[1] A. Antos, L. Devroye, and L. Gyorfi. Lower bounds for Bayes error estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 21(7):643-645, 1999.
[2] H. Avi-Itzhak and T. Diep. Arbitrarily tight upper and lower bounds on the Bayesian probability of error. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(1):89–91, 1996.
[3] B. Barz and J. Denzler. Do we train on test data? purging CIFAR of near-duplicates. Journal of Imaging, 6(6):41, 2020.
[4] R. M. Battleday, J. C. Peterson, and T. L. Griffiths. Capturing human categorization of natural images by combining deep networks and cognitive models. Nature Communications, 11(1):5418, 2020. doi: 10.1038/s41467-020-18946-z. URL https://doi.org/10.1038/s41467-020-18946-z.
[5] Y. Bengio, A. Courville, and P. Vincent. Representation learning: A review and new perspectives. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(8):1798-1828, 2013. doi: 10.1109/TPAMI.2013.50.
[6] V. Berisha, A. Wisler, A. O. Hero, and A. Spanias. Empirically estimable classification bounds based on a nonparametric divergence measure. IEEE Transactions on Signal Processing, 64(3):580-591, 2016. doi: 10.1109/TSP.2015.2477805.
[7] R. Bhatia and C. Davis. A better bound on the variance. The American Mathematical Monthly, 107(4): 353-357, 2000.
[8] D. E. Boekee and J. C. van der Lubbe. Some aspects of error bounds in feature selection. Pattern Recognition, 11(5-6):353-360, 1979.
[9] S. Boucheron, G. Lugosi, and P. Massart. Concentration Inequalities: A Nonasymptotic Theory of Independence. Oxford University Press, 2013.
[10] L. Buturovic. Improving k-nearest neighbor density and error estimates. Pattern Recognition, 26(4): 611-616, 1993.
[11] C. Chen. Theoretical comparison of a class of feature selection criteria in pattern recognition. IEEE Transactions on Computers, C-20(9):1054–1056, 1971. doi: 10.1109/T-C.1971.223402.
[12] C. H. Chen. On information and distance measures, error bounds, and feature selection. Information Sciences, 10(2):159-173, 1976.
[13] Q. Chen, F. Cao, Y. Xing, and J. Liang. Evaluating classification model against Bayes error rate. IEEE Transactions on Pattern Analysis and Machine Intelligence, pages 1-16, 2023. doi: 10.1109/TPAMI.2023.3240194.
[14] H. Chernoff. A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. The Annals of Mathematical Statistics, pages 493-507, 1952.
[15] T. M. Cover. Elements of Information Theory. John Wiley & Sons, 1999.
[16] T. M. Cover and P. Hart. Nearest neighbor pattern classification. IEEE Transactions on Information Theory, 13(1):21-27, 1967. doi: 10.1109/TIT.1967.1053964.
[17] T. Dao, G. M. Kamath, V. Syrgkanis, and L. Mackey. Knowledge distillation as semiparametric inference. In International Conference on Learning Representations, 2021. URL https://openreview.net/forum?id=m4UCf24r0Y.
[18] H. A. David and H. N. Nagaraja. Order Statistics. Wiley Online Library, 2004.
[19] P. A. Devijver. On a new class of bounds on Bayes risk in multihypothesis pattern recognition. IEEE Transactions on Computers, C-23(1):70–80, 1974. doi: 10.1109/T-C.1974.223779.
[20] P. A. Devijver and J. Kittler. Pattern Recognition. Prentice Hall, Old Tappan, NJ, July 1982.
[21] L. Devroye. On the asymptotic probability of error in nonparametric discrimination. The Annals of Statistics, 9(6):1320-1327, 1981.
[22] L. Devroye, L. Györfi, and G. Lugosi. A Probabilistic Theory of Pattern Recognition, volume 31. Springer Science & Business Media, 2013.