Neural Networks and the Bias/Variance Dilemma
Abstract
Feedforward neural networks trained by error backpropagation are examples of nonparametric regression estimators. We present a tutorial on nonparametric inference and its relation to neural networks, and we use the statistical viewpoint to highlight strengths and weaknesses of neural models. We illustrate the main points with some recognition experiments involving artificial data as well as handwritten numerals. In way of conclusion, we suggest that current-generation feedforward neural networks are largely inadequate for difficult problems in machine perception and machine learning, regardless of parallel-versus-serial hardware or other implementation issues. Furthermore, we suggest that the fundamental challenges in neural modeling are about representation rather than learning per se. This last point is supported by additional experiments with handwritten numerals.
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?
Bias in machine learning and predictive modeling is intrinsically tied to the concept of variance.
“The concept of bias in machine learning (ML) research and more generally in the field of predictive modeling is intrinsically tied to the concept of variance.14”
From Bias in artificial intelligence for medical imaging: fundamentals, detection, avoidance, mitigation, challenges, ethics, and prospects (2024) · cites this paper as [14]
Cites
Maximum Likelihood from Incomplete Data Via the <i>EM</i> Algorithm
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1977.tb01600.x · Cited by 50,444 · see citing works
Learning representations by back-propagating errors
Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986) · Nature · doi:10.1038/323533a0 · Cited by 31,892 · 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
Classification and Regression Trees.
Ryzin, J. V., Breiman, L., Friedman, J. H., Olshen, R. A., & Stone, C. J. (1986) · Journal of the American Statistical Association · doi:10.2307/2288003 · Cited by 21,028 · see citing works
Information Theory and an Extension of the Maximum Likelihood Principle
Akaike, H. (1998) · Springer series in statistics · doi:10.1007/978-1-4612-1694-0_15 · Cited by 18,384 · see citing works
Learning Internal Representations by Error Propagation
Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1985) · doi:10.21236/ada164453 · Cited by 16,501 · see citing works
Approximation by superpositions of a sigmoidal function
Cybenko, G. (1989) · Mathematics of Control, Signals, and Systems · doi:10.1007/bf02551274 · Cited by 13,883 · see citing works
Pattern classification and scene analysis
Duda, R. O., & Hart, P. E. (1973) · CERN Document Server (European Organization for Nuclear Research) · Cited by 12,895 · see citing works
Backpropagation Applied to Handwritten Zip Code Recognition
LeCun, Y., Boser, B., Denker, J. S., Henderson, D., Howard, R. E., Hubbard, W., & Jackel, L. D. (1989) · Neural Computation · doi:10.1162/neco.1989.1.4.541 · Cited by 11,891 · see citing works
Cross validatory choice and assessment of statistical predictions
Stone, M. (1974) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1974.tb00994.x · Cited by 10,881 · 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
Multivariate Adaptive Regression Splines
Friedman, J. H. (1991) · The Annals of Statistics · doi:10.1214/aos/1176347963 · Cited by 8,108 · see citing works
An introduction to computing with neural nets
Lippmann, R. P. (1987) · IEEE ASSP Magazine · doi:10.1109/massp.1987.1165576 · Cited by 7,848 · see citing works
A Learning Algorithm for Boltzmann Machines
Ackley, D., Hinton, G. E., & Sejnowski, T. (1985) · Cognitive Sciences · doi:10.1016/b978-0-08-051581-6.50053-2 · Cited by 4,462 · see citing works
Hansen, L. K., & Salamon, P. (1990) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.58871 · Cited by 4,260 · see citing works
On the approximate realization of continuous mappings by neural networks
Funahashi, K.-I. (1989) · Neural Networks · doi:10.1016/0893-6080(89)90003-8 · Cited by 4,206 · see citing works
Connectionism and cognitive architecture: A critical analysis
Fodor, J. A., & Pylyshyn, Z. W. (1988) · Cognition · doi:10.1016/0010-0277(88)90031-5 · Cited by 4,022 · see citing works
A learning algorithm for Boltzmann machines
Ackley, D. H., Hinton, G. E., & Sejnowski, T. J. (1985) · Cognitive Science · doi:10.1207/s15516709cog0901_7 · Cited by 3,402 · see citing works
Plackett, R. L., & Cox, D. R. (1971) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2344247 · Cited by 2,273 · see citing works
Estimation of Dependences Based on Empirical Data
Vapnik, V. N. (2006) · Information science and statistics · doi:10.1007/0-387-34239-7 · Cited by 2,252 · see citing works
Convergence of Stochastic Processes.
Robinson, P. M., & Pollard, D. (1985) · Economica · doi:10.2307/2553898 · Cited by 2,239 · see citing works
Friedman, J. H., & Stuetzle, W. (1981) · Journal of the American Statistical Association · doi:10.1080/01621459.1981.10477729 · Cited by 2,116 · see citing works
On the proper treatment of connectionism
Smolensky, P. (1988) · Behavioral and Brain Sciences · doi:10.1017/s0140525x00052432 · Cited by 2,112 · see citing works
Principles of Neurodynamics: Perceptrons and the Theory of Brain Mechanisms
White, B., & Rosenblatt, F. (1963) · The American Journal of Psychology · doi:10.2307/1419730 · Cited by 1,818 · see citing works
Estimating Optimal Transformations for Multiple Regression and Correlation
Breiman, L., & Friedman, J. H. (1985) · Journal of the American Statistical Association · doi:10.1080/01621459.1985.10478157 · Cited by 1,713 · see citing works
What Size Net Gives Valid Generalization?
