Decision trees do not generalize to new variations
Abstract
The family of decision tree learning algorithms is among the most widespread and studied. Motivated by the desire to develop learning algorithms that can generalize when learning highly varying functions such as those presumably needed to achieve artificial intelligence, we study some theoretical limitations of decision trees. We demonstrate formally that they can be seriously hurt by the curse of dimensionality in a sense that is a bit different from other nonparametric statistical methods, but most importantly, that they cannot generalize to variations not seen in the training set. This is because a decision tree creates a partition of the input space and needs at least one example in each of the regions associated with a leaf to make a sensible prediction in that region. A better understanding of the fundamental reasons for this limitation suggests that one should use forests or even deeper architectures instead of trees, which provide a form of distributed representation and can generalize to variations not encountered in the training data.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
A high concentration of cfDNA in plasma and CNV in chromosomes affected the pathogenesis of cancer cases.
“They concluded that a high concentration of cfDNA in plasma and CNV in chromosomes affected the pathogenesis of cancer cases.”
From Explainable, trustworthy, and ethical machine learning for healthcare: A survey (2022) · cites this paper as [118]
Cites
Breiman, L. (2001) · Machine Learning · doi:10.1023/a:1010933404324 · Cited by 133,538 · see citing works
Cortes, C., & Vapnik, V. (1995) · Machine Learning · doi:10.1007/bf00994018 · Cited by 59,421 · see citing works
Cortes, C., & Vapnik, V. N. (1995) · Machine Learning · doi:10.1023/a:1022627411411 · Cited by 34,565 · see citing works
Classification and Regression Trees.
Gordon, A. D., Breiman, L., Friedman, J. H., Olshen, R. A., & Stone, C. J. (1984) · Biometrics · doi:10.2307/2530946 · Cited by 23,834 · see citing works
Multilayer feedforward networks are universal approximators
Hornik, K., Stinchcombe, M., & White, H. (1989) · Neural Networks · doi:10.1016/0893-6080(89)90020-8 · Cited by 21,728 · see citing works
A fast learning algorithm for deep belief nets
Hinton, G. E., Osindero, S., & Teh, Y.-W. (2006) · Neural Computation · doi:10.1162/neco.2006.18.7.1527 · Cited by 16,336 · see citing works
A training algorithm for optimal margin classifiers
Boser, B. E., Guyon, I. M., & Vapnik, V. N. (1992) · Proceedings of the fifth annual workshop on Computational learning theory · doi:10.1145/130385.130401 · Cited by 11,992 · see citing works
Philosophical transactions of the Royal Society of London. B
Press, H. (1886) · Cited by 10,087 · see citing works
Classification and regression trees
Praagman, J. (1985) · European Journal of Operational Research · doi:10.1016/0377-2217(85)90321-2 · Cited by 10,053 · see citing works
Multilayer feedforward networks are universal approximators
HornikK., StinchcombeM., & WhiteH. (1989) · Neural Networks · doi:10.5555/70405.70408 · Cited by 9,266 · see citing works
Experiments with a new boosting algorithm
Freund, Y., & Schapire, R. E. (1996) · Cited by 8,189 · see citing works
Learning Deep Architectures for AI
Bengio, Y. (2009) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000006 · Cited by 7,048 · see citing works
Ho, T. K. (2002) · IAPR International Conference on Document Analysis and Recognition (ICDAR) · doi:10.1109/icdar.1995.598994 · Cited by 6,311 · see citing works
Learning Deep Architectures for AI
Bengio, Y. (2009) · now publishers, Inc. eBooks · doi:10.1561/9781601982957 · Cited by 5,037 · see citing works
Greedy layer-wise training of deep networks
Bengio, Y., Lamblin, P., Popovici, D., & Larochelle, H. (2007) · Advances in Neural Information Processing Systems 19 · doi:10.7551/mitpress/7503.003.0024 · Cited by 4,841 · see citing works
