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Bayesian function estimation using continuous wavelet dictionaries

Publication ,  Journal Article
Chu, JH; Clyde, MA; Liang, F
Published in: Statistica Sinica
2009

We present a Bayesian approach for nonparametric function estimation based on a continuous wavelet dictionary, where the unknown function is modeled by a random sum of wavelet functions at arbitrary locations and scales. By avoiding the dyadic constraints for orthonormal wavelet bases, the continuous over- complete wavelet dictionary has greater flexibility to adapt to the structure of the data, and may lead to sparser representations. The price for this flexibility is the computational challenge of searching over an infinite number of potential dictionary elements. We develop a novel reversible jump Markov chain Monte Carlo algorithm which utilizes local features in the proposal distributions to improve computational efficiency, and which leads to better mixing of the Markov chain. Performance comparison in terms of sparsity and mean squared error is carried out on standard wavelet test functions. Results on a non-equally spaced example show that our method compares favorably to methods using interpolation or imputation.

Duke Scholars

Published In

Statistica Sinica

ISSN

1017-0405

Publication Date

2009

Volume

19

Issue

4

Start / End Page

1419 / 1438

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0801 Artificial Intelligence and Image Processing
  • 0199 Other Mathematical Sciences
  • 0104 Statistics
 

Citation

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MLA
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Chu, J. H., Clyde, M. A., & Liang, F. (2009). Bayesian function estimation using continuous wavelet dictionaries. Statistica Sinica, 19(4), 1419–1438.
Chu, J. H., M. A. Clyde, and F. Liang. “Bayesian function estimation using continuous wavelet dictionaries.” Statistica Sinica 19, no. 4 (2009): 1419–38.
Chu JH, Clyde MA, Liang F. Bayesian function estimation using continuous wavelet dictionaries. Statistica Sinica. 2009;19(4):1419–38.
Chu, J. H., et al. “Bayesian function estimation using continuous wavelet dictionaries.” Statistica Sinica, vol. 19, no. 4, 2009, pp. 1419–38.
Chu JH, Clyde MA, Liang F. Bayesian function estimation using continuous wavelet dictionaries. Statistica Sinica. 2009;19(4):1419–1438.

Published In

Statistica Sinica

ISSN

1017-0405

Publication Date

2009

Volume

19

Issue

4

Start / End Page

1419 / 1438

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0801 Artificial Intelligence and Image Processing
  • 0199 Other Mathematical Sciences
  • 0104 Statistics