Fetching the paper…
Reading the bibliography…
We provide an exact non-asymptotic lower bound on the minimax expected excess risk (EER) in the agnostic probably-ap\-proximately-correct (PAC) machine learning classification model and identify minimax learning algorithms as certain maximally symmetric and minimally randomized "voting" procedures.
[author] v. Neumann, J.J. (1928). Zur Theorie der Gesellschaftsspiele. Mathematische Annalen 100 295–320
1928
Earlier work this paper cites.
[author] Hardy, G. H.G. H., Littlewood, J. E.J. E. and Pólya, G.G. (1967). Inequalities. Cambridge University Press, Cambridge Reprint of the 1952 edition
1952
Earlier work this paper cites.
[author] Sion, MauriceM. (1958). On general minimax theorems. Pacific J. Math. 8 171–176. 0097026 (20 ##3506)
1958
Earlier work this paper cites.
[author] Kingman, J. F. C.J. F. C. (1961). A convexity property of positive matrices. Quart. J. Math. Oxford Ser. (2) 12 283–284. 0138632
1961
Earlier work this paper cites.
[author] Ferguson, Thomas S.T. S. (1967). Mathematical statistics: A decision theoretic approach. Probability and Mathematical Statistics, Vol. 1. Academic Press, New York-London. 0215390
1967
Earlier work this paper cites.
[author] Vapnik, V. N.V. N. and Červonenkis, A. Ja.A. J. (1971). The uniform convergence of frequencies of the appearance of events to their probabilities. Teor. Verojatnost. i Primenen. 16 264–279. 0288823 (44 ##6018)
1971
Earlier work this paper cites.
[author] Valiant, Leslie G.L. G. (1984). A Theory of the Learnable. Commun. ACM 27 1134-1142
1984
Earlier work this paper cites.
[author] Pinelis, I. F.I. F. and Utev, S. A.S. A. (1989). Sharp exponential estimates for sums of independent random variables. Theory Probab. Appl. 34 340–346. 10.1137/1134032 MR1005745 (91a:60053)
1989
Earlier work this paper cites.
[author] Pinelis, I. F.I. F. (1991). Criterion for complete determinacy for concave-convexlike games. Math. Notes 49 277–279
1991
Earlier work this paper cites.
[author] Haussler, DavidD. (1992). Decision Theoretic Generalizations of the PAC Model for Neural Net and Other Learning Applications. Inf. Comput. 100 78–150. 10.1016/0890-5401(92)90010-D
1992
Cited alongside, same era.
[author] Kearns, Michael J.M. J. and Schapire, Robert E.R. E. (1994). Efficient distribution-free learning of probabilistic concepts. J. Comput. Syst. Sci. 48 464–497. http://dx.doi.org/10.1016/S0022-0000(05)80062-5
1994
Cited alongside, same era.
[author] Kearns, Michael J.M. J., Schapire, Robert E.R. E. and Sellie, LindaL. (1994). Toward Efficient Agnostic Learning. Machine Learning 17 115-141
1994
Cited alongside, same era.
[author] Talagrand, MichelM. (1994). Sharper Bounds for Gaussian and Empirical Processes. Ann. Probab. 22 28–76. 10.1214/aop/1176988847
1994
Cited alongside, same era.
[author] Devroye, L.L. and Lugosi, G.G. (1995). Lower bounds in pattern recognition and learning. Pattern Recognition 28 1011–1018
[author] Anthony, MartinM. and Bartlett, Peter L.P. L. (1999). Neural Network Learning: Theoretical Foundations. Cambridge University Press, Cambridge. 10.1017/CBO9780511624216 1741038 (2001b:68061)
1999
Later among the works it cites.
[author] Long, Philip M.P. M. (1999). The Complexity of Learning According to Two Models of a Drifting Environment. Mach. Learn. 37 337–354. 10.1023/A:1007666507971
1999
Later among the works it cites.
[author] Audibert, Jean-YvesJ.-Y. (2009). Fast learning rates in statistical inference through aggregation. Ann. Statist. 37 1591–1646. 10.1214/08-AOS623
2009
Later among the works it cites.
[author] Boucheron, StéphaneS., Lugosi, GáborG. and Massart, PascalP. (2013). Concentration inequalities. Oxford University Press, Oxford A nonasymptotic theory of independence, With a foreword by Michel Ledoux. 3185193
2013
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
1995
Cited alongside, same era.
[author] Haussler, DavidD. (1995). Sphere packing numbers for subsets of the Boolean n n -cube with bounded Vapnik-Chervonenkis dimension. J. Combin. Theory Ser. A 69 217–232. MR1313896 (96f:52027)
1995
Cited alongside, same era.
[author] Devroye, LucL., Györfi, LászlóL. and Lugosi, GáborG. (1996). A probabilistic theory of pattern recognition. Applications of Mathematics (New York) 31. Springer-Verlag, New York. 1383093
1996
Cited alongside, same era.
[author] Simon, Hans UlrichH. U. (1996). General bounds on the number of examples needed for learning probabilistic concepts. J. Comput. System Sci. 52 239–254. Sixth Annual Workshop on Computational Learning Theory (COLT) (Santa Cruz, CA, 1993). 10.1006/jcss.1996.0019 1393992
1996
Cited alongside, same era.
[author] Shalev-Shwartz, ShaiS. and Ben-David, ShaiS. (2014). Understanding Machine Learning: From Theory to Algorithms. Cambridge University Press
2014
Later among the works it cites.
[author] Berend, DanielD. and Kontorovich, AryehA. (2015). A finite sample analysis of the Naive Bayes classifier. Journal of Machine Learning Research 16 1519–1545
2015
Later among the works it cites.
2016
Closest in time.
[author] Pinelis, IosifI. (2016). Optimal binomial, Poisson, and normal left-tail domination for sums of nonnegative random variables. Electron. J. Probab. 21 1-19. 10.1214/16-EJP4474
2016
Closest in time.