5:15 PM - 7:15 PM
[STT43-P03] Kriging for functional data via sparse regularization
★Invited Papers
Keywords:Functional data analysis, Kriging, Sparse estimation
Functional data analysis is one of the most useful methods for analyzing data whose individual has time-course measurements. Methodologies of functional data analysis include several extensions of classical multivariate analysis such as regression analysis and principal component analysis to the framework of functional data. This work focuses on spatial data analysis for functional data.
Functional kriging is a method for predicting a time-course feature at an unobserved location as a function using longitudinal data observed at several locations in a space. Functional kriging predicts the function of the unobserved location by a linear combination of the functional data of the locations where the data are observed, under the assumption of stationarity and isotropy for the functions distributed over space. The weights of the linear combination are generally estimated by minimizing the expected squared error. In contrast, we consider a method for estimating the kriging weights using sparse estimation.
In this work, we apply the adaptive lasso regularization, one of the sparse estimation methods, to shrink some of the kriging weights toward exactly zero. This enables us to predict the time-course feature at the unobserved location using functional data at some, but not all, of the observed locations. An algorithm for minimizing the expected squared error with sparse regularization and a method for selecting tuning parameters associated with the minimization problem are also introduced. We apply the proposed method to the analysis of low-frequency seismic waveform data and then select the locations for the prediction of seismic waveforms at a particular location.
Functional kriging is a method for predicting a time-course feature at an unobserved location as a function using longitudinal data observed at several locations in a space. Functional kriging predicts the function of the unobserved location by a linear combination of the functional data of the locations where the data are observed, under the assumption of stationarity and isotropy for the functions distributed over space. The weights of the linear combination are generally estimated by minimizing the expected squared error. In contrast, we consider a method for estimating the kriging weights using sparse estimation.
In this work, we apply the adaptive lasso regularization, one of the sparse estimation methods, to shrink some of the kriging weights toward exactly zero. This enables us to predict the time-course feature at the unobserved location using functional data at some, but not all, of the observed locations. An algorithm for minimizing the expected squared error with sparse regularization and a method for selecting tuning parameters associated with the minimization problem are also introduced. We apply the proposed method to the analysis of low-frequency seismic waveform data and then select the locations for the prediction of seismic waveforms at a particular location.