Four-step Basis Pursuit with Applications

Authors

VESELÝ Vítězslav

Year of publication 2007
Type Article in Proceedings
Conference Strobl07 Trends in Harmonic Analysis, June 18-22, 2007
MU Faculty or unit

Faculty of Economics and Administration

Citation
Web Poster Strobl07
Field Applied statistics, operation research
Keywords approximation; Basis Pursuit; sparsity; ROC estimators; smoothing; forecasting; ARMA models; air pollution
Description A computationally intensive sparse parameter estimation technique based on a four-step modification of the Basis Pursuit Algorithm is presented (BPA4). In addition to some minimal theoretical background the contribution demonstrates performance and flexibility of BPA4 on four problems coming from completely diverse application fields: kernel approximation and smoothing, improved time series forecasting within an overcomplete stochastic frame of type ARMA, analysis of air pollution by suspended particulate matter and ROC curve estimation. This new computationally intensive approach allowed us to reliably identify nearly zero parameters in the respective model and thus to find numerically stable sparse parameter estimates.
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