark Rowland,
Thang Bui,
Daniel Hernandez-Lobato,
Richard Turner
;

Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:1511-1520, 2016.

#### Abstract

Black-box alpha (BB-α) is a new approximate inference method based on the minimization of α-divergences. BB-αscales to large datasets because it can be implemented using stochastic gradient descent. BB-αcan be applied to complex probabilistic models with little effort since it only requires as input the likelihood function and its gradients. These gradients can be easily obtained using automatic differentiation. By changing the divergence parameter α, the method is able to interpolate between variational Bayes (VB) (α→0) and an algorithm similar to expectation propagation (EP) (α= 1). Experiments on probit regression and neural network regression and classification problems show that BB-αwith non-standard settings of α, such as α= 0.5, usually produces better predictions than with α→0 (VB) or α= 1 (EP).

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