The DOI matches its Crossref record; 7 of the 7 references it cites were found in a registry or an index.
Boosting the margin: a new explanation for the effectiveness of voting methods
Open accessAbstract
One of the surprising recurring phenomena observed in experiments with boosting is that the test error of the generated classifier usually does not increase as its size becomes very large, and often is observed to decrease even after the training error reaches zero. In this paper, we show that this phenomenon is related to the distribution of margins of the training examples with respect to the generated voting classification rule, where the margin of an example is simply the difference between the number of correct votes and the maximum number of votes received by any incorrect label. We show that techniques used in the analysis of Vapnik’s support vector classifiers and of neural networks with small weights can be applied to voting methods to relate the margin distribution to the test error. We also show theoretically and experimentally that boosting is especially effective at increasing the margins of the training examples. Finally, we compare our explanation to those based on the bias-variance decomposition.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Cortes, C., & Vapnik, V. (1995) · Machine Learning · doi:10.1007/bf00994018 · Cited by 59,421
The Nature of Statistical Learning Theory
Vapnik, V. N. (1995) · doi:10.1007/978-1-4757-2440-0 · Cited by 39,138
A decision-theoretic generalization of on-line learning and an application to boosting
Freund, Y., & Schapire, R. E. (1997) · Journal of Computer and System Sciences · doi:10.1006/jcss.1997.1504 · Cited by 20,466
Self-citationBreiman, L. (1996) · Machine Learning · doi:10.1007/bf00058655 · Cited by 16,325
The Strength of Weak Learnability
Schapire, R. E. (1990) · Machine Learning · doi:10.1007/bf00116037 · Cited by 4,600
Self-citationOn the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
Vapnik, V. N., & Chervonenkis, A. Y. (1971) · Theory of Probability & Its Applications · doi:10.1137/1116025 · Cited by 2,448
Boosting a Weak Learning Algorithm by Majority
Freund, Y. (1995) · Information and Computation · doi:10.1006/inco.1995.1136 · Cited by 1,674
Self-citation
Cited by
Breiman, L. (2001) · Machine Learning · doi:10.1023/a:1010933404324 · Cited by 133,538
Rapid object detection using a boosted cascade of simple features
Viola, P., & Jones, M. (2005) · Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001 · doi:10.1109/cvpr.2001.990517 · Cited by 18,300
Robust Real-Time Face Detection
Viola, P., & Jones, M. J. (2004) · International Journal of Computer Vision · doi:10.1023/b:visi.0000013087.49260.fb · Cited by 14,097
Friedman, J., Hastie, T., & Tibshirani, R. (2000) · The Annals of Statistics · doi:10.1214/aos/1016218223 · Cited by 6,884
Top 10 algorithms in data mining
Wu, X., Kumar, V., Ross Quinlan, J., Ghosh, J., Yang, Q., Motoda, H., McLachlan, G. J., Ng, A., Liu, B., Yu, P. S., et al. (2008) · Knowledge and Information Systems · doi:10.1007/s10115-007-0114-2 · Cited by 5,667
Popular Ensemble Methods: An Empirical Study
Opitz, D., & Maclin, R. (1999) · Journal of Artificial Intelligence Research · doi:10.1613/jair.614 · Cited by 2,953
Ishwaran, H., Kogalur, U. B., Blackstone, E. H., & Lauer, M. S. (2008) · The Annals of Applied Statistics · doi:10.1214/08-aoas169 · Cited by 2,714
Prasad, A. M., Iverson, L. R., & Liaw, A. (2006) · Ecosystems · doi:10.1007/s10021-005-0054-1 · Cited by 1,987
Classification in the Presence of Label Noise: A Survey
Frenay, B., & Verleysen, M. (2014) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2013.2292894 · Cited by 1,777
Reconciling modern machine-learning practice and the classical bias–variance trade-off
Belkin, M., Hsu, D., Ma, S., & Mandal, S. (2019) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1903070116 · Cited by 1,595
Interpretable machine learning: Fundamental principles and 10 grand challenges
Rudin, C., Chen, C., Chen, Z., Huang, H., Semenova, L., & Zhong, C. (2022) · Statistics Surveys · doi:10.1214/21-ss133 · Cited by 958
Learn++: an incremental learning algorithm for supervised neural networks
Polikar, R., Upda, L., Upda, S. S., & Honavar, V. (2001) · IEEE Transactions on Systems, Man and Cybernetics, Part C (Applications and Reviews) · doi:10.1109/5326.983933 · Cited by 888
Robust real-time face detection
Viola, P., & Jones, M. (2005) · Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001 · doi:10.1109/iccv.2001.937709 · Cited by 898
Machine learning in acoustics: Theory and applications
