### Citations

8887 |
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
- Pearl
- 1988
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Citation Context ... conditional distributions. This is due to the fact that the full conditional distribution of any node on the graph is the same as the distribution of the node conditional on its Markov blanket (e.g. =-=Pearl, 1988-=-). The Markov blanket of a node consists of its parent nodes, co-parent nodes and child nodes. 2.7 Fitting via mean field variational Bayes Mean field variational Bayes (MFVB) (e.g. Attias, 1999, Wain... |

4182 | Regression shrinkage and selection via the lasso
- Tibshirani
- 1996
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Citation Context ...wavelets, a more appropriate choice is ρλ (x) = λx since the corresponding L1 penalty invokes a sparse solution. The L1 penalty corresponds to the least absolute shrinkage selection operator (LASSO) (=-=Tibshirani, 1996-=-) applied to the basis functions. Algorithms for solving (21) when ρλ(x) = λx are given in Osborne, Presnell & Turlach (2000) and Efron et al. (2004). The algorithm in Efron et al. (2004) efficiently ... |

2198 | Orthonormal bases of compactly supported wavelets - Daubechies - 1988 |

1856 |
Spline Models for Observational Data
- Wahba
- 1990
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Citation Context ... coefficient models, geoadditive models, subject-specific curve models, among 3 others (e.g. Ruppert, Wand & Carroll, 2003, 2009). Penalized splines include, as special cases, smoothing splines (e.g. =-=Wahba, 1990-=-), P-splines (Eilers & Marx, 1996), and pseudosplines (Hastie, 1996). A distinguishing feature of penalized splines is that the number of basis functions does not necessarily match the sample sizes, a... |

1528 | Core Team, R (2011): a language and environment for statistical computing, R Foundation for Statistical Computing - Development |

1319 | Least angle regression - Efron, Hastie, et al. - 2004 |

1278 | Denoising by soft thresholding - Donoho - 1995 |

1264 | Ideal spatial adaptation by wavelet shrinkage
- Donoho, Johnstone
- 1994
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Citation Context ...d then the 30 Discrete Wavelet Transform can be used to quickly obtain the n coefficients of the full set of wavelet basis functions, as elucidated by (19). Simple thresholds such as σ̂ε √ 2 loge(n) (=-=Donoho & Johnstone, 1994-=-) can be used select L. Specifically, the L could correspond to the largest level having coefficients exceeding the threshold. Further development is required for general xi. 5 Semiparametric Regressi... |

964 | Regularization and variable selection via the elastic net - Zou, Hastie - 2005 |

814 | Graphical models, exponential families, and variational inference
- Wainwright, Jordan
- 2008
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Citation Context ...1988). The Markov blanket of a node consists of its parent nodes, co-parent nodes and child nodes. 2.7 Fitting via mean field variational Bayes Mean field variational Bayes (MFVB) (e.g. Attias, 1999, =-=Wainwright & Jordan, 2008-=-) is a deterministic alternative to Markov chain Monte Carlo which allows faster fitting and inference. In certain circumstances MFVB can be quite accurate and there is prima facie evidence that such ... |

786 | Bayesian analysis of binary and polychotomous response data - Albert, Chib - 1993 |

731 |
Smoothing Noisy Data with Spline Functions
- Craven, Wahba
- 1979
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Citation Context ...f(λ) and the residual sum of squares (RSS) RSS(λ) = ‖y − f̂λ‖2. Examples of popular penalty parameter selection criteria of this type are Generalized Cross-Validation, GCV(λ) = RSS(λ)/[{n− edf(λ)}2] (=-=Craven & Wahba, 1979-=-) and corrected Akaike’s Information Criterion, AICC(λ) = log{RSS(λ)}+ 2{edf(λ) + 1} n− edf(λ)− 2 (Hurvich, Simonoff & Tsai, 1998). Another option for selection of λ is k-fold cross-validation, where ... |

730 |
Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach
- Green, Silverman
- 1994
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Citation Context ...efault version of Algorithm 1. We believe that the B-spline basis and penalty set-up of O’Sullivan (1986) is an excellent choice. It may be thought of as a low-rank version of smoothing splines (e.g. =-=Green & Silverman, 1994-=-) and is used in the R function smooth.spline() when the sample size exceeds 50. Wand & Ormerod (2008) describe conversion of the B-splines to canonical form. Appendix A provides details on the constr... |

