Abstract
Multivariate regression models are often used for the purpose of prognosis. Parameters of such models are estimated on the basis of learning sets, where feature vectors (independent variables) are combined with values of response (target) variable. The values of response variable can be determined only with some uncertainty in some important applications. For example, in survival analysis, the values of response variable is often censored and can be represented as intervals. The interval regression approach has been proposed for designing prognostic tools in circumstances of such type of uncertainty. The possibility of using the convex and piecewise linear (CPL) functions in designing linear prognostic models on the basis of interval learning sets is examined in the paper.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bobrowski, L.: Design of piecewise linear classifiers from formal neurons by some basis exchange technique. Pattern Recognition 24(9), 863–870 (1991)
Bobrowski, L.: Eksploracja danych oparta na wypukłych i odcinkowo-liniowych funkcjach kryterialnych (Data mining based on convex and piecewise linear (CPL) criterion functions), Technical University Białystok (2005) (in Polish)
Bobrowski, L.: Ranked linear models and sequential patterns recognition. Pattern Analysis & Applications 12(1), 1–7 (2009)
Bobrowski, L., Łukaszuk, T.: Feature selection based on relaxed linear separabilty. Biocybernetics and Biomedcal Engineering 29(2), 43–59 (2009)
Bobrowski, L.: Linear prognostic models based on interval regression with CPL functions. Symulacja w Badaniach i Rozwoju 1, 109–117 (2010) (in Polish)
Buckley, J., James, I.: Linear regression with censored data. Biometrika 66, 429–436 (1979)
Duda, O.R., Hart, P.E., Stork, D.G.: Pattern Classification. Wiley, New York (2001)
Gomez, G., Espinal, A., Lagakos, S.: Inference for a linear regression model with an interval-censored covariate. Statistics in Medicine 22, 409–425 (2003)
Johnson, R.A., Wichern, D.W.: Applied Multivariate Statistical Analysis. Prentice-Hall Inc., Englewood Cliffs (1991)
Klein, J.P., Moeschberger, M.L.: Survival Analysis, Techniques for Censored and Truncated Data. Springer, NY (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bobrowski, L. (2012). Interval Uncertainty in CPL Models for Computer Aided Prognosis. In: Hippe, Z.S., Kulikowski, J.L., Mroczek, T. (eds) Human – Computer Systems Interaction: Backgrounds and Applications 2. Advances in Intelligent and Soft Computing, vol 99. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23172-8_29
Download citation
DOI: https://doi.org/10.1007/978-3-642-23172-8_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23171-1
Online ISBN: 978-3-642-23172-8
eBook Packages: EngineeringEngineering (R0)