Cited by 115Bayesian Modeling and Causal InferenceNeural Networks and ApplicationsGaussian Processes and Bayesian Inference

Taking on the curse of dimensionality in joint distributions using neural networks

Open access
Bengio, S., Bengio, Y.·2000·IEEE Transactions on Neural Networks

Abstract

The curse of dimensionality is severe when modeling high-dimensional discrete data: the number of possible combinations of the variables explodes exponentially. In this paper, we propose a new architecture for modeling high-dimensional data that requires resources (parameters and computations) that grow at most as the square of the number of variables, using a multilayer neural network to represent the joint distribution of the variables as the product of conditional distributions. The neural network can be interpreted as a graphical model without hidden random variables, but in which the conditional distributions are tied through the hidden units. The connectivity of the neural network can be pruned by using dependency tests between the variables (thus reducing significantly the number of parameters). Experiments on modeling the distribution of several discrete data sets show statistically significant improvements over other methods such as naive Bayes and comparable Bayesian networks and show that significant improvements can be obtained by pruning the network.

Integrity signals

Registry

Crossref · 10.1109/72.846725

Cites

18 of 18 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

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?

  • Autoregressive Models work by decomposing the joint distribution of data into a product of conditional distributions using the probability chain rule.

    “Autoregressive Models (ARMs) work by decomposing the joint distribution of data into a product of conditional distributions using the probability chain rule:”

Cites

Flagged first, then by citations

Cited by

Sorted by citations

Authors
Bengio, S., & Bengio, Y.
Affiliations
Université de Montréal (CA)
Venue
IEEE Transactions on Neural Networks
Published
2000-05
Volume
11
Issue
3
Pages
550-557
ISSN
1045-9227 (ISSN-L)
OpenAlex
W2152511329
Cited by
115
References
18
Citations by year
2026: 7 · 2025: 5 · 2024: 11 · 2023: 4 · 2022: 10 · 2021: 11 · 2020: 5 · 2019: 5 · 2018: 8 · 2017: 4 · 2016: 1 · 2015: 5 · 2014: 2 · 2013: 3 · 2012: 1
FWCI
2.08
Type
journal article
Language
en
Open access
Locations
  • IEEE Transactions on Neural Networks (publishedVersion)
  • PubMed (publishedVersion)
  • Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion)
  • Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
  • Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
  • Physical Sciences › Computer Science › Artificial Intelligence › Gaussian Processes and Bayesian Inference
Keywords
curse of dimensionality, joint probability distribution, discrete data, multilayer neural networks, conditional distributions, probabilistic graphical models, hidden units, network pruning, parameter complexity, Naive Bayes comparison, Bayesian networks

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