529 |
Estimation of the mean of a multivariate normal distribution
- Stein
- 1981
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Citation Context ...(f̂λ(xi), yi). (8) It provides a meaningful and scale-free measure of the amount of fitting (Buja, Hastie & Tibshirani, 1989). Definition (8) has its roots in Stein’s unbiased risk estimation theory (=-=Stein, 1981-=-; Efron, 2004). If the vector of fitted values can be written as f̂λ = Sλ y for some n× nmatrix not depending on the yis (known as the smoother matrix) then edf(λ) = tr(Sλ). (9) For the penalized leas... |

523 |
Semiparametric Regression
- Ruppert, Wand, et al.
- 2003
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Citation Context ... estimationmethods and loss functions. 10 2.5 Fitting via frequentist mixed model representation The frequentist mixed model representation of (5) is y|u ∼ N(Xβ +Zu, σ2εI), u ∼ N(0, σ2uI). (10) (e.g. =-=Ruppert et al. 2003-=-, Section 4.9). According to this model, the log-likelihood of the model parameters is `(β, σ2u, σ 2 ε) = −12 { n log(2pi) + log |V |+ (y −Xβ)TV −1(y −Xβ)} where V = V (σ2u, σ 2 ε) ≡ Cov(y) = σ2uZZT +... |

429 | Prior distributions for variance parameters in hierarchical models - Gelman - 2006 |

403 | Flexible smoothing with B-splines and penalties
- Eilers, Marx
- 1996
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Citation Context ...dditive models, subject-specific curve models, among 3 others (e.g. Ruppert, Wand & Carroll, 2003, 2009). Penalized splines include, as special cases, smoothing splines (e.g. Wahba, 1990), P-splines (=-=Eilers & Marx, 1996-=-), and pseudosplines (Hastie, 1996). A distinguishing feature of penalized splines is that the number of basis functions does not necessarily match the sample sizes, and terminology such as low-rank o... |

399 | A statistical view of some chemometrics regression tools - Frank, Friedman - 1993 |

275 | Statistical Modeling by Wavelets, - Vidakovic - 1999 |

213 | Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion - Hurvich, Simono®, et al. - 1998 |

208 | On the LASSO and its dual - Osborne, Presnell, et al. - 2000 |

198 | Inferring parameters and structure of latent variable models by variational Bayes
- Attias
- 1999
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Citation Context ... (e.g. Pearl, 1988). The Markov blanket of a node consists of its parent nodes, co-parent nodes and child nodes. 2.7 Fitting via mean field variational Bayes Mean field variational Bayes (MFVB) (e.g. =-=Attias, 1999-=-, Wainwright & Jordan, 2008) is a deterministic alternative to Markov chain Monte Carlo which allows faster fitting and inference. In certain circumstances MFVB can be quite accurate and there is prim... |

185 | A statistical perspective on ill-posed inverse problems - O’Sullivan - 1986 |

117 | Empirical Bayes selection of wavelet thresholds - Johnstone, Silverman |

98 | Linear smoothers and additive models - BUJA, HASTIE, et al. - 1989 |

94 | The estimation of prediction error: Covariance penalties and crossvalidation (with discussion
- Efron
- 2004
(Show Context)
Citation Context .... (8) It provides a meaningful and scale-free measure of the amount of fitting (Buja, Hastie & Tibshirani, 1989). Definition (8) has its roots in Stein’s unbiased risk estimation theory (Stein, 1981; =-=Efron, 2004-=-). If the vector of fitted values can be written as f̂λ = Sλ y for some n× nmatrix not depending on the yis (known as the smoother matrix) then edf(λ) = tr(Sλ). (9) For the penalized least squares fit... |

77 | The horseshoe estimator for sparse signals. - Carvalho, Polson, et al. - 2010 |

60 | Sure independence screening in generalized linear models with NP-dimensionality. The Annals of Statistics 38 - Fan, Song - 2010 |

59 | Regularization of wavelet approximations (with discussion - Antoniadis, Fan - 2001 |

