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The machine learning literature contains several constructions for prediction intervals that are intuitively reasonable but ultimately ad-hoc in that they do not come with provable performance guarantees.
Conformalized quantile regression
Romano, Y., Patterson, E., and Candès, E. J. (2019) · 1905
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Discussion of “cross-validatory choice and assessment of statistical predictions,” by m. stone
Barnard, G. A. (1974) · 1974
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A theory of the learnable
Valiant, L. G. (1984) · 1984
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Approximation by superpositions of a sigmoidal function
Cybenko, G. (1989) · 1989
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Approximation capabilities of multilayer feedforward networks
Hornik, K. (1991) · 1991
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A practical bayesian framework for backpropagation networks
MacKay, D. J. (1992) · 1992
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Estimating the mean and variance of the target probability distribution
Nix, D. A. and Weigend, A. S. (1994) · 1994
Earlier work this paper cites.
Quantile curves without crossing
He, X. (1997) · 1997
Earlier work this paper cites.
Practical confidence and prediction intervals
Heskes, T. (1997) · 1997
Earlier work this paper cites.
Econometric Analysis of Cross Section and Panel Data
Wooldridge, J. M. (2001) · 2001
Earlier work this paper cites.
Quantile Regression
Koenker, R. (2005) · 2005
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Algorithmic Learning in a Random World
Vovk, V., Gammerman, A., and Shafer, G. (2005) · 2005
Cited alongside, same era.
A unified architecture for natural language processing: Deep neural networks with multitask learning
Collobert, R. and Weston, J. (2008) · 2008
Cited alongside, same era.
Lower upper bound estimation method for construction of neural network-based prediction intervals
Khosravi, A., Nahavandi, S., Creighton, D., and Atiya, A. F. (2011) · 2011
Cited alongside, same era.
Reliable prediction intervals with regression neural networks
Papadopoulos, H. and Haralambous, H. (2011) · 2011
Cited alongside, same era.
Deep neural networks for acoustic modeling in speech recognition
Hinton, G., Deng, L., Yu, D., Dahl, G., Mohamed, A.-r., Jaitly, N., Senior, A., Vanhoucke, V., Nguyen, P., Kingsbury, B., et al. (2012) · 2012
Cited alongside, same era.
Imagenet classification with deep convolutional neural networks
Rethinking the inception architecture for computer vision
Szegedy, C., Vanhoucke, V., Ioffe, S., Shlens, J., and Wojna, Z. (2016) · 2016
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On deep learning as a remedy for the curse of dimensionality in nonparametric regression
Bauer, B. and Kohler, M. (2017) · 2017
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UCI machine learning repository
Dua, D. and Graff, C. (2017) · 2017
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Simple and scalable predictive uncertainty estimation using deep ensembles
Lakshminarayanan, B., Pritzel, A., and Blundell, C. (2017) · 2017
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Automatic differentiation in pytorch
Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., and Lerer, A. (2017) · 2017
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Calibrated prediction intervals for neural network regressors
Keren, G., Cummins, N., and Schuller, B. (2018) · 2018
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Krizhevsky, A., Sutskever, I., and Hinton, G. E. (2012) · 2012
Cited alongside, same era.
Event labeling combining ensemble detectors and background knowledge
Fanaee-T, H. and Gama, J. (2013) · 2013
Cited alongside, same era.
Large-scale video classification with convolutional neural networks
Karpathy, A., Toderici, G., Shetty, S., Leung, T., Sukthankar, R., and Fei-Fei, L. (2014) · 2014
Cited alongside, same era.
Predicting the sequence specificities of dna-and rna-binding proteins by deep learning
Alipanahi, B., Delong, A., Weirauch, M. T., and Frey, B. J. (2015) · 2015
Cited alongside, same era.
Dropout as a bayesian approximation: Representing model uncertainty in deep learning
Gal, Y. and Ghahramani, Z. (2016) · 2016
Cited alongside, same era.
Deep Learning
Goodfellow, I., Bengio, Y., and Courville, A. (2016) · 2016
Cited alongside, same era.
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Accurate uncertainties for deep learning using calibrated regression
Kuleshov, V., Fenner, N., and Ermon, S. (2018) · 2018
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Distribution-free predictive inference for regression
Lei, J., G’Sell, M., Rinaldo, A., Tibshirani, R. J., and Wasserman, L. (2018) · 2018
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High-quality prediction intervals for deep learning: A distribution-free, ensembled approach
Pearce, T., Brintrup, A., Zaki, M., and Neely, A. (2018) · 2018
Later among the works it cites.
Frequentist uncertainty estimates for deep learning
Tagasovska, N. and Lopez-Paz, D. (2018) · 2018
Later among the works it cites.