This paper introduces Expectation Propagation (EP), a new deterministic approximation method for Bayesian inference in Bayesian networks. EP unifies two existing techniques: assumed-density filtering (ADF), an extension of the Kalman filter, and loopy belief propagation, an extension of belief propagation in Bayesian networks. EP approximates belief states by retaining only expectations, such as mean and variance, and iterates until these expectations are consistent throughout the network. This makes it applicable to hybrid networks with both discrete and continuous nodes. Experiments show EP outperforms methods like Laplace’s method, variational Bayes, and Monte Carlo in Gaussian mixture models. EP also provides an efficient algorithm for training Bayes point machine classifiers. EP extends ADF by incorporating iterative refinement of approximations through multiple passes through the network. This allows later observations to refine earlier choices, ensuring important information is retained. EP is faster than sampling and more general than extended Kalman filtering. It is only slightly more expensive than ADF by a constant factor, making it suitable for a wide range of statistical models. EP is more general than belief propagation in two ways: it can use non-disconnected approximations and can impose useful constraints on the functional form, such as multivariate Gaussian. In the clutter problem, EP is applied to approximate the posterior distribution of hidden variables. The algorithm iteratively refines approximations of each observation term, leading to a Gaussian posterior on the hidden variables. EP is shown to be more accurate than other methods, including ADF, in estimating the evidence and posterior mean. However, EP can sometimes converge to an erroneous result that captures only a single mode of the true posterior. EP is also applied to the Bayes Point Machine (BPM), a Bayesian approach to linear classification. EP provides a multivariate Gaussian approximation to the posterior over the parameter vector w, using its mean as the estimated Bayes point. This results in an efficient algorithm for training BPM classifiers. EP is shown to outperform other methods in terms of accuracy and computational efficiency on various datasets. EP iterations always have a fixed point, which can be found by minimizing an energy function. The algorithm is applicable to a wide range of statistical models and has been shown to be effective in both hybrid and discrete belief networks. The paper concludes that EP is a promising method for approximate Bayesian inference in complex networks.This paper introduces Expectation Propagation (EP), a new deterministic approximation method for Bayesian inference in Bayesian networks. EP unifies two existing techniques: assumed-density filtering (ADF), an extension of the Kalman filter, and loopy belief propagation, an extension of belief propagation in Bayesian networks. EP approximates belief states by retaining only expectations, such as mean and variance, and iterates until these expectations are consistent throughout the network. This makes it applicable to hybrid networks with both discrete and continuous nodes. Experiments show EP outperforms methods like Laplace’s method, variational Bayes, and Monte Carlo in Gaussian mixture models. EP also provides an efficient algorithm for training Bayes point machine classifiers. EP extends ADF by incorporating iterative refinement of approximations through multiple passes through the network. This allows later observations to refine earlier choices, ensuring important information is retained. EP is faster than sampling and more general than extended Kalman filtering. It is only slightly more expensive than ADF by a constant factor, making it suitable for a wide range of statistical models. EP is more general than belief propagation in two ways: it can use non-disconnected approximations and can impose useful constraints on the functional form, such as multivariate Gaussian. In the clutter problem, EP is applied to approximate the posterior distribution of hidden variables. The algorithm iteratively refines approximations of each observation term, leading to a Gaussian posterior on the hidden variables. EP is shown to be more accurate than other methods, including ADF, in estimating the evidence and posterior mean. However, EP can sometimes converge to an erroneous result that captures only a single mode of the true posterior. EP is also applied to the Bayes Point Machine (BPM), a Bayesian approach to linear classification. EP provides a multivariate Gaussian approximation to the posterior over the parameter vector w, using its mean as the estimated Bayes point. This results in an efficient algorithm for training BPM classifiers. EP is shown to outperform other methods in terms of accuracy and computational efficiency on various datasets. EP iterations always have a fixed point, which can be found by minimizing an energy function. The algorithm is applicable to a wide range of statistical models and has been shown to be effective in both hybrid and discrete belief networks. The paper concludes that EP is a promising method for approximate Bayesian inference in complex networks.