Grace Wahba

Q: What Schools Are Affiliated With Grace Wahba

Grace Wahba is affiliated with the following schools: University of California, Berkeley, University of Wisconsin–Madison, Stanford University, Cornell University

Grace Wahba's AcademicInfluence.com Rankings

Grace Wahba

Mathematics

#1525

World Rank

#2488

Historical Rank

#621

USA Rank

Statistics

#77

World Rank

#107

Historical Rank

#36

USA Rank

mathematics Degrees

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Mathematics

Grace Wahba's Degrees

PhD Statistics University of California, Berkeley

Why Is Grace Wahba Influential?

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According to Wikipedia, Grace Goldsmith Wahba is an American statistician and retired I. J. Schoenberg-Hilldale Professor of Statistics at the University of Wisconsin–Madison. She is a pioneer in methods for smoothing noisy data. Best known for the development of generalized cross-validation and "Wahba's problem", she has developed methods with applications in demographic studies, machine learning, DNA microarrays, risk modeling, medical imaging, and climate prediction.

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Grace Wahba's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Spline Models for Observational Data (1990) (6862)
Smoothing noisy data with spline functions (1978) (3720)
Generalized cross-validation as a method for choosing a good ridge parameter (1979) (2936)
Some results on Tchebycheffian spline functions (1971) (1389)
Smoothing noisy data with spline functions (1975) (1371)
A Correspondence Between Bayesian Estimation on Stochastic Processes and Smoothing by Splines (1970) (1039)
A Least Squares Estimate of Satellite Attitude (1965) (1004)
Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy (1977) (814)
Bayesian "Confidence Intervals" for the Cross-validated Smoothing Spline (1983) (681)
Some New Mathematical Methods for Variational Objective Analysis Using Splines and Cross Validation (1980) (598)
A Comparison of GCV and GML for Choosing the Smoothing Parameter in the Generalized Spline Smoothing Problem (1985) (567)
Improper Priors, Spline Smoothing and the Problem of Guarding Against Model Errors in Regression (1978) (567)
Multicategory Support Vector Machines (2004) (471)
Support vector machines, reproducing kernel Hilbert spaces, and randomized GACV (1999) (433)
Smoothing spline models for the analysis of nested and crossed samples of curves. Commentaries. Authors' reply (1998) (411)
A completely automatic french curve: fitting spline functions by cross validation (1975) (409)
Support Vector Machines for Classification in Nonstandard Situations (2002) (382)
Spline Interpolation and Smoothing on the Sphere (1981) (371)
A NOTE ON THE LASSO AND RELATED PROCEDURES IN MODEL SELECTION (2006) (310)
Smoothing spline ANOVA for exponential families, with application to the Wisconsin Epidemiological Study of Diabetic Retinopathy : the 1994 Neyman Memorial Lecture (1995) (265)
Automatic Smoothing of the Log Periodogram (1980) (230)
Minimizing GCV/GML Scores with Multiple Smoothing Parameters via the Newton Method (1991) (195)
Hybrid Adaptive Splines (1997) (194)
Reliable stereological method for estimating the number of microscopic hepatocellular foci from their transections. (1983) (173)
Optimal Convergence Properties of Variable Knot, Kernel, and Orthogonal Series Methods for Density Estimation. (1975) (153)
Smoothing Spline ANOVA with Component-Wise Bayesian “Confidence Intervals” (1993) (149)
Testing the (Parametric) Null Model Hypothesis in (Semiparametric) Partial and Generalized Spline Models (1988) (141)
A GENERALIZED APPROXIMATE CROSS VALIDATION FOR SMOOTHING SPLINES WITH NON-GAUSSIAN DATA (1996) (139)
Multivariate Bernoulli distribution (2012) (136)
Smoothing spline ANOVA models for large data sets with Bernoulli observations and the randomized GACV (2000) (127)
Gcvpack – routines for generalized cross validation (1987) (123)