Baum, E. B., & Haussler, D. H. (1989) · Neural Computation · doi:10.1162/neco.1989.1.1.151 · Cited by 1,549 · see citing works
Baum, L. E. (1972) · Medical Entomology and Zoology · Cited by 1,411 · see citing works
Neural networks and principal component analysis: Learning from examples without local minima
Baldi, P., & Hornik, K. (1989) · Neural Networks · doi:10.1016/0893-6080(89)90014-2 · Cited by 1,383 · see citing works
Auto-association by multilayer perceptrons and singular value decomposition
Bourlard, H., & Kamp, Y. (1988) · Biological Cybernetics · doi:10.1007/bf00332918 · Cited by 1,332 · see citing works
The Representation and Matching of Pictorial Structures
Fischler, M. A., & Elschlager, R. A. (1973) · IEEE Transactions on Computers · doi:10.1109/t-c.1973.223602 · Cited by 1,322 · see citing works
Huber, P. J. (1985) · The Annals of Statistics · doi:10.1214/aos/1176349519 · Cited by 1,277 · see citing works
Multiresolution elastic matching
Bajcsy, R., & Kovačič, S. (1989) · Computer Vision Graphics and Image Processing · doi:10.1016/s0734-189x(89)80014-3 · Cited by 1,118 · see citing works
The Correlation Theory of Brain Function
von der Malsburg, C. (1994) · Physics of neural networks · doi:10.1007/978-1-4612-4320-5_2 · Cited by 1,086 · see citing works
Learning and relearning in Boltzmann machines
Hinton, G. E., & Sejnowski, T. J. (2001) · Graphical Models · doi:10.7551/mitpress/3349.003.0005 · Cited by 1,037 · see citing works
Regularization Algorithms for Learning That Are Equivalent to Multilayer Networks
Poggio, T., & Girosi, F. (1990) · Science · doi:10.1126/science.247.4945.978 · Cited by 1,024 · see citing works
Bellman, R. (1964) · IEEE Transactions on Circuit Theory · doi:10.1109/tct.1964.1082221 · Cited by 1,003 · see citing works
Stochastic Complexity and Modeling
Rissanen, J. (1986) · The Annals of Statistics · doi:10.1214/aos/1176350051 · Cited by 944 · see citing works
Learning in Artificial Neural Networks: A Statistical Perspective
White, H. (1989) · Neural Computation · doi:10.1162/neco.1989.1.4.425 · Cited by 920 · see citing works
Anderson, J. A., Silverstein, J. W., Ritz, S. A., & Jones, R. S. (1977) · Psychological Review · doi:10.1037/0033-295x.84.5.413 · Cited by 891 · see citing works
A Statistical Model for Positron Emission Tomography
Vardi, Y., Shepp, L. A., & Kaufman, L. (1985) · Journal of the American Statistical Association · doi:10.1080/01621459.1985.10477119 · Cited by 863 · see citing works
Decision theoretic generalizations of the PAC model for neural net and other learning applications
Haussler, D. H. (1992) · Information and Computation · doi:10.1016/0890-5401(92)90010-d · Cited by 845 · see citing works
Neurocomputing: Foundations of Research
Anderson, J. A. D. W., & Rosenfeld, E. (1988) · Cited by 831 · see citing works
Layered Neural Networks with Gaussian Hidden Units as Universal Approximations
Hartman, E., Keeler, J. D., & Kowalski, J. M. (1990) · Neural Computation · doi:10.1162/neco.1990.2.2.210 · Cited by 785 · see citing works
The recent excitement about neural networks
Crick, F. (1989) · Nature · doi:10.1038/337129a0 · Cited by 724 · see citing works
Cross-Validatory Choice and Assessment of Statistical Predictions (With Discussion)
Stone, M. (1976) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1976.tb01573.x · Cited by 696 · see citing works
Connectionist nonparametric regression: Multilayer feedforward networks can learn arbitrary mappings
White, H. (1990) · Neural Networks · doi:10.1016/0893-6080(90)90004-5 · Cited by 683 · see citing works
A simple procedure for pruning back-propagation trained neural networks
Karnin, E. D. (1990) · IEEE Transactions on Neural Networks · doi:10.1109/72.80236 · Cited by 672 · see citing works
On the Consistency of Bayes Estimates
Diaconis, P. W., & Freedman, D. A. (1986) · The Annals of Statistics · doi:10.1214/aos/1176349830 · Cited by 614 · see citing works
von der Malsburg, C. (1986) · Springer eBooks · doi:10.1007/978-3-642-70911-1_10 · Cited by 549 · see citing works
A Theory of Adaptive Pattern Classifiers
Амари, Ш.-И. (1967) · IEEE Transactions on Electronic Computers · doi:10.1109/pgec.1967.264666 · Cited by 543 · see citing works
Skeletonization: A Technique for Trimming the Fat from a Network via Relevance Assessment
Mozer, M. C., & Smolensky, P. (1988) · neural information processing systems · Cited by 530 · see citing works
Wahba, G. (1985) · The Annals of Statistics · doi:10.1214/aos/1176349743 · Cited by 524 · see citing works
A Computer-Derived Protocol to Aid in the Diagnosis of Emergency Room Patients with Acute Chest Pain
Goldman, L., Weinberg, M. S., Weisberg, M. C., Olshen, R. A., Cook, E. F., Rk, S., Ga, L., Dennis, C. A., Wilson, C., Deckelbaum, L. I., et al. (1982) · New England Journal of Medicine · doi:10.1056/nejm198209023071004 · Cited by 502 · see citing works
Review of Neural Networks for Speech Recognition
Lippmann, R. P. (1989) · Neural Computation · doi:10.1162/neco.1989.1.1.1 · Cited by 478 · see citing works
Friedman, J. H., & Stuetzle, W. (1981) · Journal of the American Statistical Association · doi:10.2307/2287576 · Cited by 475 · see citing works
Biased and Unbiased Cross-Validation in Density Estimation
Scott, D. W., & Terrell, G. R. (1987) · Journal of the American Statistical Association · doi:10.1080/01621459.1987.10478550 · Cited by 467 · see citing works
Estimating Optimal Transformations for Multiple Regression and Correlation
Breiman, L., & Friedman, J. H. (1985) · Journal of the American Statistical Association · doi:10.2307/2288473 · Cited by 452 · see citing works
How Far Are Automatically Chosen Regression Smoothing Parameters From Their Optimum?