Self-citationAn Introduction to Kolmogorov Complexity and Its Applications
Li, M., & Vitanyi, P. M. B. (2019) · Texts in computer science · doi:10.1007/978-3-030-11298-1 · Cited by 3,752 · see citing works
Three approaches to the quantitative definition of information *
Kolmogorov, A. N. (1968) · International Journal of Computer Mathematics · doi:10.1080/00207166808803030 · Cited by 2,053 · see citing works
Proceedings of the 56th Annual ACM Symposium on Theory of Computing
(2024) · doi:10.1145/3618260 · Cited by 1,842 · see citing works
An Introduction to Kolmogorov Complexity and Its Applications
Li, M., & Vitanyi, P. M. B. (1997) · Springer eBooks · doi:10.1007/978-1-4757-2606-0 · Cited by 1,792 · see citing works
A formal theory of inductive inference. Part II
Solomonoff, R. J. (1964) · Information and Control · doi:10.1016/s0019-9958(64)90131-7 · Cited by 1,758 · see citing works
Advances in Neural Information Processing Systems 19 (NIPS 2006)
Simonotto, E., Whalley, H. C., Lawrie, S. M., Murray, L. M., McGonigle, D. J., & Storkey, A. (2006) · Cited by 1,651 · see citing works
Learning methods for generic object recognition with invariance to pose and lighting
LeCun, Y., Huang, F. J., & Bottou, L. (2004) · Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004. · doi:10.1109/cvpr.2004.1315150 · Cited by 1,324 · see citing works
Efficient Learning of Sparse Representations with an Energy-Based Model
Ranzato, M., Poultney, C., Chopra, S., & LeCun, Y. (2007) · Advances in Neural Information Processing Systems 19 · doi:10.7551/mitpress/7503.003.0147 · Cited by 1,106 · see citing works
(2007) · Cited by 937 · see citing works
SPLIT SELECTION METHODS FOR CLASSIFICATION TREES
Loh, W., & Shih, Y. (1997) · Cited by 933 · see citing works
Learning distributed representations of concepts.
Hinton, G. E. (1989) · eScholarship (California Digital Library) · Cited by 815 · see citing works
Almost optimal lower bounds for small depth circuits
Håstad, J. (1986) · doi:10.1145/12130.12132 · Cited by 630 · see citing works
∑11-Formulae on finite structures
Ajtai, M. (1983) · Annals of Pure and Applied Logic · doi:10.1016/0168-0072(83)90038-6 · Cited by 589 · see citing works
(2007) · The MIT Press eBooks · doi:10.7551/mitpress/7496.001.0001 · Cited by 539 · see citing works
Universal Artificial Intellegence
Hutter, M. (2005) · Texts in Theoretical Computer Science An EATCS Series · doi:10.1007/b138233 · Cited by 523 · see citing works
Error-Correcting Output Coding Corrects Bias and Variance
Kong, E. B., & Dietterich, T. G. (1995) · Elsevier eBooks · doi:10.1016/b978-1-55860-377-6.50046-3 · Cited by 361 · see citing works
On the power of small-depth threshold circuits
H�stad, J., & Goldmann, M. (1991) · Computational Complexity · doi:10.1007/bf01272517 · Cited by 253 · see citing works
Generative models for discovering sparse distributed representations
Hinton, G. E., & Ghahramani, Z. (1997) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.1997.0101 · Cited by 225 · see citing works
The Curse of Highly Variable Functions for Local Kernel Machines
Bengio, Y., Delalleau, O., & Roux, N. L. (2005) · Cited by 188 · see citing works
Non-Local Manifold Parzen Windows
Bengio, Y., Larochelle, H., & Vincent, P. (2005) · Cited by 47 · see citing works
Nonlocal Estimation of Manifold Structure
Bengio, Y., Monperrus, M., & Larochelle, H. (2006) · Neural Computation · doi:10.1162/neco.2006.18.10.2509 · Cited by 45 · see citing works
Global data analysis and the fragmentation problem in decision tree induction
Vilalta, R., Blix, G., & Rendell, L. A. (1997) · Lecture notes in computer science · doi:10.1007/3-540-62858-4_95 · Cited by 29 · see citing works
주철환 (1999) · 월간말 · Cited by 28 · see citing works
Paccanaro, A., & Hinton, G. E. (2000) · doi:10.1109/ijcnn.2000.857906 · Cited by 18 · see citing works
An exponential lower bound on the size of algebraic decision trees for Max
