Piecewise Bounds for Estimating Bernoulli-Logistic Latent Gaussian Models

By Benjamin M. Marlin, Mohammad Emtiyaz Khan, Kevin P. Murphy. 2011

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Variational Inference: A Review for Statisticians (2016, background): “Blei and Lafferty (2007) later adapted their idea to nonconjugate topic models, and researchers have continued to improve the original bound (Khan et al. 2010; Marlin, Khan, and Murphy 2011; Ermis and Bouchard 2014).”
Fast and Scalable Bayesian Deep Learning by Weight-Perturbation in Adam (2018, methodology): “For Bayesian logistic regression we can compute the optimal mean-field Gaussian approximations using the method described in Marlin et al. (2011) (refer to as ‘MF-Exact’), and compare it to the following methods: VOGN with minibatch size M = 1 and a momentum term (referred to as ‘VOGN-1’), and…”
Non-conjugate Variational Message Passing for Multinomial and Binary Regression (2011, background): “The second line of work applying VB to non-conjugate models involves deriving lower bounds to approximate the expectations [9, 18, 5, 10, 11] required to calculate the KL divergence.”
Monte Carlo Gradient Estimation in Machine Learning (2019, methodology): “, 2010), and piecewise bounds (Marlin et al., 2011), have been developed in local variational inference.”
Variational Bayesian Inference with Stochastic Search (2012, methodology): “Therefore, much attention has been paid to developing tight bounds of commonly occurring functions (e.g., Jaakkola & Jordan (2000), Marlin et al. (2011), Leisink & Kappen (2001)).”
Gaussian Kullback-Leibler approximate inference (2013, background): “In the Bayesian setting an important class is Bayesian generalised linear models (GLMs) for which examples include: sparse Bayesian linear models, where the Gaussian term is the likelihood and {φn}Nn=1 are factors of the sparse prior (Park and Casella, 2008); Gaussian process models, where the…”
Kullback-Leibler Proximal Variational Inference (2015, methodology): “For the Proximal method, we use the method of [23], which is quite accurate.”
SLANG: Fast Structured Covariance Approximations for Bayesian Deep Learning with Natural Gradient (2018, background): “Gaussian variational distributions with full covariance matrices have been used extensively for shallow models [6, 8, 16, 22, 24, 30, 34, 35].”