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The language of discretion
 in C. Ricks and L. Michaels (eds), The State of Language, Faber and
, 1990
"... variational inference for largescale ..."
Latent Factor Regressions for the Social Sciences∗
, 2014
"... In this paper I present a general framework for regression in the presence of complex dependence structures between units such as in timeseries crosssectional data, relational/network data, and spatial data. These types of data are challenging for standard multilevel models because they involve mu ..."
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In this paper I present a general framework for regression in the presence of complex dependence structures between units such as in timeseries crosssectional data, relational/network data, and spatial data. These types of data are challenging for standard multilevel models because they involve multiple types of structure (e.g. temporal effects and crosssectional effects) which are interactive. I show that interactive latent factor models provide a powerful modeling alternative that can address a wide range of data types. Although related models have previously been proposed in several different fields, inference is typically cumbersome and slow. I introduce a class of fast variational inference algorithms that allow for models to be fit quickly and accurately. ∗For comments and discussions on various portions of this material I thank Adam Glynn, Justin Grimmer, Gary King, Horacio Larreguy, Chris Lucas, John Marshall, Helen Milner, Brendan O’Connor, and Beth Simmons. Molly Roberts provided both enlightening discussions and code from her paper on robust standard errors. Special thanks to Dustin Tingley without whom this paper would not have been possible. An appendix containing additional details is available on my website: scholar.harvard.edu/bstewart
Variational inference for count response semiparametric regression.” arXiv preprint arXiv:1309.4199
, 2013
"... SUMMARY Fast variational approximate algorithms are developed for Bayesian semiparametric regression when the response variable is a count, i.e. a nonnegative integer. We treat both the Poisson and Negative Binomial families as models for the response variable. Our approach utilizes recently devel ..."
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SUMMARY Fast variational approximate algorithms are developed for Bayesian semiparametric regression when the response variable is a count, i.e. a nonnegative integer. We treat both the Poisson and Negative Binomial families as models for the response variable. Our approach utilizes recently developed methodology known as nonconjugate variational message passing. For concreteness, we focus on generalized additive mixed models, although our variational approximation approach extends to a wide class of semiparametric regression models such as those containing interactions and elaborate random effect structure.
Semiparametric Mean Field Variational Bayes: General Principles and Numerical Issues
, 2016
"... Abstract We introduce the term semiparametric mean field variational Bayes to describe the relaxation of mean field variational Bayes in which some density functions in the product density restriction are prespecified to be members of convenient parametric families. This notion has appeared in var ..."
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Abstract We introduce the term semiparametric mean field variational Bayes to describe the relaxation of mean field variational Bayes in which some density functions in the product density restriction are prespecified to be members of convenient parametric families. This notion has appeared in various guises in the mean field variational Bayes literature during its history and we endeavor to unify this important topic. We lay down a general framework and explain how previous relevant methodologies fall within this framework. A major contribution is elucidation of numerical issues that impact semiparametric mean field variational Bayes in practice.
Variational inference for sparse spectrum Gaussian process regression
"... Nott∗ We develop a fast deterministic variational approximation scheme for Gaussian process (GP) regression, where the spectrum of the covariance function is subjected to a sparse approximation. The approach enables uncertainty in covariance function hyperparameters to be treated without using Mont ..."
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Nott∗ We develop a fast deterministic variational approximation scheme for Gaussian process (GP) regression, where the spectrum of the covariance function is subjected to a sparse approximation. The approach enables uncertainty in covariance function hyperparameters to be treated without using Monte Carlo methods and is robust to overfitting. Our article makes three contributions. First, we present a variational Bayes algorithm for fitting sparse spectrum GP regression models, which makes use of nonconjugate variational message passing to derive fast and efficient updates. Second, inspired by related methods in classification, we propose a novel adaptive neighbourhood technique for obtaining predictive inference that is effective in dealing with nonstationarity. Regression is performed locally at each point to be predicted and the neighbourhood is determined using a measure defined based on lengthscales estimated from an initial fit. Weighting the dimensions according to the lengthscales effectively downweights variables of little relevance, leading to automatic variable selection and improved prediction. Third, we introduce a technique for accelerating convergence in nonconjugate variational message passing by adapting step sizes in the direction of the natural gradient of the lower bound. Our adaptive strategy can be easily implemented and empirical results indicate significant speed ups.
Variational inference for count response semiparametric regression BY J. LUTS AND M.P. WAND
, 2013
"... Fast variational approximate algorithms are developed for Bayesian semiparametric regression when the response variable is a count, i.e. a nonnegative integer. We treat both the Poisson and Negative Binomial families as models for the response variable. Our approach utilizes recently developed meth ..."
Abstract
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Fast variational approximate algorithms are developed for Bayesian semiparametric regression when the response variable is a count, i.e. a nonnegative integer. We treat both the Poisson and Negative Binomial families as models for the response variable. Our approach utilizes recently developed methodology known as nonconjugate variational message passing. For concreteness, we focus on generalized additive mixed models, although our variational approximation approach extends to a wide class of semiparametric regression models such as those containing interactions and elaborate random effect structure.