Grigoriev, D., Karpiński, M., & Yao, A. C.-C. (1998) · Computational Complexity · doi:10.1007/s000370050010 · Cited by 14 · see citing works
Learning despite concept variation by finding structure in attribute-based data
Pérez, E., & Rendell, L. A. (1996) · Cited by 12 · see citing works
Complexity Lower Bounds for Approximation Algebraic Computation Trees
Cucker, F., & Grigoriev, D. (1999) · Journal of Complexity · doi:10.1006/jcom.1999.0519 · Cited by 7 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Representation Learning: A Review and New Perspectives
Bengio, Y., Courville, A., & Vincent, P. (2013) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2013.50 · Cited by 13,001 · see citing works
Learning Deep Architectures for AI
Bengio, Y. (2009) · now publishers, Inc. eBooks · doi:10.1561/9781601982957 · Cited by 5,037 · see citing works
Context-dependent pre-trained deep neural networks for large-vocabulary speech recognition
Dahl, G. E., Yu, D., Deng, L., & Acero, A. (2012) · IEEE Transactions on Audio Speech and Language Processing · doi:10.1109/tasl.2011.2134090 · Cited by 3,011 · see citing works
Classification Based on Decision Tree Algorithm for Machine Learning
Charbuty, B., & Abdulazeez, A. M. (2021) · Journal of Applied Science and Technology Trends · doi:10.38094/jastt20165 · Cited by 1,887 · see citing works
Applications of Deep Learning in Biomedicine
Mamoshina, P., Vieira, A., Lane, E., & Zhavoronkov, A. (2016) · Molecular Pharmaceutics · doi:10.1021/acs.molpharmaceut.5b00982 · Cited by 701 · see citing works
Deep Learning of Representations: Looking Forward
Bengio, Y. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-39593-2_1 · Cited by 558 · see citing works
Kontschieder, P., Fiterau, M., Criminisi, A., & Bulò, S. R. (2015) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2015.172 · Cited by 519 · see citing works
Unsupervised Feature Learning and Deep Learning: A Review and New Perspectives
Bengio, Y., Courville, A. C., & Vincent, P. (2012) · Cited by 455 · see citing works
Explainable, trustworthy, and ethical machine learning for healthcare: A survey
Rasheed, K., Qayyum, A., Ghaly, M., Al-Fuqaha, A., Razi, A., & Qadir, J. (2022) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2022.106043 · Cited by 372 · see citing works
Digital medicine and the curse of dimensionality
Berisha, V., Krantsevich, C., Hahn, P. R., Hahn, S., Dasarathy, G., Turaga, P., & Liss, J. (2021) · npj Digital Medicine · doi:10.1038/s41746-021-00521-5 · Cited by 344 · see citing works
Singh, A. V., Ansari, M. H. D., Rosenkranz, D., Maharjan, R. S., Kriegel, F. L., Gandhi, K., Kanase, A., Singh, R., Laux, P., & Luch, A. (2020) · Advanced Healthcare Materials · doi:10.1002/adhm.201901862 · Cited by 311 · see citing works
Shallow vs. Deep Sum-Product Networks
Delalleau, O., & Bengio, Y. (2011) · Cited by 248 · see citing works
Representation Learning: A Review and New PerspectivesPreprint
Bengio, Y., Courville, A. C., & Vincent, P. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1206.5538 · Cited by 235 · see citing works
On the Expressive Power of Deep Architectures
Bengio, Y., & Delalleau, O. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-24477-3_1 · Cited by 209 · see citing works
On the Expressive Power of Deep Architectures
Bengio, Y., & Delalleau, O. (2011) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-24412-4_3 · Cited by 182 · see citing works
Singh, A. V., Rosenkranz, D., Ansari, M. H. D., Singh, R., Kanase, A., Singh, S. P., Johnston, B. D., Tentschert, J., Laux, P., & Luch, A. (2020) · Advanced Intelligent Systems · doi:10.1002/aisy.202000084 · Cited by 149 · see citing works
Deep Learning of Representations: Looking ForwardPreprint
Bengio, Y. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1305.0445 · Cited by 128 · see citing works
Digital Pharmaceutical Sciences
