Expectation Propagation with Factorizing Distributions: A Gaussian Approximation and Performance Results for Simple Models

We discuss the expectation propagation (EP) algorithm for approximate Bayesian inference using a factorizing posterior approximation. For neural network models, we use a central limit theorem argument to make EP tractable when the number of parameters is large. For two types of models, we show that EP can achieve optimal generalization performance when data are drawn from a simple distribution.

Risk Factors for Visual Field Progression in Treated Glaucoma

Objective: To determine intraocular pressure (IOP)-dependent and IOP-independent variables associated with visual field (VF) progression in treated glaucoma. Design: Retrospective cohort of the Glaucoma Progression Study. Methods: Consecutive, treated glaucoma patients with repeatable VF loss who had 8 or more VF examinations of either eye, using the Swedish Interactive Threshold Algorithm (24-2 SITA-Standard, Humphrey Field Analyzer II; Carl Zeiss Meditec, Inc, Dublin, California), during the period between January 1999 and September 2009 were included. Visual field progression was evaluated using automated pointwise linear regression. Evaluated data included age, sex, race, central corneal thickness, baseline VF mean deviation, mean follow-up IOP, peak IOP, IOP fluctuation, a detected disc hemorrhage, and presence of beta-zone parapapillary atrophy. Results: We selected 587 eyes of 587 patients (mean [SD] age, 64.9 [13.0] years). The mean (SD) number of VFs was 11.1 (3.0), spanning a mean (SD) of 6.4 (1.7) years. In the univariable model, older age (odds ratio [OR], 1.19 per decade; P = .01), baseline diagnosis of exfoliation syndrome (OR, 1.79; P = .01), decreased central corneal thickness (OR, 1.38 per 40 mu m thinner; P < .01), a detected disc hemorrhage (OR, 2.31; P < .01), presence of beta-zone parapapillary atrophy (OR, 2.17; P < .01), and all IOP parameters (mean follow-up, peak, and fluctuation; P < .01) were associated with increased risk of VF progression. In the multivariable model, peak IOP (OR, 1.13; P < .01), thinner central corneal thickness (OR, 1.45 per 40 mu m thinner; P < .01), a detected disc hemorrhage (OR, 2.59; P < .01), and presence of beta-zone parapapillary atrophy (OR, 2.38; P < .01) were associated with VF progression. Conclusions: IOP-dependent and IOP-independent risk factors affect disease progression in treated glaucoma. Peak IOP is a better predictor of progression than is IOP mean or fluctuation.