45 | Density estimation in Besov spaces. - Kerkyacharian, Picard - 1992 |

45 | Wavelet-based nonparametric modeling of hierarchical functions in colon carcinogenesis
- Morris, Vannucci, et al.
- 2003
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Citation Context ...nnucci, Brown & Carroll (2003), Morris & Carroll (2006) and Zhao & Wu (2008). A feature of the wavelet-based longitudinal data analysis literature is a tendency to work in the coefficient space (e.g. =-=Morris et al. 2003-=-). In this section we demonstrate that sound analyses can be conducted using direct approaches, analogous to those in the penalized spline longitudinal data analysis literature. The penalized wavelet ... |

44 |
BUGS: Bayesian Inference Using Gibbs Sampling.
- Spiegelhalter, Thomas, et al.
- 1998
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Citation Context ...the data. The blue curves correspond to the posterior mean fit of (42) and (43). The light blue shading conveys pointwise 95% credible sets for each fitted curve. These fits were obtained using BUGS (=-=Spiegelhalter et al. 2003-=-), accessed from within R via the BRugs package (Ligges et al. 2009). The BUGS code is listed in Appendix F. A burnin of size 15000 was used, followed by 5000 iterations which were then thinned by a f... |

44 | Semiparametric stochastic mixed models for longitudinal data. - Zhang, Lin, et al. - 1998 |

41 | Bayesian Smoothing and Regression Splines for Measurement Error Problems,” - Berry, Carroll, et al. - 2002 |

32 | Mixed effects smoothing spline analysis of variance. - Wang - 1998 |

31 | Wavelet Methods in Statistics with R - Nason - 2008 |

30 | e elements of statistical learning, Second Edition - Hastie, Tibshirani, et al. - 2009 |

29 | Exact risk analysis of wavelet regression. - Marron, Adka, et al. - 1998 |

27 |
Thin-plate regression splines
- Wood
- 2003
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Citation Context ...ple size exceeds 50. In the generalized additive (mixed) model R package mgcv (Wood, 2010) the univariate function estimates use yet another variant of penalized splines: low-rank thin plate splines (=-=Wood, 2003-=-). In the early sections of this article we will confine discussion to the simple nonparametric regression model, and return to various semiparametric extensions in later sections. So, for now, we foc... |

24 | On semiparametric regression with O’Sullivan penalized splines.
- Wand, Ormerod
- 2008
(Show Context)
Citation Context ...ic form λ ∑K k=1 ∑K k′=1Ωkk′ukuk′ where Ωkk′ depends on the basis functions. However, one can always linearly transform the zk(·) so that the canonical penalty λ ∑K k=1 u 2 k is appropriate (see e.g. =-=Wand & Ormerod, 2008-=-, Section 4). Throughout this article we assume that the zk(·) are in canonical form. 1.3.1 Basis construction At the heart of contemporary penalized splines are algorithms, and corresponding software... |

20 | Simple fitting of subject-specific curves for longitudinal data. - Durban, Harezlak, et al. - 2005 |

20 | Exact and approximate posterior moments for a normal location parameter. - Pericchi, Smith - 1992 |

19 |
Pseudosplines
- Hastie
- 1996
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Citation Context ...dels, among 3 others (e.g. Ruppert, Wand & Carroll, 2003, 2009). Penalized splines include, as special cases, smoothing splines (e.g. Wahba, 1990), P-splines (Eilers & Marx, 1996), and pseudosplines (=-=Hastie, 1996-=-). A distinguishing feature of penalized splines is that the number of basis functions does not necessarily match the sample sizes, and terminology such as low-rank or fixed-rank smoothing has emerged... |

17 | Bayesian hyper-lassos with non-convex penalization. - Griffin, Brown - 2012 |

17 | Semiparametric regression during 2003-2007. - Ruppert, Wand, et al. - 2009 |

15 | Mean field variational Bayes for elaborate distributions. Bayesian Analysis, - Wand, Ormerod, et al. - 2011 |

14 | 2002: Flexible smoothing with P-splines: a unified approach - Currie, Durban |

13 | Variational bayesian inference for parametric and nonparametric regression with missing data - Wand, Faes, et al. - 2011 |

11 | Longitudinal Data Analysis: A Handbook of Modern Statistical Methods. Chapman & Hall/CRC, - Fitzmaurice, Davidian, et al. - 2008 |