Härdle, W. K., Hall, P. M., & Marron, J. S. (1988) · Journal of the American Statistical Association · doi:10.1080/01621459.1988.10478568 · Cited by 400 · see citing works
Nonparametric Maximum Likelihood Estimation by the Method of Sieves
Geman, S., & Hwang, C.-R. (1982) · The Annals of Statistics · doi:10.1214/aos/1176345782 · Cited by 370 · see citing works
Self-citationA completely automatic french curve: fitting spline functions by cross validation
Wahba, G., & Wold, S. (1975) · Communications in Statistics · doi:10.1080/03610927508827223 · Cited by 369 · see citing works
Links between Markov models and multilayer perceptrons
Bourlard, H., & Wellekens, C. J. (1990) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.62605 · Cited by 350 · see citing works
Structural Image Restoration through Deformable Templates
Amit, Y., Grenander, U., & Piccioni, M. (1991) · Journal of the American Statistical Association · doi:10.1080/01621459.1991.10475053 · Cited by 325 · see citing works
A Statistical Model for Positron Emission Tomography
Vardi, Y., Shepp, L. A., & Kaufman, L. (1985) · Journal of the American Statistical Association · doi:10.2307/2288030 · Cited by 299 · see citing works
Stopping Rule for the MLE Algorithm Based on Statistical Hypothesis Testing
Veklerov, E., & Llacer, J. (1987) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.1987.4307849 · Cited by 254 · see citing works
Generalization and Parameter Estimation in Feedforward Nets: Some Experiments
Morgan, N., & Bourlard, H. (1989) · neural information processing systems · Cited by 225 · see citing works
Generalized Deformable Models, Statistical Physics, and Matching Problems
Yuille, A. (1990) · Neural Computation · doi:10.1162/neco.1990.2.1.1 · Cited by 222 · see citing works
Automatic smoothing parameter selection: A survey
Marron, J. S. (1988) · Empirical Economics · doi:10.1007/bf01972448 · Cited by 195 · see citing works
Elastic Matching of Line Drawings
Burr, D. (1981) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.1981.4767176 · Cited by 185 · see citing works
Consistent inference of probabilities in layered networks: predictions and generalizations
Tishby, Левин, & Solla (1989) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.1989.118274 · Cited by 161 · see citing works
Complexity Regularization with Application to Artificial Neural Networks
Barron, A. R. (1991) · Springer eBooks · doi:10.1007/978-94-011-3222-0_42 · Cited by 160 · see citing works
How Far Are Automatically Chosen Regression Smoothing Parameters From Their Optimum?
