An Approximate Minimum Degree Ordering Algorithm
SIAM Journal on Matrix Analysis and Applications
On computing certain elements of the inverse of a sparse matrix
Communications of the ACM
A family of algorithms for approximate bayesian inference
A family of algorithms for approximate bayesian inference
Gaussian Markov Random Fields: Theory And Applications (Monographs on Statistics and Applied Probability)
Gaussian Processes for Classification: Mean-Field Algorithms
Neural Computation
Assessing Approximate Inference for Binary Gaussian Process Classification
The Journal of Machine Learning Research
Bayesian Inference and Optimal Design for the Sparse Linear Model
The Journal of Machine Learning Research
Expectation Propagation for Rating Players in Sports Competitions
PKDD 2007 Proceedings of the 11th European conference on Principles and Practice of Knowledge Discovery in Databases
The variational gaussian approximation revisited
Neural Computation
Loopy belief propagation for approximate inference: an empirical study
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Sparse Spatio-temporal Gaussian processes with general likelihoods
ICANN'11 Proceedings of the 21th international conference on Artificial neural networks - Volume Part I
Nested expectation propagation for Gaussian process classification
The Journal of Machine Learning Research
Bayesian computing with INLA: New features
Computational Statistics & Data Analysis
Perturbative corrections for approximate inference in Gaussian latent variable models
The Journal of Machine Learning Research
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We consider the problem of improving the Gaussian approximate posterior marginals computed by expectation propagation and the Laplace method in latent Gaussian models and propose methods that are similar in spirit to the Laplace approximation of Tierney and Kadane (1986). We show that in the case of sparse Gaussian models, the computational complexity of expectation propagation can be made comparable to that of the Laplace method by using a parallel updating scheme. In some cases, expectation propagation gives excellent estimates where the Laplace approximation fails. Inspired by bounds on the correct marginals, we arrive at factorized approximations, which can be applied on top of both expectation propagation and the Laplace method. The factorized approximations can give nearly indistinguishable results from the non-factorized approximations and their computational complexity scales linearly with the number of variables. We experienced that the expectation propagation based marginal approximations we introduce are typically more accurate than the methods of similar complexity proposed by Rue et al. (2009).