Determining Dependency structures and estimating nonlinear regression errors without doing regression
(1995) In International Journal of Modern Physics B 6(4). p.611-616- Abstract
- A general method is discussed, the δ-test, which establishes functional dependencies given a table of measurements. The approach is based on calculating conditional probabilities from data densities. Imposing the requirement of continuity of the underlying function the obtained values of the conditional probabilities carry information on the variable dependencies. The power of the method is illustrated on synthetic time-series with different time-lag dependencies and noise levels. For N data points the computational demand is N2. Also, the same method is used for estimating nonlinear regression errors and their distributions without performing regression. Comparing the predicted residual errors with those from linear models provides a... (More)
- A general method is discussed, the δ-test, which establishes functional dependencies given a table of measurements. The approach is based on calculating conditional probabilities from data densities. Imposing the requirement of continuity of the underlying function the obtained values of the conditional probabilities carry information on the variable dependencies. The power of the method is illustrated on synthetic time-series with different time-lag dependencies and noise levels. For N data points the computational demand is N2. Also, the same method is used for estimating nonlinear regression errors and their distributions without performing regression. Comparing the predicted residual errors with those from linear models provides a signal for nonlinearity. The virtue of the method in the context of feedforward neural networks is stressed with respect to preprocessing data and tracking residual errors. (Less)
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- author
- Peterson, Carsten LU
- organization
- publishing date
- 1995
- type
- Contribution to journal
- publication status
- published
- subject
- in
- International Journal of Modern Physics B
- volume
- 6
- issue
- 4
- pages
- 611 - 616
- publisher
- World Scientific Publishing
- ISSN
- 0217-9792
- DOI
- 10.1142/S0129183195000514
- language
- English
- LU publication?
- yes
- id
- 0ee4248e-7d5c-4931-b53b-573d8ae6ce00
- date added to LUP
- 2019-05-31 08:46:27
- date last changed
- 2019-08-13 13:20:00
@article{0ee4248e-7d5c-4931-b53b-573d8ae6ce00, abstract = {{A general method is discussed, the δ-test, which establishes functional dependencies given a table of measurements. The approach is based on calculating conditional probabilities from data densities. Imposing the requirement of continuity of the underlying function the obtained values of the conditional probabilities carry information on the variable dependencies. The power of the method is illustrated on synthetic time-series with different time-lag dependencies and noise levels. For N data points the computational demand is N2. Also, the same method is used for estimating nonlinear regression errors and their distributions without performing regression. Comparing the predicted residual errors with those from linear models provides a signal for nonlinearity. The virtue of the method in the context of feedforward neural networks is stressed with respect to preprocessing data and tracking residual errors.}}, author = {{Peterson, Carsten}}, issn = {{0217-9792}}, language = {{eng}}, number = {{4}}, pages = {{611--616}}, publisher = {{World Scientific Publishing}}, series = {{International Journal of Modern Physics B}}, title = {{Determining Dependency structures and estimating nonlinear regression errors without doing regression}}, url = {{http://dx.doi.org/10.1142/S0129183195000514}}, doi = {{10.1142/S0129183195000514}}, volume = {{6}}, year = {{1995}}, }