10 |
Semiparametric regression and graphical models”,
- Wand
- 2008
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Citation Context ...ing various non-standard situations. Examples include measurement error (e.g. Berry, Carroll & Ruppert, 2002), missing data (e.g. Faes, Ormerod & Wand, 2011) and robustness (e.g. Staudenmayer, Lake & =-=Wand, 2009-=-). In Marley & Wand (2010) we should how MCMC, with the help of BUGS, can handle a 39 wide range of non-standard semiparametric regression problems. As Section 3 shows, penalized wavelets can be handl... |

9 | A comparison of mixed model splines for curve fitting - Welham, Cullis, et al. - 2007 |

5 | Robustness for general design mixed models using the t-distribution - Staudenmayer, Lake, et al. - 2009 |

4 | Penalized wavelet monotone regression - Antoniadis, Bigot, et al. - 2007 |

4 | Nonparametric wavelet regression for binary response - Antoniadis, Leblanc - 2000 |

2 | A wavelet approach to shape analysis for spinal curves - Aykroyd, Mardia - 2003 |

2 |
T: Radiation pneumonitis: Correlation of Toxicity with the Pulmonary Metabolic Radiation Response
- Hart, MR, et al.
- 2011
(Show Context)
Citation Context ..., σε ∼ Half-Cauchy(Aε), γik| pik ind.∼ Bernoulli(pik), pik ind.∼ Beta(Ap, Bp). (43) Figure 21 shows data where such modelling is beneficial. The data are from a respiratory pneumonitis study (source: =-=Hart et al., 2008-=-) and the panels display the logarithm of normalized fluorodeoxyglucose uptake against radiation dose for each of 21 lung cancer patients. The red points in Figure 21 show the data. The blue curves co... |

2 | Infer.Net 2.4. Microsoft Research Cambridge - Minka, Winn, et al. - 2009 |

2 | M.: Using infer.NET for statistical analyses - Wang, Wand - 2011 |

1 |
ncvreg 2.3. Regularization paths for SCAD- and MCP-penalized regression models. R package. http://cran.r-project.org
- Breheny
- 2011
(Show Context)
Citation Context ...ogistic log-likelihood −yT (Xβ +Zu) + 1T log{1+ exp(Xβ +Zu)}+ λ K∑ k=1 SCAD(|uk|, 3) (34) and λ chosen via 10-fold cross-validation. TheR functions ncvreg() and cv.ncvreg() within the package ncvreg (=-=Breheny, 2011-=-) were used to obtain the fits in Figure 17. The design matrices in X and Z (34) have exactly the same form as those used in Section 3 31 for Gaussian response penalized wavelet regression. A striking... |

1 | glmnet 1.1: lasson and elastic-net regularized generalized linear models. R package. http://cran.r-project.org - Friedman, Hastie, et al. - 2009 |

1 | lars 0.9. Least angle regression, lasso and forward stagewise regression. R package. http://cran.r-project.org - Hastie, Efron - 2007 |

1 | BRugs 0.5: OpenBUGS and its R/S-PLUS interface BRugs. http://www.stats.ox.ac.uk/pub/RWin/src/contrib - Marley, Wand - 2010 |

1 |
wavethresh 4.5. Wavelets statistics and transforms. R package. http://cran.r-project.org
- Nason
- 2010
(Show Context)
Citation Context ...tions of a single (“mother”) wavelet function. Figure 6 shows four wavelet functions from the basic Daubechies family. The numbers correspond to the amount of smoothness. In the R package wavethresh (=-=Nason, 2010-=-) this is referenced using family="DaubExPhase" and the smoothness number is denoted by filter.number. Note, however, that the Daubechies wavelet functions do not admit explicit algebraic expressions ... |

1 |
Generalized AdditiveModels: An Introduction with R. Boca
- Wood
- 2006
(Show Context)
Citation Context ... extensions of nonparametric regression when several continuous predictor variables are available. If the response is non-Gaussian then the term generalized additive model (Hastie & Tibshirani, 1990; =-=Wood, 2006-=-) is commonly used for the former type. With simplicity in mind, we will restrict discussion to the case of two predictor variables x1 and x2. The treatment of the general case is similar, but at the ... |

1 | mgcv 1.7. GAMs with GCV/AIC/REML smoothness estimation and GAMMs by PQL. R package. http://cran.r-project.org - Wood - 2011 |