Härdle, W. K., Hall, P., & Marron, J. S. (1988) · Journal of the American Statistical Association · doi:10.2307/2288922 · Cited by 152 · see citing works
Universal Donsker Classes and Metric Entropy
Dudley, R. M. (2010) · Springer eBooks · doi:10.1007/978-1-4419-5821-1_19 · Cited by 149 · see citing works
Bootstrap Choice of Bandwidth for Density Estimation
Faraway, J. J., & Jhun, M. (1990) · Journal of the American Statistical Association · doi:10.1080/01621459.1990.10474983 · Cited by 126 · see citing works
Collins, Ghosh, & Scofield (1988) · IEEE International Conference on Neural Networks/IEEE ... International Conference on Neural Networks · doi:10.1109/icnn.1988.23960 · Cited by 104 · see citing works
Exhaustive Thermodynamical Analysis of Boolean Learning Networks
Carnevali, P., & Patarnello, S. (1987) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/4/10/020 · Cited by 103 · see citing works
Universal Donsker Classes and Metric Entropy
Dudley, R. M. (1987) · The Annals of Probability · doi:10.1214/aop/1176991978 · Cited by 101 · see citing works
Wahba, G. (1982) · Elsevier eBooks · doi:10.1016/b978-0-12-307502-4.50028-3 · Cited by 99 · see citing works
Recognizing Hand-Printed Letters and Digits Using Backpropagation Learning
Martin, G. L., & Pittman, J. A. (1991) · Neural Computation · doi:10.1162/neco.1991.3.2.258 · Cited by 91 · see citing works
Biased and Unbiased Cross-Validation in Density Estimation
Scott, D. W., & Terrell, G. R. (1987) · Journal of the American Statistical Association · doi:10.2307/2289391 · Cited by 86 · see citing works
The “rubber-mask” technique—I. Pattern measurement and analysis
Widrow, B. C. (1973) · Pattern Recognition · doi:10.1016/0031-3203(73)90042-3 · Cited by 84 · see citing works
Statistical properties of artificial neural networks
Barron, A. R. (2003) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.1989.70117 · Cited by 81 · see citing works
On empirical spectral analysis of stochastic processes
Grenander, U. (1952) · Arkiv för matematik · doi:10.1007/bf02591360 · Cited by 76 · see citing works
A Proposal for More Powerful Learning Algorithms
Baum, E. B. (1989) · Neural Computation · doi:10.1162/neco.1989.1.2.201 · Cited by 73 · see citing works
Schwartz, D. B., Samalam, V. K., Solla, S. A., & Denker, J. S. (1990) · Neural Computation · doi:10.1162/neco.1990.2.3.374 · Cited by 73 · see citing works
von der Malsburg, C., & Bienenstock, E. (1986) · Springer eBooks · doi:10.1007/978-3-642-82657-3_26 · Cited by 72 · see citing works
Self-citationDualistic geometry of the manifold of higher-order neurons
Амари, Ш.-И. (1991) · Neural Networks · doi:10.1016/0893-6080(91)90040-c · Cited by 69 · see citing works
On the Nonconsistency of Maximum Likelihood Nonparametric Density Estimators
Schuster, E. F., & Gregory, G. G. (1981) · Springer eBooks · doi:10.1007/978-1-4613-9464-8_43 · Cited by 62 · see citing works
A cross validated bayesian retrieval algorithm for nonlinear remote sensing experiments
O’Sullivan, F., & Wahba, G. (1985) · Journal of Computational Physics · doi:10.1016/0021-9991(85)90121-4 · Cited by 62 · see citing works
Convergence rates of "thin plate" smoothing splines wihen the data are noisy
Wahba, G. (1979) · Lecture notes in mathematics · doi:10.1007/bfb0098499 · Cited by 61 · see citing works
The Perceptron Algorithm is Fast for Nonmalicious Distributions
Baum, E. B. (1990) · Neural Computation · doi:10.1162/neco.1990.2.2.248 · Cited by 61 · see citing works
Haussler, D. H. (1989) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1989.63453 · Cited by 61 · see citing works
The Bootstrap Widrow-Hoff Rule as a Cluster-Formation Algorithm
Hinton, G. E., & Nowlan, S. J. (1990) · Neural Computation · doi:10.1162/neco.1990.2.3.355 · Cited by 43 · see citing works
Structural Image Restoration Through Deformable Templates
Amit, Y., Grenander, U., & Piccioni, M. (1991) · Journal of the American Statistical Association · doi:10.2307/2290581 · Cited by 43 · see citing works
Projection pursuit learning networks for regression
Maechler, M., Martin, D., Schimert, J., Csoppenszky, M. A., & Hwang, J. N. (2002) · IEEE International Conference on Tools with Artificial Intelligence (ICTAI) · doi:10.1109/tai.1990.130362 · Cited by 38 · see citing works
Dynamic behavior of constrained back propagation networks
Chauvin, Y. (1990) · neural information processing systems · Cited by 38 · see citing works
Bootstrap Choice of Bandwidth for Density Estimation
Faraway, J. J., & Jhun, M. (1990) · Journal of the American Statistical Association · doi:10.2307/2289609 · Cited by 35 · see citing works
When are k-nearest neighbor and back propagation accurate for feasible sized sets of examples?
Baum, E. B. (1990) · Lecture notes in computer science · doi:10.1007/3-540-52255-7_24 · Cited by 29 · see citing works
Synchronous Boltzmann Machines and Gibbs Fields: Learning Algorithms
Azencott, R. (1990) · Neurocomputing · doi:10.1007/978-3-642-76153-9_6 · Cited by 20 · see citing works
Experiments with Representation in Neural Networks: Object Motion, Speech, and Arithmetic
Anderson, J. A., Rossen, M. L., Viscuso, S. R., & Sereno, M. E. (1990) · Springer series in synergetics · doi:10.1007/978-3-642-48779-8_3 · Cited by 14 · see citing works
Speech recognition using time-delay neural networks
Waibel, A. H., Hanazawa, T., Shikano, K., Hinton, G. E., & Lang, K. (1988) · The Journal of the Acoustical Society of America · doi:10.1121/1.2025362 · Cited by 13 · see citing works
Elastic matching and pattern recognition in neural networks.
Bienenstock, E., & Doursat, R. (1989) · Cited by 11 · see citing works
Self-citationMultilayer perceptrons and data analysis.
