Penalized partially linear models using sparse representations with an application to fMRI time series
In this paper, we consider modeling the nonparametric component in partially linear models (PLMs) using linear sparse representations, e.g., wavelet expansions. Two types of representations are investigated, namely, orthogonal bases (complete) and redundant overcomplete expansions. For bases, we int...
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Published in | IEEE transactions on signal processing Vol. 53; no. 9; pp. 3436 - 3448 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
New York, NY
IEEE
01.09.2005
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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Abstract | In this paper, we consider modeling the nonparametric component in partially linear models (PLMs) using linear sparse representations, e.g., wavelet expansions. Two types of representations are investigated, namely, orthogonal bases (complete) and redundant overcomplete expansions. For bases, we introduce a regularized estimator of the nonparametric part. The important contribution here is that the nonparametric part can be parsimoniously estimated by choosing an appropriate penalty function for which the hard and soft thresholding estimators are special cases. This allows us to represent in an effective manner a broad class of signals, including stationary and/or nonstationary signals and avoids excessive bias in estimating the parametric component. We also give a fast estimation algorithm. The method is then generalized to handle the case of overcomplete representations. A large-scale simulation study is conducted to illustrate the finite sample properties of the estimator. The estimator is finally applied to real neurophysiological functional magnetic resonance imaging (MRI) data sets that are suspected to contain both smooth and transient drift features. |
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AbstractList | In this paper, we consider modeling the nonparametric component in partially linear models (PLMs) using linear sparse representations, e.g., wavelet expansions. Two types of representations are investigated, namely, orthogonal bases (complete) and redundant overcomplete expansions. For bases, we introduce a regularized estimator of the nonparametric part. The important contribution here is that the nonparametric part can be parsimoniously estimated by choosing an appropriate penalty function for which the hard and soft thresholding estimators are special cases. This allows us to represent in an effective manner a broad class of signals, including stationary and/or nonstationary signals and avoids excessive bias in estimating the parametric component. We also give a fast estimation algorithm. The method is then generalized to handle the case of overcomplete representations. A large-scale simulation study is conducted to illustrate the finite sample properties of the estimator. The estimator is finally applied to real neurophysiological functional magnetic resonance imaging (MRI) data sets that are suspected to contain both smooth and transient drift features. The estimator is finally applied to real neurophysiological functional magnetic resonance imaging (MRI) data sets that are suspected to contain both smooth and transient drift features. |
Author | Bullmore, E. Fadili, J.M. |
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Cites_doi | 10.1017/S026646660420202X 10.1214/aos/1176347115 10.2307/1390659 10.1016/0167-7152(86)90067-2 10.1016/j.csda.2003.10.018 10.1109/42.759109 10.1214/aos/1176350695 10.1109/TMI.2003.809587 10.1214/aos/1034276628 10.1111/j.0006-341X.1999.00699.x 10.1137/S1064827596304010 10.1198/1061860032076 10.1109/TIP.2005.852206 10.1080/01621459.1994.10476774 10.1080/01621459.1997.10474001 10.1109/78.277854 10.1007/978-3-642-57700-0 10.1016/0378-3758(89)90037-2 10.2307/2337118 10.1198/016214501753208942 10.1111/j.1467-9892.1992.tb00103.x 10.1006/nimg.2001.0955 10.1198/1061860043434 10.1137/S0036139997327794 10.1137/1.9781611971309 10.1007/BF01404567 10.1016/S0167-9473(98)00054-1 10.1016/S0165-1684(97)83621-3 10.1093/biomet/77.1.1 10.1080/01621459.1990.10476211 10.1007/978-1-4899-4541-9 |
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Keywords | penalized estimation Threshold detection sparse representations Time series Non parametric estimation Functional analysis Nuclear magnetic resonance imaging Modeling Linear model neuroimaging Penalty function fMRI Simulation partially linear models wavelets Medical imagery Sparse representation Stationary signal Fast algorithm Functional imaging |
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References | ref35 ref13 ref34 ref12 ref37 ref15 ref36 ref14 ref31 ref30 heckman (ref3) 1986; 48 gao (ref10) 1992 ref11 ref39 ref17 ref38 ref16 ref19 ref18 meyer (ref28) 1992 horn (ref41) 1997 anderson (ref33) 1984 ref23 ref26 ref25 ref20 ref22 speckman (ref9) 1988; 50 amato (ref27) 1997; 42 ref29 ref8 ref7 hastie (ref2) 1990 ref4 gribonval (ref24) 2004 jansen (ref32) 1997; 56 fadili (ref21) 2001 ref6 ref5 ref40 härdle (ref1) 2000 |
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Snippet | In this paper, we consider modeling the nonparametric component in partially linear models (PLMs) using linear sparse representations, e.g., wavelet... The estimator is finally applied to real neurophysiological functional magnetic resonance imaging (MRI) data sets that are suspected to contain both smooth and... |
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SubjectTerms | Algorithms Biological and medical sciences Biological system modeling Biomedical engineering Biomedical imaging Computer Science Computer simulation Computerized, statistical medical data processing and models in biomedicine Econometrics Economic models Engineering Sciences Estimators fMRI Humans Large-scale systems Linear regression Magnetic resonance imaging Mathematical analysis Medical management aid. Diagnosis aid Medical sciences Neuroimaging partially linear models penalized estimation Polynomials Redundant Representations Signal and Image processing sparse representations Studies Time series Vectors wavelets |
Title | Penalized partially linear models using sparse representations with an application to fMRI time series |
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