Damiati, S. A. (2020) · AAPS PharmSciTech · doi:10.1208/s12249-020-01747-4 · Cited by 90 · see citing works
Inferring user knowledge level from eye movement patterns
Cole, M., Jacek Gwizdka, A., Liu, C., Belkin, N. J., & Zhang, X. (2012) · Information Processing & Management · doi:10.1016/j.ipm.2012.08.004 · Cited by 86 · see citing works
(Q)SAR modelling of nanomaterial toxicity: A critical review
Karakuş, C. Ö., Yue, C. X., Liu, J. J., Wilkins, T., & Wang, X. Z. (2015) · Particuology · doi:10.1016/j.partic.2014.12.001 · Cited by 84 · see citing works
Local Deep Kernel Learning for Efficient Non-linear SVM Prediction
Jose, C., Goyal, P., Aggrwal, P., & Varma, M. (2013) · International Conference on Machine Learning · Cited by 80 · see citing works
Lithofacies identification using support vector machine based on local deep multi-kernel learning
Liu, X., Zhou, L., Chen, X.-H., & Li, J. (2020) · Petroleum Science · doi:10.1007/s12182-020-00474-6 · Cited by 76 · see citing works
Deep learning and Boosted trees for injuries prediction in power infrastructure projects
Oyedele, A. O., Ajayi, A., Oyedele, L. O., Delgado, J. M. D., Akanbi, L., Akinadé, O. O., Owolabi, H. A., & Bilal, M. (2021) · Applied Soft Computing · doi:10.1016/j.asoc.2021.107587 · Cited by 47 · see citing works
Random Bits Forest: a Strong Classifier/Regressor for Big Data
Wang, Y., Li, Y., Pu, W., Wen, K., Shugart, Y. Y., Xiong, M., & Li, J. (2016) · Scientific Reports · doi:10.1038/srep30086 · Cited by 44 · see citing works
Integrating representation learning and skill learning in a human-like intelligent agent
Li, N., Matsuda, N., Cohen, W. W., & Koedinger, K. R. (2014) · Artificial Intelligence · doi:10.1016/j.artint.2014.11.002 · Cited by 43 · see citing works
Evolving Culture Versus Local Minima
Bengio, Y. (2014) · Studies in computational intelligence · doi:10.1007/978-3-642-55337-0_3 · Cited by 35 · see citing works
Nanotoxicity prediction using computational modelling - review and future directions
Saini, B., & Srivastava, S. (2018) · IOP Conference Series Materials Science and Engineering · doi:10.1088/1757-899x/348/1/012005 · Cited by 27 · see citing works
Literature Review of (Q)SAR Modelling of Nanomaterial Toxicity
Karakuş, C. Ö., Yue, C. X., Liu, J. J., Wilkins, T., & Wang, X. Z. (2017) · Advances in experimental medicine and biology · doi:10.1007/978-3-319-47754-1_5 · Cited by 27 · see citing works
A Bibliometrics-Based Systematic Review of Safety Risk Assessment for IBS Hoisting Construction
Junjia, Y., Alias, A. H., Haron, N. A., & Bakar, N. A. (2023) · Buildings · doi:10.3390/buildings13071853 · Cited by 27 · see citing works
Measuring the Gap Between HMM-Based ASR and TTS
Dines, J., Yamagishi, J., & King, S. (2010) · IEEE Journal of Selected Topics in Signal Processing · doi:10.1109/jstsp.2010.2079315 · Cited by 25 · see citing works
Kim, E., Caraballo, P. J., Castro, M. R., Pieczkiewicz, D. S., & Simon, G. (2019) · Journal of Medical Systems · doi:10.1007/s10916-019-1321-6 · Cited by 25 · see citing works
Confident Privacy Decision-Making in IoT Environments
Lee, H., & Kobsa, A. (2019) · ACM Transactions on Computer-Human Interaction · doi:10.1145/3364223 · Cited by 23 · see citing works
Evolving Culture vs Local MinimaPreprint
Bengio, Y. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1203.2990 · Cited by 22 · see citing works
Cho, K., & Bengio, Y. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1406.7362 · Cited by 22 · see citing works
Dahl, G. E. (2015) · TSpace (University of Toronto) · Cited by 20 · see citing works
Sarvestani, Z. M., Jamali, J., Taghizadeh, M., & Dindarloo, M. H. F. (2023) · Journal of Cancer Research and Clinical Oncology · doi:10.1007/s00432-023-04571-y · Cited by 17 · see citing works
Ludwig, S. A., & Kong, J. (2017) · Medical & Biological Engineering & Computing · doi:10.1007/s11517-017-1658-2 · Cited by 14 · see citing works
Cardiac Disease Prediction using Machine Learning Algorithms
