Above are papers related to the following paper: [Paper_ID] Paper #6910. 	[Title] Smoothing Spline ANOVA for Exponential Families, with Application to the Wisconsin Epidemiological Study of Diabetic [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #31489. 	[Title] Minimax Estimation via Wavelet Shrinkage  a pleasure to acknowledge friendly conversations with Gerard Kerkyacharian, [Abstract] We attempt to recover an unknown function from noisy, sampled data. Using orthonormal bases of compactly supported wavelets we develop a nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coefficients. The shrinkage can be tuned to be nearly minimax over any member of a wide range of Triebel- and Besov-type smoothness constraints, and asymptotically minimax over Besov bodies with p q. Linear estimates cannot achieve even the minimax rates over Triebel and Besov classes with p &lt; 2, so our method can significantly outperform every linear method (kernel, smoothing spline, sieve, : : : ) in a minimax sense. Variants of our method based on simple threshold nonlinearities are nearly minimax. Our method possesses the interpretation of spatial adaptivity: it reconstructs using a kernel which may vary in shape and bandwidth from point to point, depending on the data. Least favorable distributions for certain of the Triebel and Besov scales generate objects with sparse wavelet transforms. Many real objects have similarly sparse transforms, which suggests that these minimax results are relevant for practical problems. Sequels to this paper discuss practical implementation, spatial adaptation properties and applications to inverse problems. Acknowledgements. This work was completed while the first author was on leave from U.C. Berkeley, where his research was supported by NSF DMS 88-10192, by NASA Contract NCA2-488, and by a grant from ATT Foundation. The second author was supported in part by NSF grants DMS 84-51750, 86-00235, and NIH PHS grant GM21215-12. Supersedes an earlier version, titled "Wavelets and Optimal Function Estimation", dated November 10, 1990, and issued as Technical reports by the Departments of Statistics at both Stanford and at U.C. Berkeley. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #263553. 	[Title] A Generalized Approximate Cross Validation for Smoothing Splines with Non-Gaussian Data 1 [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6913. 	[Title] On Convergence of the EM Algorithm and the Gibbs Sampler  SUMMARY [Abstract] In this article we investigate the relationship between the two popular algorithms, the EM algorithm and the Gibbs sampler. We show that the approximate rate of convergence of the Gibbs sampler by Gaussian approximation is equal to that of the corresponding EM type algorithm. This helps in implementing either of the algorithms as improvement strategies for one algorithm can be directly transported to the other. In particular, by running the EM algorithm we know approximately how many iterations are needed for convergence of the Gibbs sampler. We also obtain a result that under conditions, the EM algorithm used for finding the maximum likelihood estimates can be slower to converge than the corresponding Gibbs sampler for Bayesian inference which uses proper prior distributions. We illustrate our results in a number of realistic examples all based on the generalized linear mixed models. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #662416. 	[Title] USING SMOOTHING SPLINE ANOVA TO EXAMINE THE RELATION OF RISK FACTORS TO THE INCIDENCE AND [Abstract]  Please summarise all the given information.

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Above are papers related to the following paper: [Paper_ID] Paper #1152150. 	[Title]  [Abstract] TECHNICAL REPORT NO. 947 June 5, 1995 Please summarise all the given information.

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Above are papers related to the following paper: [Paper_ID] Paper #444191. 	[Title] Automatic Smoothing Spline Projection Pursuit  Automatic Smoothing Spline Projection Pursuit. [Abstract] kj = 1. The standard PPR algorithm of Friedman and Stuet-zle (1981) estimates the smooth functions f j using the supersmoother nonparametric scatterplot smoother. Friedman's algorithm constructs a model with M max linear combinations, then prunes back to a simpler model of size M M max , where M and M max are specified by the user. This paper discusses an alternative algorithm in which the smooth functions are estimated using smoothing splines. The direction coefficients ff j , the amount of smoothing in each direction, and the number of terms M and M max are determined to optimize a single generalized cross-validation measure. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1117219. 	[Title] Testing the Generalized Linear Model Null Hypothesis versus `Smooth' Alternatives 1 [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #662572. 	[Title] Spatial-Temporal Analysis of Temperature Using Smoothing Spline ANOVA [Abstract]  Please summarise all the given information.

