Consistency of weighted majority votes

Advances in Neural Information Processing Systems

Volumn 4, Issue January, 2014, Pages 3446-3454

  Berend, Daniel ^a   Kontorovich, Aryeh ^a  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

BAYESIAN ANALYSIS; DECISION-THEORETIC; ERROR ESTIMATES; FREQUENTIST; MAJORITY VOTE; STATISTICAL LEARNING;

INFORMATION SCIENCE;

EID: 84937915825     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (34)

1. J.A.N. de Caritat marquis de Condorcet. Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix. AMS Chelsea Publishing Series. Chelsea Publishing Company, 1785.
2. S. Nitzan, J. Paroush. Optimal decision rules in uncertain dichotomous choice situations. International Economic Review, 23(2): 289-297, 1982.
3. T. Hastie, R. Tibshirani, J. Friedman. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. 2009.
4. J. Neyman, E. S. Pearson. On the problem of the most efficient tests of statistical hypotheses. Phil. Trans. Royal Soc. A: Math., Physi. Eng. Sci., 231(694-706): 289-337, 1933.
5. N. Littlestone, M. K. Warmuth. The weighted majority algorithm. In FOCS, 1989.
6. N. Littlestone, M. K. Warmuth. The weighted majority algorithm. Inf. Comput., 108(2): 212-261, 1994.
7. N. Cesa-Bianchi, G. Lugosi. Prediction, learning, and games. 2006.
8. Y. Freund, R. E. Schapire. A decision-theoretic generalization of on-line learning and an application to boosting. J. Comput. Syst. Sci., 55(1): 119-139, 1997.
9. R. E. Schapire, Y. Freund. Boosting. Foundations and algorithms. 2012.
10. A. P. Dawid and A. M. Skene. Maximum likelihood estimation of observer error-rates using the EM algorithm. Applied Statistics, 28(1): 20-28, 1979.
11. F. Parisi, F. Strino, B. Nadler, Y. Kluger. Ranking and combining multiple predictors without labeled data. Proc. Nat. Acad. Sci., 2014+.
12. H. Li, B. Yu, D. Zhou. Error rate bounds in crowdsourcing models. CoRR, abs/1307.2674, 2013.
13. C. Gao, D. Zhou. Minimax Optimal Convergence Rates for Estimating Ground Truth from Crowdsourced Labels (arXiv: 1310.5764), 2014.
14. A. Lacasse, F. Laviolette, M. Marchand, P. Germain, N. Usunier. PAC-Bayes bounds for the risk of the majority vote and the variance of the gibbs classifier. In NIPS, 2006.
15. F. Laviolette, M. Marchand. PAC-Bayes risk bounds for stochastic averages and majority votes of sample-compressed classifiers. JMLR, 8: 1461-1487, 2007.
16. J.-F. Roy, F. Laviolette, M. Marchand. From PAC-Bayes bounds to quadratic programs for majority votes. In ICML, 2011.
17. Y. Mansour, A. Rubinstein, M. Tennenholtz. Robust aggregation of experts signals, preprint 2013.
18. E. Eban, E. Mezuman, A. Globerson. Discrete chebyshev classifiers. In ICML (2), 2014.
19. D. Berend, J. Paroush. When is Condorcet's jury theorem valid? Soc. Choice Welfare, 15(4): 481-488, 1998.
20. P. J. Boland, F. Proschan, Y. L. Tong. Modelling dependence in simple and indirect majority systems. J. Appl. Probab., 26(1): 81-88, 1989.
21. D. Berend, L. Sapir. Monotonicity in Condorcet's jury theorem with dependent voters. Social Choice and Welfare, 28(3): 507-528, 2007.
22. D. P. Helmbold and P. M. Long. On the necessity of irrelevant variables. JMLR, 13: 2145-2170, 2012.
23. D. A. McAllester, L. E. Ortiz. Concentration inequalities for the missing mass and for histogram rule error. JMLR, 4: 895-911, 2003.
24. M. J. Kearns, L. K. Saul. Large deviation methods for approximate probabilistic inference. In UAI, 1998.
25. D. Berend, A. Kontorovich. On the concentration of the missing mass. Electron. Commun. Probab., 18(3), 1-7, 2013.
26. M. Raginsky, I. Sason. Concentration of measure inequalities in information theory, communications and coding. Foundations and Trends in Communications and Information Theory, 10(1-2): 1-247, 2013.
27. D. Berend, A. Kontorovich. A finite-sample analysis of the naive Bayes classifier. Preprint, 2014.
28. E. Baharad, J. Goldberger, M. Koppel, S. Nitzan. Distilling the wisdom of crowds: weighted aggregation of decisions on multiple issues. Autonomous Agents and Multi-Agent Systems, 22(1): 31-42, 2011.
29. E. Baharad, J. Goldberger, M. Koppel, S. Nitzan. Beyond condorcet: optimal aggregation rules using voting records. Theory and Decision, 72(1): 113-130, 2012.
30. J.-Y. Audibert, R. Munos, C. Szepesvári. Tuning bandit algorithms in stochastic environments. In ALT, 2007.
31. V. Mnih, C. Szepesvári, J.-Y. Audibert. Empirical Bernstein stopping. In ICML, 2008.
32. A. Maurer, M. Pontil. Empirical Bernstein bounds and sample-variance penalization. In COLT, 2009.
33. A. Kontorovich. Obtaining measure concentration from Markov contraction. Markov Proc. Rel. Fields, 4: 613-638, 2012.
34. D. Berend, A. Kontorovich. A sharp estimate of the binomial mean absolute deviation with applications. Statistics & Probability Letters, 83(4): 1254-1259, 2013.