Gallinari, P., Thiria, S., & Fogelman, F. S. (1988) · Cited by 6 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Deep learning in neural networks: an overview
Schmidhuber, J. (2015) · Neural Networks · doi:10.1016/j.neunet.2014.09.003 · Cited by 18,570 · see citing works
A Tutorial on Support Vector Machines for Pattern Recognition
Burges, C. J. C. (1998) · Data Mining and Knowledge Discovery · doi:10.1023/a:1009715923555 · Cited by 16,437 · see citing works
Geurts, P., Ernst, D., & Wehenkel, L. (2006) · Machine Learning · doi:10.1007/s10994-006-6226-1 · Cited by 9,300 · see citing works
Wrappers for feature subset selection
Kohavi, R., & John, G. H. (1997) · Artificial Intelligence · doi:10.1016/s0004-3702(97)00043-x · Cited by 8,940 · 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
Statistical pattern recognition: a review
Jain, A. K., Duin, P., & Mao, J. (2000) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.824819 · Cited by 6,795 · see citing works
(2009) · Minds at UW (University of Wisconsin) · Cited by 4,791 · see citing works
Chapelle, O., Schölkopf, B., & Zien, A. (2006) · The MIT Press eBooks · doi:10.7551/mitpress/9780262033589.001.0001 · Cited by 4,560 · see citing works
Forecasting with artificial neural networks:
Zhang, G., Eddy Patuwo, B., & Y. Hu, M. (1998) · International Journal of Forecasting · doi:10.1016/s0169-2070(97)00044-7 · Cited by 4,229 · see citing works
Gigerenzer, G., & Gaissmaier, W. (2011) · Annual Review of Psychology · doi:10.1146/annurev-psych-120709-145346 · Cited by 4,037 · see citing works
Simple Heuristics That Make Us Smart
Gigerenzer, G., & Todd, P. M. (1999) · Cited by 3,562 · see citing works
An introduction to kernel-based learning algorithms
Müller, K. R., Mika, S., Rätsch, G., Tsuda, K., & Schölkopf, B. (2001) · IEEE Transactions on Neural Networks · doi:10.1109/72.914517 · Cited by 3,485 · see citing works
Support vector machines in remote sensing: a review
Mountrakis, G., Im, J., & Ogole, C. (2011) · ISPRS Journal of Photogrammetry and Remote Sensing · doi:10.1016/j.isprsjprs.2010.11.001 · Cited by 3,473 · see citing works
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 · see citing works
Human-level concept learning through probabilistic program induction
Lake, B. M., Salakhutdinov, R., & Tenenbaum, J. B. (2015) · Science · doi:10.1126/science.aab3050 · Cited by 2,817 · see citing works
Galar, M., Fernández, A., Barrenechea, E., Bustince, H., & Herrera, F. (2011) · IEEE Transactions on Systems Man and Cybernetics Part C (Applications and Reviews) · doi:10.1109/tsmcc.2011.2161285 · Cited by 2,820 · see citing works
Hierarchical Mixtures of Experts and the EM Algorithm
Jordan, M. I., & Jacobs, R. A. (1994) · Neural Computation · doi:10.1162/neco.1994.6.2.181 · Cited by 2,730 · see citing works
An Empirical Comparison of Voting Classification Algorithms: Bagging, Boosting, and Variants
Bauer, E. J., & Kohavi, R. (1999) · Machine Learning · doi:10.1023/a:1007515423169 · Cited by 2,627 · see citing works
Recent advances and applications of machine learning in solid-state materials science
Schmidt, J., Marques, M. R. G., Botti, S., & Marques, M. A. L. (2019) · npj Computational Materials · doi:10.1038/s41524-019-0221-0 · Cited by 2,655 · see citing works
Building machines that learn and think like people
Lake, B. M., Ullman, T. D., Tenenbaum, J. B., & Gershman, S. J. (2017) · Behavioral and Brain Sciences · doi:10.1017/s0140525x16001837 · Cited by 2,550 · see citing works
Ensemble deep learning: A review
Ganaie, M. A., Hu, M., Malik, A. K., Tanveer, M., & Suganthan, P. N. (2022) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2022.105151 · Cited by 2,282 · see citing works
Active Learning with Statistical Models
Cohn, D. A., Zoubin Ghahramani, A., & Jordan, M. I. (1996) · Journal of Artificial Intelligence Research · doi:10.1613/jair.295 · Cited by 2,054 · see citing works
Ensembling neural networks: Many could be better than all
Zhou, Z.-H., Wu, J., & Tang, W. (2002) · Artificial Intelligence · doi:10.1016/s0004-3702(02)00190-x · Cited by 1,964 · see citing works
Practical Recommendations for Gradient-Based Training of Deep Architectures
Bengio, Y. (2012) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-35289-8_26 · Cited by 2,259 · see citing works
Neural Network Ensembles, Cross Validation, and Active Learning
Krogh, A., & Vedelsby, J. (1994) · Cited by 1,838 · see citing works
Homo Heuristicus: Why Biased Minds Make Better Inferences
Gigerenzer, G., & Brighton, H. (2009) · Topics in Cognitive Science · doi:10.1111/j.1756-8765.2008.01006.x · Cited by 1,801 · see citing works
Neural networks for classification: a survey
Zhang, G. (2000) · IEEE Transactions on Systems Man and Cybernetics Part C (Applications and Reviews) · doi:10.1109/5326.897072 · Cited by 1,672 · see citing works
Prechelt, L. (1998) · Lecture Notes in Computer Science · doi:10.1007/3-540-49430-8_3 · Cited by 1,649 · see citing works
Introduction to multi-layer feed-forward neural networks
Svozil, D., Kvasnicka, V., & Pospichal, J. (1997) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/s0169-7439(97)00061-0 · Cited by 1,600 · see citing works
Unke, O. T., Chmiela, S., Sauceda, H. E., Gastegger, M., Poltavsky, I., Schütt, K. T., Tkatchenko, A., & Müller, K.-R. (2021) · Chemical Reviews · doi:10.1021/acs.chemrev.0c01111 · Cited by 1,647 · see citing works
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 · see citing works
Mitosis Detection in Breast Cancer Histology Images with Deep Neural Networks
