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Uncertainty quantification is at the core of the reliability and robustness of machine learning.
Inverse probability
R. A. Fisher · 1930
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Approximation by superpositions of a sigmoidal function
G. Cybenko · 1989
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Simulation output analysis using standardized time series
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Approximation capabilities of multilayer feedforward networks
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Quantile regression
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Analyzing bagging
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Shannon sampling ii: Connections to learning theory
S. Smale and D.-X. Zhou · 2005
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Algorithmic learning in a random world
V. Vovk, A. Gammerman, and G. Shafer · 2005
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Fixed-width output analysis for Markov chain Monte Carlo
G. L. Jones, M. Haran, B. S. Caffo, and R. Neath · 2006
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Quantile regression forests
N. Meinshausen · 2006
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Stochastic simulation: algorithms and analysis
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Consistency and robustness of kernel-based regression in convex risk minimization
A. Christmann and I. Steinwart · 2007
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How svms can estimate quantiles and the median
A. Christmann and I. Steinwart · 2007
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Fast nonparametric conditional density estimation
M. P. Holmes, A. G. Gray, and C. L. Isbell Jr · 2007
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Model selection in kernel based regression using the influence function
M. Debruyne, M. Hubert, and J. A. Suykens · 2008
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Lower upper bound estimation method for construction of neural network-based prediction intervals
A. Khosravi, S. Nahavandi, D. Creighton, and A. F. Atiya · 2010
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Improved algorithms for linear stochastic bandits
Y. Abbasi-Yadkori, D. Pál, and C. Szepesvári · 2011
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Reproducing kernel Hilbert spaces in probability and statistics
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Potential surprises
F. R. Hampel · 2011
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Comprehensive review of neural network-based prediction intervals and new advances
A. Khosravi, S. Nahavandi, D. Creighton, and A. F. Atiya · 2011
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Von Mises calculus for statistical functionals
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The jackknife and bootstrap
J. Shao and D. Tu · 2012
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Distribution-free prediction bands for non-parametric regression
J. Lei and L. Wasserman · 2014
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Reliable classification: Learning classifiers that distinguish aleatoric and epistemic uncertainty
R. Senge, S. Bösner, K. Dembczyński, J. Haasenritter, O. Hirsch, N. Donner-Banzhoff, and E. Hüllermeier · 2014
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Delving deep into rectifiers: Surpassing human-level performance on imagenet classification
K. He, X. Zhang, S. Ren, and J. Sun · 2015
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Probabilistic backpropagation for scalable learning of bayesian neural networks
J. M. Hernández-Lobato and R. Adams · 2015
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Why m heads are better than one: Training a diverse ensemble of deep networks
On the convergence rate of training recurrent neural networks
Z. Allen-Zhu, Y. Li, and Z. Song · 2019
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On exact computation with an infinitely wide neural net
S. Arora, S. S. Du, W. Hu, Z. Li, R. R. Salakhutdinov, and R. Wang · 2019
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The limits of distribution-free conditional predictive inference
R. F. Barber, E. J. Candes, A. Ramdas, and R. J. Tibshirani · 2019
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Predictive inference with the jackknife+
R. F. Barber, E. J. Candes, A. Ramdas, and R. J. Tibshirani · 2019
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Generalization bounds of stochastic gradient descent for wide and deep neural networks
Y. Cao and Q. Gu · 2019
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S. Lee, S. Purushwalkam, M. Cogswell, D. Crandall, and D. Batra · 2015
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A conformal prediction approach to explore functional data
J. Lei, A. Rinaldo, and L. Wasserman · 2015
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Divide and conquer kernel ridge regression: A distributed algorithm with minimax optimal rates
Y. Zhang, J. Duchi, and M. Wainwright · 2015
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Dropout as a bayesian approximation: Representing model uncertainty in deep learning
Y. Gal and Z. Ghahramani · 2016
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Nonparametric conditional density estimation in a high-dimensional regression setting
R. Izbicki and A. B. Lee · 2016
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A unified framework for constructing, tuning and assessing photometric redshift density estimates in a selection bias setting
P. E. Freeman, R. Izbicki, and A. B. Lee · 2017
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Approximating continuous functions by relu nets of minimal width
B. Hanin and M. Sellke · 2017
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Gradient descent finds global minima of deep neural networks
S. Du, J. Lee, H. Li, L. Wang, and X. Zhai · 2019
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Deep ensembles: A loss landscape perspective
S. Fort, H. Hu, and B. Lakshminarayanan · 2019
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On the accuracy of influence functions for measuring group effects
P. W. Koh, K.-S. Ang, H. H. Teo, and P. Liang · 2019
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Wide neural networks of any depth evolve as linear models under gradient descent
J. Lee, L. Xiao, S. Schoenholz, Y. Bahri, R. Novak, J. Sohl-Dickstein, and J. Pennington · 2019
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Enhanced convolutional neural tangent kernels
Z. Li, R. Wang, D. Yu, S. S. Du, W. Hu, R. Salakhutdinov, and S. Arora · 2019
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Conformalized quantile regression
Y. Romano, E. Patterson, and E. Candes · 2019
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G. Yang · 2019
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Random forest prediction intervals
H. Zhang, J. Zimmerman, D. Nettleton, and D. J. Nordman · 2019
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HDI-forest: highest density interval regression forest
L. Zhu, J. Lu, and Y. Chen · 2019
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Frequentist uncertainty in recurrent neural networks via blockwise influence functions
A. Alaa and M. Van Der Schaar · 2020
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Pitfalls of in-domain uncertainty estimation and ensembling in deep learning
A. Ashukha, A. Lyzhov, D. Molchanov, and D. Vetrov · 2020
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Influence functions in deep learning are fragile
S. Basu, P. Pope, and S. Feizi · 2020
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Generalization error bounds of gradient descent for learning over-parameterized deep relu networks
Y. Cao and Q. Gu · 2020
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Conditional density estimation tools in python and r with applications to photometric redshifts and likelihood-free cosmological inference
N. Dalmasso, T. Pospisil, A. B. Lee, R. Izbicki, P. E. Freeman, and A. I. Malz · 2020
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Bayesian deep ensembles via the neural tangent kernel
B. He, B. Lakshminarayanan, and Y. W. Teh · 2020
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Simple and effective regularization methods for training on noisily labeled data with generalization guarantee
W. Hu, Z. Li, and D. Yu · 2020
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Tensor programs ii: Neural tangent kernel for any architecture
G. Yang · 2020
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A type of generalization error induced by initialization in deep neural networks
Y. Zhang, Z.-Q. J. Xu, T. Luo, and Z. Ma · 2020
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Neural contextual bandits with ucb-based exploration
D. Zhou, L. Li, and Q. Gu · 2020
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Gradient descent optimizes over-parameterized deep relu networks
D. Zou, Y. Cao, D. Zhou, and Q. Gu · 2020
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Understanding the under-coverage bias in uncertainty estimation
Y. Bai, S. Mei, H. Wang, and C. Xiong · 2021
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Learning prediction intervals for regression: Generalization and calibration
H. Chen, Z. Huang, H. Lam, H. Qian, and H. Zhang · 2021
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Aleatoric and epistemic uncertainty in machine learning: An introduction to concepts and methods
E. Hüllermeier and W. Waegeman · 2021
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Efficient uncertainty quantification and reduction for over-parameterized neural networks
Z. Huang, H. Lam, and H. Zhang · 2023
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