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- W2464755887 abstract "Recently, the increasing interest on big data is posing many new challenges to the mainstream of statistics. On the Bayesian side, commonly used stochastic approximation methods, such as MCMC methods do not scale with the sample size. To address this issue, several MCMC algorithms have been proposed which essentially reduce the original problem into smaller pieces and then combine them in order to obtain an approximation of the target. On the other hand, deterministic approximations such as the Laplace method or Variational Bayes (VB) methods scale with sample size, but they are not without limitations and they rely on strong assumptions. We present a VB algorithm that overcomes the main limitations of traditional VB algorithms since it does not require block independence or model conjugacy. The proposed algorithm finds the multivariate skew-$t$ density that minimises a slightly modified version of the Kullback--Leibler (KL) divergence between this density and the target. We approximate the multivariate integral involved in the modified KL divergence with the improved Laplace method of Ruli et al. (2015). With respect to typical VB approximations, the proposed method is able to capture the non--Gaussianity of the target without imposing independence constraints among blocks. The usefulness of the method is illustrated by simulated and real--life datasets." @default.
- W2464755887 created "2016-07-22" @default.
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- W2464755887 date "2016-05-04" @default.
- W2464755887 modified "2023-10-16" @default.
- W2464755887 title "Non-conjugate Variational Bayes Approximation" @default.
- W2464755887 hasPublicationYear "2016" @default.
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