Taking on the curse of dimensionality in joint distributions using neural networks
Open accessAbstract
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.
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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:”
From Diffusion Models: A Comprehensive Survey of Methods and Applications (2024) · cites this paper as [13]
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- Authors
- Bengio, S., & Bengio, Y.
- Affiliations
- Université de Montréal (CA)
- ORCID
- Bengio, Y.
- 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 ›
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