On function-on-function regression: partial least squares approach

Beyaztaş, Ufuk; Shang, Han Lin

doi:10.1007/s10651-019-00436-1

Cited by 25 publications

(31 citation statements)

References 37 publications

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“…For this reason, obtaining the sample estimates of the Escoufier's operators becomes problematic because they need to be estimated from the discretely observed observations (see Aguilera et al 2010). To address this issue, Preda and Schiltz (2011) and Beyaztas and Shang (2020a) proposed to use standard PLS regression of the basis expansion coefficients of the functional variables to approximate the FPLS components. In this context, several basis expansion methods, such as B-spline, Fourier, wavelet, radial, and Bernstein polynomial bases, have been proposed to project infinite-dimensional functional variables onto the finite-dimensional space.…”

Section: The Functional Plsmentioning

confidence: 99%

“…In addition, when a large number of basis functions is used, the aforementioned estimation methods suffer from the multicollinearity problem Saporta 2005, Aguilera et al 2016). Moreover, in such a case, these methods may be computationally intensive (Beyaztas and Shang 2020a). Compared with general basis expansion methods, the dimension reduction techniques such as functional principal component (FPC) regression (Aguilera et al 1999, Yao et al 2005, Hall and Hosseini-Nasab 2006, Chiou et al 2016) and functional partial least squares (FPLS) regression Schiltz 2011, Beyaztas andShang 2020a) solve multicollinearity problem and decrease the computation burden in a high-dimensional setting.…”

Section: Introductionmentioning

confidence: 99%

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A partial least squares approach for function-on-function interaction regression

Beyaztaş

Shang

2021

Comput Stat

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The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors. Existing methods to estimate the model parameters may be sensitive to outlying observations, common in empirical applications. In addition, these methods may be severely affected by such observations, leading to undesirable estimation and prediction results. A robust estimation method, based on iteratively reweighted simple partial least squares, is introduced to improve the prediction accuracy of the function-on-function linear regression model in the presence of outliers. The performance of the proposed method is based on the number of partial least squares components used to estimate the function-on-function linear regression model. Thus, the optimum number of components is determined via a data-driven error criterion. The finite-sample performance of the proposed method is investigated via several Monte Carlo experiments and an empirical data analysis. In addition, a nonparametric bootstrap method is applied to construct pointwise prediction intervals for the response function. The results are compared with some of the existing methods to illustrate the improvement potentially gained by the proposed method.

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Section: The Functional Plsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A partial least squares approach for function-on-function interaction regression

Beyaztaş

Shang

2021

Comput Stat

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“…Estimation of these coefficients in B is straightforward in an equivalent Yule-Walker equation [47] or a Nadaraya-Watson kernel estimator [48]. The method of partial least squares can reduce computation time [49]. This study adopts the standard method of partial least squares.…”

Section: Prediction Models In the First Stagementioning

confidence: 99%

Precipitation Modeling for Extreme Weather Based on Sparse Hybrid Machine Learning and Markov Chain Random Field in a Multi-Scale Subspace

Lee

Chen²

2021

Water

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This paper proposes to apply a Markov chain random field conditioning method with a hybrid machine learning method to provide long-range precipitation predictions under increasingly extreme weather conditions. Existing precipitation models are limited in time-span, and long-range simulations cannot predict rainfall distribution for a specific year. This paper proposes a hybrid (ensemble) learning method to perform forecasting on a multi-scaled, conditioned functional time series over a sparse l1 space. Therefore, on the basis of this method, a long-range prediction algorithm is developed for applications, such as agriculture or construction works. Our findings show that the conditioning method and multi-scale decomposition in the parse space l1 are proved useful in resisting statistical variation due to increasingly extreme weather conditions. Because the predictions are year-specific, we verify our prediction accuracy for the year we are interested in, but not for other years.

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“…It chooses the latent factors 1 , 2 , ⋯ , that has a strong correlation with y and can be easily calculated [27], [28].…”

Section: Establishment Of Sensor Calibration Model a Introduction To Basic Principlesmentioning

confidence: 99%

Research on Data Correction Method of Micro Air Quality Detector Based on Combination of Partial Least Squares and Random Forest Regression

Liu

Wang

et al. 2021

IEEE Access

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The issue of air quality has attracted more and more attention. The main methods for monitoring the concentration of pollutants in the air include national monitoring station monitoring and micro air quality detector testing. Since the electrochemical sensor of the micro air quality detector is susceptible to interference, the monitored data has a certain deviation. In this paper, the combined model of partial least square regression and random forest regression (PLS-RFR) is used to correct the detection data of the micro air quality detector. First, correlation analysis is used to find out the factors that affect the concentration of pollutants. Second, partial least squares regression is used to give the quantitative relationship of the influence of each influencing factor on the concentration of pollutants. Finally, the predicted value of partial least squares regression and various influencing factors are used as independent variables, and the pollutant concentration monitored by the national monitoring station is used as the dependent variable, and the PLS-RFR model is obtained with the help of random forest software package. Relative mean absolute percent error, mean absolute error, goodness of fit, and root mean square error are used as evaluation indicators to compare PLS-RFR model, support vector machine model and multilayer perceptron neural network. The results show that no matter which evaluation index, the overall prediction effect of the PLS-RFR model is the best, and the model has a good prediction effect in the training set or the test set, indicating that the model has good generalization ability. This model can play an active role in the promotion and deployment of micro air quality detectors.INDEX TERMS Micro air quality detector, random forest regression, partial least squares regression, data correction model.

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On function-on-function regression: partial least squares approach

Cited by 25 publications

References 37 publications

A partial least squares approach for function-on-function interaction regression

A partial least squares approach for function-on-function interaction regression

Precipitation Modeling for Extreme Weather Based on Sparse Hybrid Machine Learning and Markov Chain Random Field in a Multi-Scale Subspace

Research on Data Correction Method of Micro Air Quality Detector Based on Combination of Partial Least Squares and Random Forest Regression

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