Trisal, A., Sagar, V., & Jameel, R. (2022) · International Conference on Computational Intelligence and Sustainable Engineering Solutions (CISES) · doi:10.1109/cises54857.2022.9844370 · Cited by 13 · see citing works
Joint optimization of linear and nonlinear models for sequential regression
Fazla, A., Aydin, M. E., & Kozat, S. S. (2022) · Digital Signal Processing · doi:10.1016/j.dsp.2022.103802 · Cited by 10 · see citing works
A Qualitative Evaluation of Random Forest Feature Learning
Tang, A., & Foong, J. T. (2014) · Advances in intelligent systems and computing · doi:10.1007/978-3-319-07692-8_34 · Cited by 10 · see citing works
Techniques of Decision Tree Induction
Grąbczewski, K. (2013) · Studies in computational intelligence · doi:10.1007/978-3-319-00960-5_2 · Cited by 10 · see citing works
Kumano, S., & Akutsu, T. (2022) · Neural Computation · doi:10.1162/neco_a_01486 · Cited by 9 · see citing works
Wedagedara, H., Witharana, C., Fahey, R. T., Cerrai, D., Parent, J. R., & Perera, A. S. (2024) · Applied Sciences · doi:10.3390/app14124991 · Cited by 8 · see citing works
Towards Interpretable Reinforcement Learning with State Abstraction Driven by External Knowledge
Bougie, N., & Ichise, R. (2020) · IEICE Transactions on Information and Systems · doi:10.1587/transinf.2019edp7170 · Cited by 8 · see citing works
Artificial Intelligence Powered Insights into Nanotoxicology
Thiruvengadam, S., Chakraborty, T., & Prasanna, M. (2024) · International Journal of Advancement in Life Sciences Research · doi:10.31632/ijalsr.2024.v07i02.005 · Cited by 6 · see citing works
Uncertainty-aware learning for improvements in image quality of the Canada–France–Hawaii Telescope
Gilda, S., Draper, S. C., Fabbro, S., Mahoney, W., Prunet, S., Withington, K., Wilson, M. B., Ting, Y.-S., & Sheinis, A. (2021) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stab3243 · Cited by 6 · see citing works
Kang, Y., Huang, S.-T., & Wu, P. (2021) · SN Computer Science · doi:10.1007/s42979-021-00670-0 · Cited by 6 · see citing works
Bain, C. M., Shi, D., Banad, Y. M., Boness, C. L., & Loeffelman, J. E. (2026) · Frontiers in Psychology · doi:10.3389/fpsyg.2026.1819366 · Cited by 5 · see citing works
A neural decision forest scheme with application to EMG gesture classification
Rodriguez, D., Piryatinska, A., & Zhang, X. (2016) · 2016 SAI Computing Conference (SAI) · doi:10.1109/sai.2016.7555990 · Cited by 5 · see citing works
Hardware Architecture for High-Speed Object Detection Using Decision Tree Ensemble
Mitsunari, K., Yu, J., Onoye, T., & Hashimoto, M. (2018) · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences · doi:10.1587/transfun.e101.a.1298 · Cited by 5 · see citing works
Zhang, Z., Raza, A., Yang, M., Lu, Y., & Hu, Y. (2025) · Computers and Electronics in Agriculture · doi:10.1016/j.compag.2025.111140 · Cited by 4 · see citing works
Behavioral insights of adaptive splitting decision trees in evolving data stream classification
Assis, D. N., Barddal, J. P., & Enembreck, F. (2025) · Knowledge and Information Systems · doi:10.1007/s10115-025-02395-5 · Cited by 4 · see citing works
Discovering environmental health effects of transport scenarios through agent-based simulations
Sonnenschein, T., Scheider, S., de Wit, G. A., Woodcock, J., & Vermeulen, R. C. H. (2025) · Environment International · doi:10.1016/j.envint.2025.109866 · Cited by 4 · see citing works
Nanoinformatics: Predicting Toxicity Using Computational Modeling
Saini, B., & Srivastava, S. (2018) · SpringerBriefs in applied sciences and technology · doi:10.1007/978-981-13-0544-3_6 · Cited by 4 · see citing works
Interpretable, Transparent, and Auditable Machine Learning: An Alternative to Factor Investing
Philps, D., Tilles, D., & Law, T. (2021) · The Journal of Financial Data Science · doi:10.3905/jfds.2021.1.077 · Cited by 4 · see citing works
MEME: Generating RNN Model Explanations via Model ExtractionPreprint