Bianco, M. J., Gerstoft, P., Traer, J., Ozanich, E., Roch, M. A., Gannot, S., & Deledalle, C.-A. (2019) · The Journal of the Acoustical Society of America · doi:10.1121/1.5133944 · Cited by 609
Auto-Context and Its Application to High-Level Vision Tasks and 3D Brain Image Segmentation
Tu, Z., & Bai, X. (2010) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2009.186 · Cited by 578
FloatBoost learning and statistical face detection
Li, S. Z., & Zhang, Z. (2004) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2004.68 · Cited by 525
The Role of Occam's Razor in Knowledge Discovery
Domingos, P. (1999) · Data Mining and Knowledge Discovery · doi:10.1023/a:1009868929893 · Cited by 459
An analysis of the Viola-Jones face detection algorithm
Wang, Y.-Q. (2014) · Image Processing On Line · doi:10.5201/ipol.2014.104 · Cited by 354
Does learning require memorization? a short tale about a long tail
Feldman, V. (2020) · Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing · doi:10.1145/3357713.3384290 · Cited by 287
A Comprehensive Analysis on Wearable Acceleration Sensors in Human Activity Recognition
Janidarmian, M., Roshan Fekr, A., Radecka, K., & Zilic, Z. (2017) · Sensors · doi:10.3390/s17030529 · Cited by 217
To understand deep learning we need to understand kernel learning
Belkin, M., Ma, S., & Mandal, S. (2018) · arXiv · doi:10.48550/arxiv.1802.01396 · Cited by 201
Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning
Allen-Zhu, Z., & Li, Y. (2020) · arXiv · doi:10.48550/arxiv.2012.09816 · Cited by 178
Harmless interpolation of noisy data in regression
Muthukumar, V., Vodrahalli, K., & Sahai, A. (2019) · 2019 IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.2019.8849614 · Cited by 162
A stopping criterion for active learning
Vlachos, A. (2008) · Computer Speech & Language · doi:10.1016/j.csl.2007.12.001 · Cited by 153
Scenario-Based Insider Threat Detection From Cyber Activities
Chattopadhyay, P., Wang, L., & Tan, Y.-P. (2018) · IEEE Transactions on Computational Social Systems · doi:10.1109/tcss.2018.2857473 · Cited by 115
Yang, P., Yoo, P. D., Fernando, J., Zhou, B. B., Zhang, Z., & Zomaya, A. Y. (2014) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2013.2257480 · Cited by 90
On the Existence of Simpler Machine Learning Models
Semenova, L., Rudin, C., & Parr, R. (2022) · 2022 ACM Conference on Fairness Accountability and Transparency · doi:10.1145/3531146.3533232 · Cited by 90
Effects of ApoE4 and maternal history of dementia on hippocampal atrophy
Andrawis, J. P., Hwang, K. S., Green, A. E., Kotlerman, J., Elashoff, D., Morra, J. H., Cummings, J. L., Toga, A. W., Thompson, P. M., & Apostolova, L. G. (2012) · Neurobiology of Aging · doi:10.1016/j.neurobiolaging.2010.07.020 · Cited by 54
Fast data selection for SVM training using ensemble margin
Guo, L., & Boukir, S. (2015) · Pattern Recognition Letters · doi:10.1016/j.patrec.2014.08.003 · Cited by 49
Deep decision tree transfer boosting
Jiang, S., Mao, H., Ding, Z., & Fu, Y. (2020) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2019.2901273 · Cited by 46
Data-driven reverse engineering of signaling pathways using ensembles of dynamic models
Henriques, D., Villaverde, A. F., Rocha, M., Saez-Rodriguez, J., & Banga, J. R. (2017) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1005379 · Cited by 44
A machine learning model for screening thermodynamic stable lead-free halide double perovskites
Liang, G.-Q., & Zhang, J. (2022) · Computational Materials Science · doi:10.1016/j.commatsci.2021.111172 · Cited by 44
Predicting online shopping cart abandonment with machine learning approaches
Rausch, T. M., Derra, N. D., & Wolf, L. (2022) · International Journal of Market Research · doi:10.1177/1470785320972526 · Cited by 36
Suzuki, S., & Oguri, K. (2009) · 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society · doi:10.1109/iembs.2009.5332505 · Cited by 31
Sample Subset Optimization for Classifying Imbalanced Biological Data
Yang, P., Zhang, Z., Zhou, B. B., & Zomaya, A. Y. (2011) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-20847-8_28 · Cited by 31
Quantum computing and supervised machine learning
Oneto, L., Ridella, S., & Anguita, D. (2017) · Quantum Inspired Computational Intelligence · doi:10.1016/b978-0-12-804409-4.00002-4 · Cited by 11
(2008) · ScholarlyCommons (University of Pennsylvania)
Metadata
- Authors
- Bartlett, P., Freund, Y., Lee, W. S., & Schapire, R. E.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1998-10-01
- Volume
- 26
- Issue
- 5
- Pages
- 1651-1686
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W1975846642
- Cited by
- 2,306
- References
- 7
- FWCI
- 68.70
- Type
- journal article
- Language
- en
- Open access
- bronze
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