Cireşan, D. C., Giusti, A., Gambardella, L. M., & Schmidhuber, J. (2013) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-40763-5_51 · Cited by 1,536 · see citing works
Regularization Theory and Neural Networks Architectures
Girosi, F., Jones, M., & Poggio, T. (1995) · Neural Computation · doi:10.1162/neco.1995.7.2.219 · Cited by 1,345 · see citing works
Mining concept-drifting data streams using ensemble classifiers
Wang, H., Fan, W., Yu, P. S., & Han, J. (2003) · ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) · doi:10.1145/956750.956778 · Cited by 1,275 · see citing works
Shape Quantization and Recognition with Randomized Trees
Amit, Y., & Geman, D. (1997) · Neural Computation · doi:10.1162/neco.1997.9.7.1545 · Cited by 1,277 · see citing works
LeCun, Y., Bottou, L., Orr, G., & Müller, K. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-35289-8_3 · Cited by 1,268 · see citing works
Gevrey, M., Dimopoulos, I. F., & Lek, S. (2003) · Ecological Modelling · doi:10.1016/s0304-3800(02)00257-0 · Cited by 1,251 · see citing works
Predictive Analytics in Information Systems Research1
Shmueli, G., & Koppius, O. R. (2011) · MIS Quarterly · doi:10.2307/23042796 · Cited by 1,328 · see citing works
Building better biomarkers: brain models in translational neuroimaging
Woo, C.-W., Chang, L. J., Lindquist, M. A., & Wager, T. D. (2017) · Nature Neuroscience · doi:10.1038/nn.4478 · Cited by 1,056 · see citing works
Marketing Analytics for Data-Rich Environments
Wedel, M., & Kannan, P. K. (2016) · Journal of Marketing · doi:10.1509/jm.15.0413 · Cited by 1,261 · see citing works
Arcing classifier (with discussion and a rejoinder by the author)
Breiman, L. (1998) · The Annals of Statistics · doi:10.1214/aos/1024691079 · Cited by 1,104 · see citing works
Neural Networks: A Review from a Statistical Perspective
Cheng, B., & Titterington, D. M. (1994) · Statistical Science · doi:10.1214/ss/1177010638 · Cited by 1,056 · see citing works
Hand, D. J. (2007) · Drug Safety · doi:10.2165/00002018-200730070-00010 · Cited by 1,057 · see citing works
Training with Noise is Equivalent to Tikhonov Regularization
Bishop, C. M. (1995) · Neural Computation · doi:10.1162/neco.1995.7.1.108 · Cited by 1,325 · see citing works
On Bias, Variance, 0/1—Loss, and the Curse-of-Dimensionality
Friedman, J. H. (1997) · Data Mining and Knowledge Discovery · doi:10.1023/a:1009778005914 · Cited by 1,038 · see citing works
Automatic early stopping using cross validation: quantifying the criteria
Prechelt, L. (1998) · Neural Networks · doi:10.1016/s0893-6080(98)00010-0 · Cited by 995 · see citing works
Diversity creation methods: a survey and categorisation
Gavin Brown, B., Wyatt, J., Harris, R., & Yao, X. (2004) · Information Fusion · doi:10.1016/j.inffus.2004.04.004 · Cited by 1,003 · see citing works
Prechelt, L. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-35289-8_5 · Cited by 952 · see citing works
Neural networks and their applications
Bishop, C. M. (1994) · Review of Scientific Instruments · doi:10.1063/1.1144830 · Cited by 944 · see citing works
Machine learning assisted design of high entropy alloys with desired property
Wen, C., Zhang, Y., Wang, C., Xue, D., Bai, Y., Antonov, S., Dai, L.-H., Lookman, T., & Su, Y. (2019) · Acta Materialia · doi:10.1016/j.actamat.2019.03.010 · Cited by 946 · see citing works
LeCun, Y., Bottou, L., Orr, G., & Müller, K. R. (1998) · Lecture notes in computer science · doi:10.1007/3-540-49430-8_2 · Cited by 920 · see citing works
Overfitting in Neural Nets: Backpropagation, Conjugate Gradient, and Early Stopping
Caruana, R., Lawrence, S., & Giles, C. L. (2000) · Cited by 906 · see citing works
Artificial neural networks as a tool in ecological modelling, an introduction
Lek, S., & Guégan, J. (1999) · Ecological Modelling · doi:10.1016/s0304-3800(99)00092-7 · Cited by 891 · see citing works
A Survey on Distributed Machine Learning
Verbraeken, J., Wolting, M., Katzy, J., Kloppenburg, J., Verbelen, T., & Rellermeyer, J. S. (2020) · ACM Computing Surveys · doi:10.1145/3377454 · Cited by 902 · see citing works
The neural basis of cognitive development: A constructivist manifesto
Quartz, S. R., & B, T. J. S. A. (1997) · Behavioral and Brain Sciences · doi:10.1017/s0140525x97001581 · Cited by 856 · see citing works
A review of machine learning applications in wildfire science and management
Jain, P., Coogan, S. C. P., Subramanian, S. G., Crowley, M., Taylor, S., & Flannigan, M. (2020) · Environmental Reviews · doi:10.1139/er-2020-0019 · Cited by 850 · see citing works
Bühlmann, P., & Yu, B. (2003) · Journal of the American Statistical Association · doi:10.1198/016214503000125 · Cited by 838 · see citing works
Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems
Keith, J. A., Vassilev-Galindo, V., Cheng, B., Chmiela, S., Gastegger, M., Müller, K.-R., & Tkatchenko, A. (2021) · Chemical Reviews · doi:10.1021/acs.chemrev.1c00107 · Cited by 849 · see citing works
Feature Selection for Classification of Hyperspectral Data by SVM
Pal, M., & Foody, G. M. (2010) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2009.2039484 · Cited by 818 · see citing works
Unsupervised Statistical Learning of Higher-Order Spatial Structures from Visual Scenes
Fiser, J., & Aslin, R. Ν. (2001) · Psychological Science · doi:10.1111/1467-9280.00392 · Cited by 806 · see citing works
A strategy to apply machine learning to small datasets in materials science
Zhang, Y., & Ling, C. (2018) · npj Computational Materials · doi:10.1038/s41524-018-0081-z · Cited by 791 · see citing works
SUSTAIN: A Network Model of Category Learning.
