IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v57y2014i1p129-165.html
   My bibliography  Save this article

A generative model and a generalized trust region Newton method for noise reduction

Author

Listed:
  • Seppo Pulkkinen
  • Marko Mäkelä
  • Napsu Karmitsa

Abstract

In practical applications related to, for instance, machine learning, data mining and pattern recognition, one is commonly dealing with noisy data lying near some low-dimensional manifold. A well-established tool for extracting the intrinsically low-dimensional structure from such data is principal component analysis (PCA). Due to the inherent limitations of this linear method, its extensions to extraction of nonlinear structures have attracted increasing research interest in recent years. Assuming a generative model for noisy data, we develop a probabilistic approach for separating the data-generating nonlinear functions from noise. We demonstrate that ridges of the marginal density induced by the model are viable estimators for the generating functions. For projecting a given point onto a ridge of its estimated marginal density, we develop a generalized trust region Newton method and prove its convergence to a ridge point. Accuracy of the model and computational efficiency of the projection method are assessed via numerical experiments where we utilize Gaussian kernels for nonparametric estimation of the underlying densities of the test datasets. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Seppo Pulkkinen & Marko Mäkelä & Napsu Karmitsa, 2014. "A generative model and a generalized trust region Newton method for noise reduction," Computational Optimization and Applications, Springer, vol. 57(1), pages 129-165, January.
  • Handle: RePEc:spr:coopap:v:57:y:2014:i:1:p:129-165
    DOI: 10.1007/s10589-013-9581-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-013-9581-4
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s10589-013-9581-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Michael E. Tipping & Christopher M. Bishop, 1999. "Probabilistic Principal Component Analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 611-622.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pulkkinen, Seppo, 2015. "Ridge-based method for finding curvilinear structures from noisy data," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 89-109.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wang, Zihan & Daeipour, Mohamad & Xu, Hongyi, 2023. "Quantification and propagation of Aleatoric uncertainties in topological structures," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    2. Xin Xu & Yang Lu & Yupeng Zhou & Zhiguo Fu & Yanjie Fu & Minghao Yin, 2021. "An Information-Explainable Random Walk Based Unsupervised Network Representation Learning Framework on Node Classification Tasks," Mathematics, MDPI, vol. 9(15), pages 1-14, July.
    3. Dorota Toczydlowska & Gareth W. Peters & Man Chung Fung & Pavel V. Shevchenko, 2017. "Stochastic Period and Cohort Effect State-Space Mortality Models Incorporating Demographic Factors via Probabilistic Robust Principal Components," Risks, MDPI, vol. 5(3), pages 1-77, July.
    4. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Papers 2310.17278, arXiv.org, revised Jan 2024.
    5. Chen, Tao & Martin, Elaine & Montague, Gary, 2009. "Robust probabilistic PCA with missing data and contribution analysis for outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3706-3716, August.
    6. Chen, Andrew Y. & McCoy, Jack, 2024. "Missing values handling for machine learning portfolios," Journal of Financial Economics, Elsevier, vol. 155(C).
    7. Wang, Shao-Hsuan & Huang, Su-Yun, 2022. "Perturbation theory for cross data matrix-based PCA," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    8. Cook, R. Dennis, 2022. "A slice of multivariate dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    9. Wentao Qu & Xianchao Xiu & Huangyue Chen & Lingchen Kong, 2023. "A Survey on High-Dimensional Subspace Clustering," Mathematics, MDPI, vol. 11(2), pages 1-39, January.
    10. Ligon, Ethan, 2017. "Estimating household welfare from disaggregate expenditures," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt5gc4h1fm, Department of Agricultural & Resource Economics, UC Berkeley.
    11. Jiaju Miao & Pawel Polak, 2023. "Online Ensemble of Models for Optimal Predictive Performance with Applications to Sector Rotation Strategy," Papers 2304.09947, arXiv.org.
    12. Marconi, Gabriele, 2014. "European higher education policies and the problem of estimating a complex model with a small cross-section," MPRA Paper 87600, University Library of Munich, Germany.
    13. Jingying Yang, 2024. "Element Aggregation for Estimation of High-Dimensional Covariance Matrices," Mathematics, MDPI, vol. 12(7), pages 1-16, March.
    14. Jingtao Wang & Gregory J. Fonseca & Jun Ding, 2024. "scSemiProfiler: Advancing large-scale single-cell studies through semi-profiling with deep generative models and active learning," Nature Communications, Nature, vol. 15(1), pages 1-27, December.
    15. Dorota Toczydlowska & Gareth W. Peters, 2018. "Financial Big Data Solutions for State Space Panel Regression in Interest Rate Dynamics," Econometrics, MDPI, vol. 6(3), pages 1-45, July.
    16. Jung, WoongHee & Taflanidis, Alexandros A., 2023. "Efficient global sensitivity analysis for high-dimensional outputs combining data-driven probability models and dimensionality reduction," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    17. Matteo Barigozzi, 2023. "Asymptotic equivalence of Principal Components and Quasi Maximum Likelihood estimators in Large Approximate Factor Models," Papers 2307.09864, arXiv.org, revised Jun 2024.
    18. Joni Virta & Niko Lietzén & Henri Nyberg, 2024. "Robust signal dimension estimation via SURE," Statistical Papers, Springer, vol. 65(5), pages 3007-3038, July.
    19. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    20. Johannes Burge & Priyank Jaini, 2017. "Accuracy Maximization Analysis for Sensory-Perceptual Tasks: Computational Improvements, Filter Robustness, and Coding Advantages for Scaled Additive Noise," PLOS Computational Biology, Public Library of Science, vol. 13(2), pages 1-32, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:57:y:2014:i:1:p:129-165. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.