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Variational inference (VI) provides fast approximations of a Bayesian posterior in part because it formulates posterior approximation as an optimization problem: to find the closest distribution to the exact posterior over some family of distributions.
A stochastic approximation method
H. Robbins and S. Monro · 1951
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On estimation of a probability density function and mode
E. Parzen · 1962
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Non-parametric estimation of a multivariate probability density
V. A. Epanechnikov · 1969
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Prediction analyses for binary data
B. Brown · 1980
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A limited memory algorithm for bound constrained optimization
R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu · 1995
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A desicion-theoretic generalization of on-line learning and an application to boosting
Y. Freund and R. E. Schapire · 1995
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Approximating posterior distributions in belief networks using mixtures
C. M. Bishop, N. Lawrence, T. Jaakkola, and M. I. Jordan · 1998
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Improving the mean field approximation via the use of mixture distributions
T. Jaakkola and M. I. Jordan · 1998
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A short introduction to boosting
Y. Freund, R. Schapire, and N. Abe · 1999
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Adaptive proposal distribution for random walk Metropolis algorithm
H. Haario, E. Saksman, and J. Tamminen · 1999
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An introduction to variational methods for graphical models
M. I. Jordan, Z. Ghahramani, T. S. Jaakkola, and L. K. Saul · 1999
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Mixture density estimation
J. Q. Li and A. R. Barron · 1999
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Additive logistic regression: a statistical view of boosting (with discussion and a rejoinder by the authors)
J. Friedman, T. Hastie, and R. Tibshirani · 2000
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Greedy function approximation: a gradient boosting machine
J. H. Friedman · 2001
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An adaptive Metropolis algorithm
H. Haario, E. Saksman, and J. Tamminen · 2001
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Information Theory, Inference, and Learning Algorithms , chapter 33
D. J. C. MacKay · 2003
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Sequential greedy approximation for certain convex optimization problems
T. Zhang · 2003
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Inadequacy of interval estimates corresponding to variational Bayesian approximations
B. Wang and M. Titterington · 2004
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Nonparametric belief propagation for self-localization of sensor networks
A. T. Ihler, J. W. Fisher, R. L. Moses, and A. S. Willsky · 2005
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Nonparametric variational inference
S. Gershman, M. Hoffman, and D. Blei · 2012
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Distributed and adaptive darting Monte Carlo through regenerations
S. Ahn, Y. Chen, and M. Welling · 2013
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Bayesian inference for logistic models using Pólya–gamma latent variables
N. G. Polson, J. G. Scott, and J. Windle · 2013
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The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo
M. D. Hoffman and A. Gelman · 2014
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Auto-encoding variational Bayes
D. P. Kingma and M. Welling · 2014
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Wormhole Hamiltonian Monte Carlo
S. Lan, J. Streets, and B. Shahbaba · 2014
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Pattern Recognition and Machine Learning , chapter 10
C. M. Bishop · 2006
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Applications of empirical processes in learning theory: algorithmic stability and generalization bounds
A. Rakhlin · 2006
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Graphical models, exponential families, and variational inference
M. J. Wainwright and M. I. Jordan · 2008
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Examples of adaptive MCMC
G. O. Roberts and J. S. Rosenthal · 2009
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Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations
H. Rue, S. Martino, and N. Chopin · 2009
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Two problems with variational expectation maximisation for time-series models
R. E. Turner and M. Sahani · 2011
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Black box variational inference
R. Ranganath, S. Gerrish, and D. M. Blei · 2014
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Linear response methods for accurate covariance estimates from mean field variational Bayes
R. J. Giordano, T. Broderick, and M. I. Jordan · 2015
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Automatic variational inference in Stan
A. Kucukelbir, R. Ranganath, A. Gelman, and D. Blei · 2015
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Variational inference: A review for statisticians
D. M. Blei, A. Kucukelbir, and J. D. McAuliffe · 2016
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Stan: A probabilistic programming language
B. Carpenter, A. Gelman, M. Hoffman, D. Lee, B. Goodrich, M. Betancourt, M. A. Brubaker, J. Guo, P. Li, and A. Riddell · 2016
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Variational boosting: Iteratively refining posterior approximations
A. C. Miller, N. Foti, and R. P. Adams · 2016
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