Love, B. C., Medin, D. L., & Gureckis, T. M. (2004) · Psychological Review · doi:10.1037/0033-295x.111.2.309 · Cited by 778 · see citing works
Machine Learning Methods Without Tears: A Primer for Ecologists
Olden, J. D., Lawler, J. J., & Poff, N. L. (2008) · The Quarterly Review of Biology · doi:10.1086/587826 · Cited by 823 · see citing works
Précis of Simple heuristics that make us smart
Todd, P. M., & Gigerenzer, G. (2000) · Behavioral and Brain Sciences · doi:10.1017/s0140525x00003447 · Cited by 718 · see citing works
Exploratory Modeling for Policy Analysis
Bankes, S. C. (1993) · Operations Research · doi:10.1287/opre.41.3.435 · Cited by 712 · see citing works
MultiBoosting: A Technique for Combining Boosting and Wagging
Webb, G. I. (2000) · Machine Learning · doi:10.1023/a:1007659514849 · Cited by 701 · see citing works
Understanding Random Forests: From Theory to PracticePreprint
Louppe, G. (2014) · arXiv (Cornell University) · doi:10.13140/2.1.1570.5928 · Cited by 940 · see citing works
Automatic Detection of Cerebral Microbleeds From MR Images via 3D Convolutional Neural Networks
Dou, Q., Chen, H., Yu, L., Zhao, L., Qin, J., Wang, D., Mok, V. C., Shi, L., & Heng, P.-A. (2016) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2016.2528129 · Cited by 679 · see citing works
Artificial neural networks in bankruptcy prediction: General framework and cross-validation analysis
Zhang, G., Y. Hu, M., Eddy Patuwo, B., & C. Indro, D. (1999) · European Journal of Operational Research · doi:10.1016/s0377-2217(98)00051-4 · Cited by 677 · see citing works
Ren, Y., Zhang, L., & Suganthan, P. N. (2016) · IEEE Computational Intelligence Magazine · doi:10.1109/mci.2015.2471235 · Cited by 681 · see citing works
Predictive Analytics in Information Systems Research
Shmueli, G., & Koppius, O. (2010) · doi:10.2139/ssrn.1606674 · Cited by 676 · see citing works
Ensemble approaches for regression
Mendes‐Moreira, J., Soares, C., Jorge, A., & de Sousa, J. F. (2012) · ACM Computing Surveys · doi:10.1145/2379776.2379786 · Cited by 665 · see citing works
The discovery of structural form
Kemp, C., & Tenenbaum, J. B. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0802631105 · Cited by 656 · see citing works
Stability of feature selection algorithm: A review
Khaire, U. M., & Dhanalakshmi, R. (2019) · Journal of King Saud University - Computer and Information Sciences · doi:10.1016/j.jksuci.2019.06.012 · Cited by 648 · see citing works
Local feature analysis: a general statistical theory for object representation
Penev, P. S., & Atick, J. J. (1996) · Network Computation in Neural Systems · doi:10.1088/0954-898x/7/3/002 · Cited by 628 · see citing works
Neural Networks and Related Methods for Classification
Ripley, B. D. (1994) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1994.tb01990.x · Cited by 627 · see citing works
Stability of feature selection algorithms: a study on high-dimensional spaces
Kalousis, A., Prados, J., & Hilario, M. (2006) · Knowledge and Information Systems · doi:10.1007/s10115-006-0040-8 · Cited by 616 · see citing works
Metaheuristic design of feedforward neural networks: A review of two decades of research
Ojha, V., Abraham, A., & Snåšel, V. (2017) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2017.01.013 · Cited by 613 · see citing works
The development of features in object concepts
Schyns, P. G., Goldstone, R. L., & Thibaut, J. (1998) · Behavioral and Brain Sciences · doi:10.1017/s0140525x98000107 · Cited by 598 · see citing works
Settles, B. (2012) · Synthesis Lectures on Artificial Intelligence and Machine Learning · doi:10.2200/s00429ed1v01y201207aim018 · Cited by 605 · see citing works
A systematic review on overfitting control in shallow and deep neural networks
Bejani, M. M., & Ghatee, M. (2021) · Artificial Intelligence Review · doi:10.1007/s10462-021-09975-1 · Cited by 598 · see citing works
Factorial Hidden Markov Models
Ghahramani, Z., & Jordan, M. I. (1997) · Machine Learning · doi:10.1023/a:1007425814087 · Cited by 1,157 · see citing works
Jones, M., & Love, B. C. (2011) · Behavioral and Brain Sciences · doi:10.1017/s0140525x10003134 · Cited by 533 · see citing works
Three learning phases for radial-basis-function networks
Schwenker, F., Kestler, H. A., & Palm, G. (2001) · Neural Networks · doi:10.1016/s0893-6080(01)00027-2 · Cited by 533 · see citing works