Generalized Inverses in Reproducing Kernel Spaces: An Approach to Regularization of Linear Operator Equations (1974) (114)
Ill Posed Problems: Numerical and Statistical Methods for Mildly, Moderately and Severely Ill Posed Problems with Noisy Data. (1980) (109)
Data-Based Optimal Smoothing of Orthogonal Series Density Estimates (1981) (107)
Variable Selection and Model Building via Likelihood Basis Pursuit (2004) (105)
Inequality-Constrained Multivariate Smoothing Splines with Application to the Estimation of Posterior Probabilities (1987) (104)
Soft and hard classification by reproducing kernel Hilbert space methods (2002) (103)
SPLINE FUNCTIONS AND STOCHASTIC PROCESSES. (1969) (101)
Semiparametric Analysis of Variance with Tensor Product Thin Plate Splines (1993) (100)
Adaptive Tuning of Numerical Weather Prediction Models: Randomized GCV in Three- and Four-Dimensional Data Assimilation (1995) (97)
Problem 65-1: A least squares estimate of satellite attitude (1966) (96)
Constrained Regularization for Ill Posed Linear Operator Equations, with Applications in Meteorology and Medicine. (1982) (96)
Convergence rates of approximate least squares solutions of linear integral and operator equations of the first kind (1974) (93)
Cloud Classification of Satellite Radiance Data by Multicategory Support Vector Machines (2004) (80)
Partial and interaction spline models for the semiparametric estimation of functions of several variables (1986) (79)
Periodic splines for spectral density estimation: the use of cross validation for determining the degree of smoothing (1975) (79)
How to Smooth Curves and Surfaces with Splines and Cross-Validation (1979) (76)
A cross validated bayesian retrieval algorithm for nonlinear remote sensing experiments (1985) (76)
Design Problems for Optimal Surface Interpolation. (1979) (76)
Cross-Validated Spline Methods for the Estimation of Three-Dimensional Tumor Size Distributions from Observations on Two-Dimensional Cross Sections (1984) (75)
Neural Networks and Related Methods for Classification - Discussion (1994) (75)
The computation of generalized cross-validation functions through householder tridiagonalization with applications to the fitting of interaction spline models (1989) (73)
Surface fitting with scattered noisy data on Euclidean D-space and on the sphere (1984) (72)
Interpolating Spline Methods for Density Estimation I. Equi-Spaced Knots (1975) (69)
Bootstrap confidence intervals for smoothing splines and their comparison to bayesian confidence intervals (1995) (69)
When is the optimal regularization parameter insensitive to the choice of the loss function (1990) (68)
Multivariate Function and Operator Estimation, Based on Smoothing Splines and Reproducing Kernels (1992) (68)
Good Ridge Parameter (1979) (66)
Convergence rates of certain approximate solutions to Fredholm integral equations of the first kind (1973) (64)
On the Regression Design Problem of Sacks and Ylvisaker (1971) (64)
Framework for kernel regularization with application to protein clustering. (2005) (59)
Partial Spline Models for the Inclusion of Tropopause and Frontal Boundary Information in Otherwise Smooth Two- and Three-Dimensional Objective Analysis (1986) (59)
THREE TOPICS IN ILL-POSED PROBLEMS (1987) (58)
The Bias-Variance Tradeoff and the Randomized GACV (1998) (58)
Convergence rates of "thin plate" smoothing splines wihen the data are noisy (1979) (56)
Erratum: Spline Interpolation and Smoothing on the Sphere (1982) (56)
A Polynomial Algorithm for Density Estimation (1971) (52)
On the Distribution of Some Statistics Useful in the Analysis of Jointly Stationary Time Series (1968) (51)
Statistical Properties and Adaptive Tuning of Support Vector Machines (2002) (50)
Spatial-Temporal Analysis of Temperature Using Smoothing Spline ANOVA (1998) (50)
Doubly penalized likelihood estimator in heteroscedastic regression (2004) (50)
Optimal Smoothing of Density Estimates (1977) (48)