Kazhdan, D., Dimanov, B., Jamnik, M., & Lió, P. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2012.06954 · Cited by 4 · see citing works
Deep Learning Techniques For Improving Breast Cancer Detection And Diagnosis
Abed, A. H. (2022) · International Journal of Advanced Networking and Applications · doi:10.35444/ijana.2022.13606 · Cited by 3 · see citing works
Predicting Bicyclist Maneuvers using Explicit and Implicit CommunicationPreprint
Grigoropoulos, G., Malcolm, P., Keler, A., Busch, F., & Bogenberger, K. (2022) · Research Square · doi:10.21203/rs.3.rs-2108504/v1 · Cited by 3 · see citing works
Interpretable Non-linear Survival Analysis with Evolutionary Symbolic Regression
Rovito, L., & Virgolin, M. (2025) · Genetic and Evolutionary Computation Conference (GECCO) · doi:10.1145/3712256.3726446 · Cited by 2 · see citing works
Testing Closeness of Multivariate Distributions via Ramsey Theory
Diakonikolas, I., Kane, D. M., & Liu, S. (2024) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/3618260.3649657 · Cited by 2 · see citing works
Extended Decision Tree with or Relationship for HMM-Based Speech Synthesis
Wang, Y., Tao, J., Yang, M., & Li, Y. (2013) · Asian Conference on Pattern Recognition · doi:10.1109/acpr.2013.94 · Cited by 2 · see citing works
Improving Generalization Ability of Classifier with Multiple Imputation Techniques
Patil, D. V., & Bichkar, R. S. (2012) · Communications in computer and information science · doi:10.1007/978-3-642-31686-9_37 · Cited by 2 · see citing works
Giang, N. H., Tran, D. H., Hoang, N. T. D., & Nguyen, T. T. (2022) · Water Practice & Technology · doi:10.2166/wpt.2022.120 · Cited by 2 · see citing works
Textual outlier detection with an unsupervised method using text similarity and density peak
Sereshki, M. T., Zanjireh, M. M., & Bahaghighat, M. (2023) · Acta Universitatis Sapientiae Informatica · doi:10.2478/ausi-2023-0008 · Cited by 2 · see citing works
Dive into Decision Trees and Forests: A Theoretical DemonstrationPreprint
Zhang, J. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2101.08656 · Cited by 3 · see citing works
Bain, C. M., Shi, D., Loeffelman, J. E., Norris, J. E., & Ethridge, L. E. (2024) · doi:10.31234/osf.io/j695a · Cited by 2 · see citing works
Measuring the prediction difficulty of individual cases in a dataset using machine learning
Kwon, H., Greenberg, M., Josephson, C. B., & Lee, J. (2024) · Scientific Reports · doi:10.1038/s41598-024-61284-z · Cited by 1 · see citing works
Real-time human body parts localization from dynamic vision sensor
Mao, W., Wang, Q., Wang, X., Guo, P. Y., Wang, S., Shao, G., Lee, K., & Park, P. K. J. (2015) · Proceedings - International Conference on Image Processing · doi:10.1109/icip.2015.7351715 · Cited by 1 · see citing works
On the Generative Power of ReLU Network for Generating Similar Strings
Ghafoor, M., & Akutsu, T. (2024) · IEEE Access · doi:10.1109/access.2024.3387306 · Cited by 1 · see citing works
PAC-learning gains of Turing machines over circuits and neural networks
Pinon, B., Jungers, R. M., & Delvenne, J. (2022) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2022.133585 · Cited by 1 · see citing works
Regularizing Deep Models for Visual Recognition
Tashnizi, E. B. (2016) · UWSpace (University of Waterloo) · Cited by 1 · see citing works
Giang, N. H., Hieu, T. D., & Do, H. N. T. (2021) · Research Square · doi:10.21203/rs.3.rs-1005920/v1 · Cited by 1 · see citing works
From memristors to compositional machine learning
Nugent, A., & Molter, T. (2017) · Proceedings of the Neuromorphic Computing Symposium · doi:10.1145/3183584.3183615
“However, as Bengio pointed out [Bengio et al. 2010], if we consider the output of a tree to be an integer specifying the DT leaf or path, then we can consider the output of a decision tree forest (DTF) as the encoding of a vector whose elements are these integers, one per tree in the forest.”
