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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.
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“The bias-variance trade-off implies that a model should balance under-fitting and over-fitting: rich enough to express underlying structure in data, simple enough to avoid fitting spurious patterns.”
From Reconciling modern machine-learning practice and the classical bias–variance trade-off (2019) · cites this paper as [17]
In the citing paper
“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]
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Metadata
- 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 ›
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