Support Vector Machines, Reproducing Kernel Hilbert Spaces and the Randomized Gacv 1 1 Support Vector Machines, Reproducing Kernel Hilbert Spaces and the Randomized Gacv (1998) (48)
An introduction to model building with repro-ducing kernel hilbert spaces (2000) (46)
LASSO-Patternsearch algorithm with application to ophthalmology and genomic data. (2006) (46)
Gacv for support vector machines (2000) (45)
Regularization and approximation of linear operator equations in reproducing kernel spaces (1974) (43)
Smoothing Spline ANOVA for Multivariate Bernoulli Observations With Application to Ophthalmology Data (2001) (43)
Behavior near zero of the distribution of GCV smoothing parameter estimates (1995) (43)
Optimal spline smoothing of fMRI time series by generalized cross-validation (2003) (42)
Vector Splines on the Sphere, with Application to the Estimation of Vorticity and Divergence from Discrete, Noisy Data (1982) (40)
Detecting disease-causing genes by LASSO-Patternsearch algorithm (2007) (39)
Generalized Approximate Cross Validation For Support Vector Machines, Or, Another Way To Look At Mar (1999) (39)
Soft Classiication, A. K. A. Risk Estimation, via Penalized Log Likelihood and Smoothing Spline Analysis of Variance (1993) (39)
On the Estimation of Functions of Several Variables from Aggregated Data. (1982) (38)
Statistical Decision Theory and Related Topics III (1982) (36)
Using distance covariance for improved variable selection with application to learning genetic risk models (2015) (36)
Using distance correlation and SS-ANOVA to assess associations of familial relationships, lifestyle factors, diseases, and mortality (2012) (36)
A class of approximate solutions to linear operator equations (1973) (35)
Adaptive Tuning of Numerical Weather Prediction Models: Simultaneous Estimation of Weighting, Smoothing, and Physical Parameters (1998) (34)
Smoothing and Ill-Posed Problems (1979) (32)
Data mining, neural nets, trees — Problems 2 and 3 of Genetic Analysis Workshop 15 (2007) (31)
ON THE APPROXIMATE SOLUTION OF FREDHOLM INTEGRAL EQUATIONS OF THE FIRST KIND (1969) (30)
Examining the relative influence of familial, genetic, and environmental covariate information in flexible risk models (2009) (30)
Regression Design for Some Equivalence Classes of Kernels (1974) (30)
Some Tests of Independence for Stationary Multivariate Time Series (1971) (30)
Histosplines with Knots Which are Order Statistics (1976) (29)
Generalization and regularization in nonlinear learning systems (1998) (29)
Estimation of the Coefficients in a Multidimensional Distributed Lag Model (1969) (29)
Structured Machine Learning for Soft Classification with Smoothing Spline ANOVA and Stacked Tuning, Testing, and Evaluation (1993) (27)
Statistical tests and identifiability conditions for pooling and analyzing multisite datasets (2018) (25)
Soft Classification, a. k. a. Risk Estimation, via Penalized Log Likelihood and Smoothing Spline Ana (1993) (23)
Using smoothing spline anova to examine the relation of risk factors to the incidence and progression of diabetic retinopathy. (1997) (22)
Discussion: Multivariate Adaptive Regression Splines (1991) (21)
Optimal Properties and Adaptive Tuning of Standard and Nonstandard Support Vector Machines (2003) (20)
Optimal use of sampled tissue sections for estimating the number of hepatocellular foci. (1984) (19)
Dicussion on the meeting on ‘Statistical approaches to inverse problems’ (2004) (18)
8. Fredholm Integral Equations of the First Kind (1990) (18)
Smoothing Spline ANOVA for Exponential Families , with Application to theWisconsin Epidemiological Study of Diabetic Retinopathy 1 2 (1995) (17)
Interpolating Surfaces: High Order Convergence Rates and Their ASsociated Designs, with Application to X-Ray Image Reconstruction. (1978) (17)
An Averaging Method for the Stiff Highly Oscillatory Problem (1976) (17)
Variational methods in simultaneous optimum interpolation and initialization (1982) (17)