NanoSAR: In Silico Modelling of Nanomaterial Toxicity
Karakuş, C. Ö. (2016) · White Rose eTheses Online (University of Leeds, The University of Sheffield, University of York)
Imbalanced Remote Sensing Ship Image Classification
Huang, S. (2019) · International Journal of Performability Engineering · doi:10.23940/ijpe.19.06.p22.17091715
Interpretations of Deep Learning by Forests and Haar WaveletsPreprint
Huang, C. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1906.06706
Towards Ubiquitous Privacy Decision Support: Machine Prediction of Privacy Decisions in IoT
Lee, H., & Kobsa, A. (2020) · Internet of things · doi:10.1007/978-3-030-44907-0_5
Deep Learning of Paradigms: The Outlook
Jhansi, A., Lavanya, K., & Kavarakuntla, T. (2020) · Learning and analytics in intelligent systems · doi:10.1007/978-3-030-46943-6_8
Structured Data Encoder for Neural Networks Based on Gradient Boosting Decision Tree
Hu, W., Liu, X., Huang, Y., Wang, Y., Zhang, M., & Zhao, H. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-60239-0_41
VLSI Tree-Based Inference Design Applications for Low-Power Learning
Nagaraju, V., Suresh, G. V., Uthayakumar, C., & Jijina, G. O. (2021) · Journal of Physics Conference Series · doi:10.1088/1742-6596/1964/6/062047
Machine Learning Classification for Video Cleaning
Yao, B., & Li, W. (2023) · IEEE International Symposium on Broadband Multimedia Systems and Broadcasting (BMSB) · doi:10.1109/bmsb58369.2023.10211506
On Strong Anti-learning of Parity
Lisitsa, A., & Vernitski, A. (2024) · Communications in computer and information science · doi:10.1007/978-3-031-53036-4_19
Efficiency of the Combination of Machine Learning Models in the Evaluation of Weather Parameters
Mubakilayi, Y., Ntumba, S., Kafunda, P. K., Cimanga, S., & Kabulu, G. (2023) · Jurnal CoreIT Jurnal Hasil Penelitian Ilmu Komputer dan Teknologi Informasi · doi:10.24014/coreit.v9i1.21713
Bain, C. M., Shi, D., Ethridge, L. E., Norris, J. E., & Loeffelman, J. E. (2024) · Research Square · doi:10.21203/rs.3.rs-4425792/v1
Subgroup Analysis via Model-based Rule Forest
Cheng, I.-L., Hsu, C., Ku, C., Lee, P.-J., & Kang, Y. (2024) · IEEE International Conference on Information Reuse and Integration (IRI) · doi:10.1109/iri62200.2024.00063
Performance Measurement of LLM Classification for Imbalanced Class sizes
Dunne, J. (2025) · Irish Signals and Systems Conference · doi:10.1109/issc67739.2025.11291262
An EXplainable Artificial Intelligence Credit Rating System
El-Qadi, A. (2023) · theses.fr (ABES) · doi:10.70675/2d09695dz9d70z4602zb460zfd801584e220
Sinclair, S., Liu, C., Batpurev, K., Bruce, M. J., Neil, J., Thomson, J., Hauser, C. E., Farmilo, B. J., & White, M. (2026) · Ecological Informatics · doi:10.1016/j.ecoinf.2026.103993
- Authors
- Bengio, Y., Delalleau, O., & Simard, C.
- Affiliations
- Université de Montréal (CA)
- Corresponding author
- Delalleau, Olivier
- Venue
- Computational Intelligence
- Publisher
- Wiley
- Published
- 2010-11
- Volume
- 26
- Issue
- 4
- Pages
- 449-467
- ISSN
- 0824-7935 (ISSN-L)
- 1467-8640
- OpenAlex
- W2106004777
- Cited by
- 89
- References
- 41
- Citations by year
- 2026: 2 · 2025: 5 · 2024: 9 · 2023: 6 · 2022: 8 · 2021: 10 · 2020: 9 · 2019: 4 · 2018: 3 · 2017: 3 · 2016: 5 · 2015: 4 · 2014: 4 · 2013: 6 · 2012: 5
- FWCI
- 14.31
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Computational Intelligence (publishedVersion)
- Funders
- Canadian Institute for Advanced Research
- Topics
- Physical Sciences › Computer Science › Information Systems › Data Mining Algorithms and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Algorithms
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Keywords
- decision tree, generalization, curse of dimensionality, input space partitioning, random forest, distributed representations, nonparametric learning
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