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Above are papers related to the following paper: [Paper_ID] Paper #1154103. 	[Title]  [Abstract] TECHNICAL REPORT NO. 967 August 1996 Please summarise all the given information.

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Above are papers related to the following paper: [Paper_ID] Paper #124224. 	[Title] Behavior Near Zero of the Distribution of GCV Smoothing Parameter Estimates 1 [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #169280. 	[Title] A Flexible Model For Human Circadian Rhythms [Abstract] Many hormones and other physiological processes vary in a circadian pattern. Although a sine/cosine function can be used to model these patterns, this functional form is not appropriate when there is asymmetry between the peak and nadir phases. In this paper we describe a semi-parametric periodic spline function that can be fit to circadian rhythms. The model includes both phase and amplitude so that the time and the magnitude of the peak or nadir can be estimated. We also describe tests of fit for components in the model. Data from an experiment to study immunological responses in humans are used to demonstrate the methods. Please summarise all the given information.

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Above are papers related to the following paper: [Paper_ID] Paper #4330. 	[Title] Hierarchical Mixtures of Experts and the EM Algorithm [Abstract] We present a tree-structured architecture for supervised learning. The statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM's). Learning is treated as a maximum likelihood problem; in particular, we present an Expectation-Maximization (EM) algorithm for adjusting the parameters of the architecture. We also develop an on-line learning algorithm in which the parameters are updated incrementally. Comparative simulation results are presented in the robot dynamics domain. This report describes research done at the Dept. of Brain and Cognitive Sciences, the Center for Biological and Computational Learning, and the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for CBCL is provided in part by a grant from the NSF (ASC-9217041). Support for the laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Dept. of Defense. The authors were supported by a grant from the McDonnell-Pew Foundation, by a grant from ATR Human Information Processing Research Laboratories, by a grant from Siemens Corporation, by by grant IRI-9013991 from the National Science Foundation, by grant N00014-90-J-1942 from the Office of Naval Research, and by NSF grant ECS-9216531 to support an Initiative in Intelligent Control at MIT. Michael I. Jordan is a NSF Presidential Young Investigator. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6898. 	[Title] Sample Size Calculations for Smoothing Splines Based on Bayesian Confidence Intervals [Abstract] Bayesian confidence intervals of a smoothing spline are often used to distinguish two curves. In this paper, we provide an asymptotic formula for sample size calculations based on Bayesian confidence intervals. Approximations and simulations on special functions indicate that this asymptotic formula is reasonably accurate. Key Words: Bayesian confidence intervals; sample size; smoothing spline. fl Address: Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106-3110. Tel.: (805)893-4870. Fax: (805)893-2334. E-mail: yuedong@pstat.ucsb.edu. Supported by the National Institute of Health under Grants R01 EY09946, P60 DK20572 and P30 HD18258. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1123188. 	[Title] GRKPACK: FITTING SMOOTHING SPLINE ANOVA MODELS FOR EXPONENTIAL FAMILIES [Abstract] Wahba, Wang, Gu, Klein and Klein (1995) introduced Smoothing Spline ANalysis of VAriance (SS ANOVA) method for data from exponential families. Based on RKPACK, which fits SS ANOVA models to Gaussian data, we introduce GRKPACK: a collection of Fortran subroutines for binary, binomial, Poisson and Gamma data. We also show how to calculate Bayesian confidence intervals for SS ANOVA estimates. Please summarise all the given information.

Paper #6910 has the title `Smoothing Spline ANOVA for Exponential Families, with Application to the Wisconsin Epidemiological Study of Diabetic
` and the abstract `nan`.
Question: Which category should Paper #6910 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #6910 has the title `Smoothing Spline ANOVA for Exponential Families, with Application to the Wisconsin Epidemiological Study of Diabetic
` and the abstract `nan`.
Question: Which category should Paper #6910 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Neural_Networks