Numerical experiments with the thin plate histospline (1981) (17)
The approximate solution of linear operator equations when the data are noisy (1976) (16)
Design Criteria and Eigensequence Plots for Satellite-Computed Tomography (1985) (16)
LASSO-Patternsearch algorithm with application to ophthalmology data (2006) (15)
Learning Higher-Order Graph Structure with Features by Structure Penalty (2011) (15)
Distance shrinkage and Euclidean embedding via regularized kernel estimation (2014) (15)
4. Estimating the Smoothing Parameter (1990) (15)
Hypothesis Testing in Unsupervised Domain Adaptation with Applications in Alzheimer's Disease (2016) (13)
Discussion: Linear Smoothers and Additive Models (1989) (13)
[Monotone Regression Splines in Action]: Comment (1988) (13)
Smoothing Spline ANOVA Fits for Very Large, Nearly Regular Data Sets, with Application to Historical (1995) (13)
A CORRESPONDENCE BETWEEN BAYESIAN ESTIMATION ON (2016) (13)
Comment [on "Smooth pycnophylactic interpolation for geographical regions"]. (1979) (13)
Multivariate thin plate spline estimates for the posterior probabilities in the classification problem (1983) (13)
Estimating Tree-Structured Covariance Matrices via Mixed-Integer Programming (2009) (12)
Adaptive tuning of numerical weather prediction models: Part I: randomized GCV and related methods i (1995) (12)
An introduction to reproducing kernel hilbert spaces and why they are so useful (2003) (11)
Smoothing Splines (2011) (11)
A note on generalized cross-validation with replicates (1992) (11)
Discussion: Projection Pursuit (1985) (11)
ON THE NUMERICAL SOLUTION OF FREDHOLM INTEGRAL EQUATIONS OF THE FIRST KIND. (1969) (10)
Comment on "Support Vector Machines with Applications" (2006) (10)
Discussion: Consistent Nonparametric Regression (1977) (10)
Some Results on Tchebychefian Spline Functions (1971) (9)
Some exponentially decreasing error bounds for a numerical inversion of the Laplace transform (1975) (9)
On the Minimization of a Quadratic Functional Subject to a Continuous Family of Linear Inequality Constraints (1973) (9)
Margin-like quantities and generalized approximate cross validation for support vector machines (1999) (9)
Regularization and Cross Validation Methods for Nonlinear, Implicit, Ill-posed Inverse Problems (1990) (9)
On the Relation Between the GACV and Joachims’ ξα Method for Tuning Support Vector Machines, With Extensions to the Non-Standard Case (2001) (9)
When can Multi-Site Datasets be Pooled for Regression? Hypothesis Tests, $\ell_2$-consistency and Neuroscience Applications (2017) (8)
Subpixel Curvature Estimation of the Corpus Callosum via Splines and its Application to Autism (2004) (8)
Splines in Nonparametric Regression (2006) (8)
Rates of convergence of some estimators for a semiparametric model (1988) (8)
Simulation studies of smoothing parameter estimates and bayesian confidence intervals in bernoulli ss anova models (1995) (8)
Parameter estimation in linear dynamic systems (1980) (7)
Getting better contour plots with S and GCVPACK (1993) (7)
An introduction to smoothing spline ANOVA models in RKHS, with examples in geographical data, medicine, atmospheric sciences and machine learning (2003) (7)
Magnetic Resonance Image Segmentation with Thin Plate Spline Thresholding (2006) (7)
The partitioned LASSO-patternsearch algorithm with application to gene expression data (2012) (7)
Group variable selection via convex log‐exp‐sum penalty with application to a breast cancer survivor study (2013) (6)
Graph-based data analysis: tree-structured covariance estimation, prediction by regularized kernel estimation and aggregate database query processing for probabilistic inference (2008) (6)
Penalized Likelihood Regression in Reproducing Kernel Hilbert Spaces with Randomized Covariate Data (2010) (6)
A Canonical Form For the Problem of Estimating Smooth Surfaces. (1975) (5)
ESTIMATING DERIVATIVES FROM OUTER SPACE. (1969) (5)
