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Bayesian Neural Networks with Latent Variables (BNN+LVs) capture predictive uncertainty by explicitly modeling model uncertainty (via priors on network weights) and environmental stochasticity (via a latent input noise variable).
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Jerzy Neyman and Elizabeth L Scott · 1948
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Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters
Jack Kiefer and Jacob Wolfowitz · 1956
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A class of invariant consistent tests for multivariate normality
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A practical bayesian framework for backpropagation networks
David JC MacKay · 1992
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Air Monitoring by Spectroscopic Techniques
M.W. Sigrist, S.M. W, J.D. Winefordner, and I.M. Kolthoff · 1994
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Regression with input-dependent noise: A gaussian process treatment
Paul W Goldberg, Christopher KI Williams, and Christopher M Bishop · 1998
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WA Wright · 1999
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The incidental parameter problem since 1948
Tony Lancaster · 2000
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Consistency of posterior distributions for neural networks
H. K. Lee · 2000
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Estimating mutual information
Alexander Kraskov, Harald Stögbauer, and Peter Grassberger · 2004
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Doubly penalized likelihood estimator in heteroscedastic regression
Ming Yuan and Grace Wahba · 2004
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Heteroscedastic gaussian process regression
Quoc V Le, Alex J Smola, and Stéphane Canu · 2005
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Most likely heteroscedastic gaussian process regression
Kristian Kersting, Christian Plagemann, Patrick Pfaff, and Wolfram Burgard · 2007
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Hierarchical gaussian process latent variable models
Neil D Lawrence and Andrew J Moore · 2007
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Springer New York, New York, NY, 2008
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Gaussian process training with input noise
Andrew McHutchon and Carl E Rasmussen · 2011
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Mcmc using hamiltonian dynamics
Radford M Neal et al · 2011
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Asymptotic normality of posterior distributions for generalized linear mixed models
Hossein Baghishani and Mohsen Mohammadzadeh · 2012
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A kernel two-sample test
Arthur Gretton, Karsten M Borgwardt, Malte J Rasch, Bernhard Schölkopf, and Alexander Smola · 2012
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Bayesian learning for neural networks , volume 118
Radford M Neal · 2012
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Gaussian process regression with heteroscedastic or non-gaussian residuals
Chunyi Wang and Radford M Neal · 2012
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Auto-Encoding Variational Bayes
Diederik P. Kingma and Max Welling · 2013
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What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?
Alex Kendall and Yarin Gal · 2017
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Improving the identifiability of neural networks for bayesian inference
Arya A Pourzanjani, Richard M Jiang, and Linda R Petzold · 2017
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Mine: mutual information neural estimation
Mohamed Ishmael Belghazi, Aristide Baratin, Sai Rajeswar, Sherjil Ozair, Yoshua Bengio, Aaron Courville, and R Devon Hjelm · 2018
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Decomposition of uncertainty in bayesian deep learning for efficient and risk-sensitive learning
Stefan Depeweg, Jose-Miguel Hernandez-Lobato, Finale Doshi-Velez, and Steffen Udluft · 2018
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Information-Directed Exploration for Deep Reinforcement Learning
Nikolay Nikolov, Johannes Kirschner, Felix Berkenkamp, and Andreas Krause · 2018
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Variational inference for uncertainty on the inputs of gaussian process models
Andreas C Damianou, Michalis K Titsias, and Neil D Lawrence · 2014
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Adam: A method for stochastic optimization
Diederik P Kingma and Jimmy Ba · 2014
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Bayesian inference with posterior regularization and applications to infinite latent svms
Jun Zhu, Ning Chen, and Eric P Xing · 2014
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Weight uncertainty in neural networks
Charles Blundell, Julien Cornebise, Koray Kavukcuoglu, and Daan Wierstra · 2015
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Probabilistic electricity price forecasting with variational heteroscedastic gaussian process and active learning
Peng Kou, Deliang Liang, Lin Gao, and Jianyong Lou · 2015
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Alireza Makhzani, Jonathon Shlens, Navdeep Jaitly, Ian Goodfellow, and Brendan Frey · 2015
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The information autoencoding family: A lagrangian perspective on latent variable generative models
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Avoiding latent variable collapse with generative skip models
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Heteroscedastic bayesian optimisation in scientific discovery
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