A survey of fuzzy clustering algorithms for pattern recognition. I
Baraldi, A., & Blonda, P. N. (1999) · IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics) · doi:10.1109/3477.809032 · Cited by 530 · see citing works
Learning to Learn: Introduction and Overview
Thrun, S., & Pratt, L. (1998) · Learning to Learn · doi:10.1007/978-1-4615-5529-2_1 · Cited by 521 · see citing works
Constructive Incremental Learning from Only Local Information
Schaal, S., & Atkeson, C. G. (1998) · Neural Computation · doi:10.1162/089976698300016963 · Cited by 516 · see citing works
Statistical aspects of neural networks
Ripley, B. D. (1993) · Springer eBooks · doi:10.1007/978-1-4899-3099-6_2 · Cited by 515 · see citing works
Ahmad, T., Zhang, H., & Yan, B. (2020) · Sustainable Cities and Society · doi:10.1016/j.scs.2020.102052 · Cited by 504 · see citing works
Reinforcement learning and episodic memory in humans and animals: an integrative framework
Gershman, S. J., & Daw, N. D. (2017) · Annual Review of Psychology · doi:10.1146/annurev-psych-122414-033625 · Cited by 446 · see citing works
Kwok, T.-Y., & Yeung, D. (1997) · IEEE Transactions on Neural Networks · doi:10.1109/72.572102 · Cited by 490 · see citing works
Overfitting and neural networks: conjugate gradient and backpropagation
Lawrence, S., & Giles, C. L. (2000) · Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium · doi:10.1109/ijcnn.2000.857823 · Cited by 491 · see citing works
Ensembles of Multiple Models and Architectures for Robust Brain Tumour Segmentation
Kamnitsas, K., Bai, W., Ferrante, E., McDonagh, S., Sinclair, M. D., Pawlowski, N., Rajchl, M., Lee, M., Kainz, B., Rueckert, D., et al. (2018) · Lecture notes in computer science · doi:10.1007/978-3-319-75238-9_38 · Cited by 485 · see citing works
Algorithmic Bias in Autonomous Systems
Danks, D., & London, A. J. (2017) · Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2017/654 · Cited by 472 · see citing works
A neural network model for survival data
Faraggi, D., & Simon, R. M. (1995) · Statistics in Medicine · doi:10.1002/sim.4780140108 · Cited by 467 · see citing works
Bayesian Population Decoding of Motor Cortical Activity Using a Kalman Filter
Wu, W. L., Gao, Y., Bienenstock, E., Donoghue, J. P., & Black, M. J. (2005) · Neural Computation · doi:10.1162/089976606774841585 · Cited by 460 · see citing works
Self-citationThe Role of Occam's Razor in Knowledge Discovery
Domingos, P. (1999) · Data Mining and Knowledge Discovery · doi:10.1023/a:1009868929893 · Cited by 459 · see citing works
Empirical Mode Decomposition based ensemble deep learning for load demand time series forecasting
Qiu, X., Ren, Y., Suganthan, P. N., & Amaratunga, G. A. J. (2017) · Applied Soft Computing · doi:10.1016/j.asoc.2017.01.015 · Cited by 449 · see citing works
Liu, H., Ong, Y.-S., & Cai, J. (2017) · Structural and Multidisciplinary Optimization · doi:10.1007/s00158-017-1739-8 · Cited by 446 · see citing works
Computational and evolutionary aspects of language
Nowak, M. A., Komarova, N. L., & Niyogi, P. (2002) · Nature · doi:10.1038/nature00771 · Cited by 437 · see citing works
- Authors
- Geman, S., Bienenstock, E., & Doursat, R.
- Affiliations
- Brown University (US)
- ESPCI Paris (FR)
- ORCID
- Doursat, René
- Venue
- Neural Computation
- Publisher
- MIT Press
- Published
- 1992-01
- Volume
- 4
- Issue
- 1
- Pages
- 1-58
- ISSN
- 0899-7667 (ISSN-L)
- 1530-888X
- OpenAlex
- W2076118331
- Cited by
- 3,578
- References
- 96
- Citations by year
- 2026: 125 · 2025: 131 · 2024: 115 · 2023: 128 · 2022: 148 · 2021: 201 · 2020: 181 · 2019: 142 · 2018: 126 · 2017: 97 · 2016: 115 · 2015: 99 · 2014: 103 · 2013: 82 · 2012: 110
- FWCI
- 60.04
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Neural Computation (publishedVersion)
- e-space (Manchester Metropolitan University) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Algorithms
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and ELM
- Keywords
- bias-variance trade-off, feedforward neural networks, backpropagation, nonparametric regression, nonparametric inference, handwritten digit recognition, machine perception, neural network representations, statistical 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