Variable Selection via Basis Pursuit for Non-Gaussian Data (2001) (5)
Cross Validated Spline Methods for Direct and Indirect Sensing Experiments. (1982) (5)
The Asymptotic Behavior of the Nonlinear Estimators of the Diffusion Tensor and Tensor-Derived Quantities with Implications for Group Analysis (2006) (5)
Statistical Model Building, Machine Learning, and the Ah-Ha Moment (2013) (5)
Multivariate Model Building With Additive Interaction and Tensor Product Thin Plate Splines (1991) (5)
[A Statistical Perspective on Ill-Posed Inverse Problems]: Comment (1986) (4)
The Asymptotic Distribution of Diffusion Tensor and Fractional Anisotropy Estimates (2006) (4)
Statistical Learning in Medical Data Analysis (2007) (4)
Multivariate Model Building and Model Identification (1990) (4)
SIGNAL PROBABILITY ESTIMATION WITH PENALIZED LIKELIHOOD METHOD ON WEIGHTED DATA (2006) (4)
Backfitting in smoothing spline anova, with application to historical global temperature data (1996) (4)
Approximate Regularized Solutions to Linear Operator Equations When the Data-Vector Is Not in the Range of the Operator. (1973) (4)
2005 Joint Statistical Meetings Biometrics Section , Section on Nonparametric Statistics , ENAR (2005) (4)
5. Confidence Intervals (1990) (3)
Optimal Spline Smoothing of FMRI Time Series (2002) (3)
Determination of an optimal mesh for a collocation-projection method for solving two-point boundary value problems (1979) (3)
Penalized Log Likelihood Density Estimation , via Smoothing-Spline ANOVA and ranGACV-Comments to Hansen and Kooperberg , ‘ Spline Adaptation in Extended Linear Models ’ (3)
Representer Theorem (2019) (3)
REPRODUCING KERNEL HILBERT SPACES - TWO BRIEF REVIEWS (2003) (3)
A New Approach to the Numerical Evaluation of the Inverse Radon Transform with Discrete, Noisy Data (1981) (3)
Cross Validation and Constrained Regularization Methods for Mildly Ill Posed Problems. Revision. (1980) (3)
Convergence Properties of the Method of Regularization for Noisy Linear Operation Equations. (1973) (3)
Encoding Dissimilarity Data for Statistical Model Building. (2010) (3)
A Linear Mixed Effects Clustering Model for Multi-species Time Course Gene Expression Data 1 (2008) (3)
On the optimal choice of nodes in the collocation-projection method for solving linear operator equations (1976) (3)
Partial Spline Models for the Estimation of the Three Dimensional Atmospheric Temperature Distribution from Satellite Radiance Data and Tropopause Height Information (1986) (2)
Positive definite functions, Reproducing Kernel Hilbert Spaces and all that (2014) (2)
A Nonparametric Method for Estimation of Arterial Wall Shear Stress (2003) (2)
Quantitative Study of Smoothing Spline-ANOVA Based Fingerprint Methods for Attribution of Global War (1999) (2)
Optimizing the limit setting potential of a multivariate analysis using the Bayes posterior ratio (2003) (2)
Implications of Heterogeneous Variance of Tensor-Derived Quantities for Group Comparisons (2007) (2)
Adaptive Tuning, Four Dimensional Variational Data Assimilation, and Representers in Rkhs Adaptive Tuning, 4d-var and Representers in Rkhs (1998) (2)
11. Numerical Methods (1990) (2)
Using distance covariance for improved variable selection (2014) (2)
Minimax Optimal Rates of Estimation In Functional ANOVA Models When Data On Derivatives Are Available (2017) (1)
Penalized likelihood regression in reproducing kernel Hilbert spaces with randomized covariate non-Gaussian data (2009) (1)
Using distance covariance for improved variable selection with applications to genetic risk models (2014) (1)
Kernel Regularization and Dimension Reduction (2006) (1)
The Multicategory Support Vector Machine, with Application to the Classification of Simulated and Real MODIS Data into Clear, Ice Cloud and Water Cloud Categories. (2003) (1)
NO . 1155 September 4 , 2009 Encoding Dissimilarity Data for Statistical Model Building (2009) (1)
Learning graph structure with parametric and non-parametric models (2012) (1)
6. Partial Spline Models (1990) (1)
Spline Functions: Overview (2017) (1)
IPAM Graduate Summer School : Intelligent Extraction of Information From Graphs and High Dimensional Data (2005) (1)
23 Statistical Learning in Medical Data Analysis (2007) (1)
PRACTICAL TECHNIQUES OF OPTIMAL SMOOTHING, WITH APPLICATION TO THE NUMERICAL DIFFERENTIATION OF NOISY DATA AND SMOOTHING OF LOG SPECTRAL DENSITY ESTIMATES (1979) (1)
On the dynamic estimation of relative weights for observation and forecast in numerical weather prediction (1988) (0)
3. Equivalence and Perpendicularity, or, What's so Special about Splines? (1990) (0)
2. More Splines (1990) (0)
Statistical Models for Control, Optimization, Reliability, and Life Testing. (1973) (0)
2 What is an RKHS ? (2019) (0)
10. Additive and Interaction Splines (1990) (0)
Bootstrap Con dence Intervals for Smoothing Splines and theirComparison to Bayesian ` Con dence Intervals ' 1 (2011) (0)
Doubly Penalized Likelihood Estimator in Heteroscedastic Regression 1 (0)
Based on " a Framework for Kernel Regularization with Application to Protein Clustering " , by and Joint Work on Kernel Regularization Tuning with Fan Lu (in Progress) (2006) (0)
Adaptive tuning, 4-D Var and representers in RKHS (2001) (0)
Magnetic Resonance Image Segmentation with Thin Plate Spline (2006) (0)
Cross spectral distribution theory for mixed spectra and estimation of prediction filter coefficients (1987) (0)
Statistical Models for Time Series and Life Testing with Applications in Engineering Systems. (1977) (0)
Automatic Classification of High Angular Resolution Diffusion Data 1 (2005) (0)
12. Special Topics (1990) (0)
Smoothing, Regularization and Ill-Posed Inverse Problems; Robust and Convex Estimation of Functions of Several Variables. (1983) (0)
Combining Observations with Models: Penalized Likelihood and Related Methods in Numerical Weather Prediction (2000) (0)
Dissimilarity Data in Statistical Model Building and Machine Learning Grace Wahba (2011) (0)
The ( Nonstandard ) Multicategory Suport Vector Machine , with Application to Classification of Satellite-Observed Radiance Profiles (0)
Statistical Models for Control and Optimization Techniques. (1972) (0)
Magnetic Resonance Image Segmentation with Thin Plate Spline Thresholding 1 (2006) (0)
9. Further Nonlinear Generalizations (1990) (0)
A Property of Some Normal Matrices: 10645 (2000) (0)
A Family of Summation Formulae (1968) (0)
Based on " a Framework for Kernel Regularization with Application to Protein Clustering " , by and Joint Work on Kernel Regularization Tuning with Fan Lu and S ¨ Undüz Keles¸(in Progress) (2006) (0)
On the Optimal Choice of Nodes in the C-P Method for Solving Linear Operator Equations. (1973) (0)
Emanuel Parzen and a Tale of Two Kernels (2017) (0)
Emanuel Parzen: A Memorial, and a Model With the Two Kernels That He Championed (2018) (0)
7. Finite-Dimensional Approximating Subspaces (1990) (0)
Backward multiple imputation estimation of the conditional lifetime expectancy function with application to censored human longevity data (2015) (0)
Corrections (1973) (0)
Applications of Distance Correlation in Biomedical Data Grace Wahba and Jing Kong Based on Jing Kong's PhD dissertation, to appear and "Using distance covariance for improved variable selection" UW-Madison Statistics Dept TR1177 (2014) (0)
STATISTICAL ALGORITHMS FOR HARMONIZING BIOMARKER DISTRIBUTIONS ACROSS DIFFERENT COHORTS, SITES AND ASSAYS: APPLICATIONS TO CSF MEASUREMENTS (2017) (0)
NASA installs massively parallel processor (2006) (0)
NO . 1166 August 23 , 2011 The Partitioned LASSO-Pattersearch Algorithm With Application to Gene Expression Data (2011) (0)
2 Likelihood Basis Pursuit 2 . 1 Smoothing Spline ANOVA for Exponential (2006) (0)
Spline Function: Overview (2014) (0)
Design criteria and eigensequence plots for satellite-computed tomography. [in meteorology] (1985) (0)

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