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28
Bayesian network and nonparametric heteroscedastic regression for nonlinear modeling of genetic network
 Proc. 1st IEEE Computer Society Bioinformatics Conference
, 2002
"... We propose a new statistical method for constructing a genetic network from microarray gene expression data by using a Bayesian network. An essential point of Bayesian network construction is in the estimation of the conditional distribution of each random variable. We consider fitting nonparametric ..."
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Cited by 38 (18 self)
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We propose a new statistical method for constructing a genetic network from microarray gene expression data by using a Bayesian network. An essential point of Bayesian network construction is in the estimation of the conditional distribution of each random variable. We consider fitting nonparametric regression models with heterogeneous error variances to the microarray gene expression data to capture the nonlinear structures between genes. A problem still remains to be solved in selecting an optimal graph, which gives the best representation of the system among genes. We theoretically derive a new graph selection criterion from Bayes approach in general situations. The proposed method includes previous methods based on Bayesian networks. We demonstrate the effectiveness of the proposed method through the analysis of Saccharomyces cerevisiae gene expression data newly obtained by disrupting 100 genes. 1.
Bayesian Smoothing and Regression Splines for Measurement Error Problems
 Journal of the American Statistical Association
, 2001
"... In the presence of covariate measurement error, estimating a regression function nonparametrically is extremely dicult, the problem being related to deconvolution. Various frequentist approaches exist for this problem, but to date there has been no Bayesian treatment. In this paper we describe Bayes ..."
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Cited by 22 (7 self)
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In the presence of covariate measurement error, estimating a regression function nonparametrically is extremely dicult, the problem being related to deconvolution. Various frequentist approaches exist for this problem, but to date there has been no Bayesian treatment. In this paper we describe Bayesian approaches to modeling a exible regression function when the predictor variable is measured with error. The regression function is modeled with smoothing splines and regression P{splines. Two methods are described for exploration of the posterior. The rst is called iterative conditional modes (ICM) and is only partially Bayesian. ICM uses a componentwise maximization routine to nd the mode of the posterior. It also serves to create starting values for the second method, which is fully Bayesian and uses Markov chain Monte Carlo techniques to generate observations from the joint posterior distribution. Using the MCMC approach has the advantage that interval estimates that directly model and adjust for the measurement error are easily calculated. We provide simulations with several nonlinear regression functions and provide an illustrative example. Our simulations indicate that the frequentist mean squared error properties of the fully Bayesian method are better than those of ICM and also of previously proposed frequentist methods, at least in the examples we have studied. KEY WORDS: Bayesian methods; Eciency; Errors in variables; Functional method; Generalized linear models; Kernel regression; Measurement error; Nonparametric regression; P{splines; Regression Splines; SIMEX; Smoothing Splines; Structural modeling. Short title. Nonparametric Regression with Measurement Error Author Aliations Scott M. Berry (Email: scott@berryconsultants.com) is Statistical Scientist,...
F: Functional additive models
 J Am Stat Assoc
"... In commonly used functional regression models, the regression of a scalar or functional response on the functional predictor is assumed to be linear. This means the response is a linear function of the functional principal component scores of the predictor process. We relax the linearity assumption ..."
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Cited by 11 (5 self)
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In commonly used functional regression models, the regression of a scalar or functional response on the functional predictor is assumed to be linear. This means the response is a linear function of the functional principal component scores of the predictor process. We relax the linearity assumption and propose to replace it by an additive structure. This leads to a more widely applicable and much more flexible framework for functional regression models. The proposed functional additive regression models are suitable for both scalar and functional responses. The regularization needed for effective estimation of the regression parameter function is implemented through a projection on the eigenbasis of the covariance operator of the functional components in the model. The utilization of functional principal components in an additive rather than linear way leads to substantial broadening of the scope of functional regression models and emerges as a natural approach, as the uncorrelatedness of the functional principal components is shown to lead to a straightforward implementation of the functional additive model, just based on a sequence of onedimensional smoothing steps and without need for backfitting. This facilitates the theoretical analysis, and we establish asymptotic
Nonlinear and Nonparametric Regression and Instrumental Variables
 Variables,”Journal of the American Statistical Association
, 2003
"... We consider regression when the predictor is measured with error and an instrumental variable is available. The regression function can be modeled linearly, nonlinearly, or nonparametrically. Our major new result shows that the regression function and all parameters in the measurement error model ..."
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Cited by 10 (5 self)
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We consider regression when the predictor is measured with error and an instrumental variable is available. The regression function can be modeled linearly, nonlinearly, or nonparametrically. Our major new result shows that the regression function and all parameters in the measurement error model are identified under relatively weak conditions, much weaker than previously known to imply identifiability. In addition, we develop an apparently new characterization of the instrumental variable estimator: it is in fact a classical "correction for attenuation " method based on a particular estimate of the variance of the measurement error. This estimate of the measurement error variance allows us to construct functional nonparametric regression estimates, by which we mean that no assumptions are made about the distribution of the unobserved predictor. The general identifiability results also allow us to construct structural methods of estimation under parametric assumptions on the distribution of the unobserved predictor. The functional method uses SIMEX and the structural method uses Bayesian computing machinery. The Bayesian estimator is found to significantly outperform the functional approach.
2007): “Nonparametric matching and efficient estimators of homothetically separable functions
 Econometrica
"... For vectors x and w, letr(x, w) be a function that can be nonparametrically estimated consistently and asymptotically normally. We provide consistent, asymptotically normal estimators for the functions g and h, where r(x, w) =h[g(x),w], g is linearly homogeneous and h is monotonic in g. This framewo ..."
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Cited by 9 (4 self)
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For vectors x and w, letr(x, w) be a function that can be nonparametrically estimated consistently and asymptotically normally. We provide consistent, asymptotically normal estimators for the functions g and h, where r(x, w) =h[g(x),w], g is linearly homogeneous and h is monotonic in g. This framework encompasses homothetic and homothetically separable functions. Such models reduce the curse of dimensionality, provide a natural generalization of linear index models, and are widely used in utility, production, and cost function applications. One of our estimator’s of g is oracle efficient, achieving the same performance as an estimator based on local least squares knowing h. We provide simulation evidence on the small sample performance of our estimators, and an empirical production function application.
NONLINEAR METHODS OF CARDIOVASCULAR PHYSICS AND THEIR CLINICAL APPLICABILITY
, 2006
"... In this tutorial we present recently developed nonlinear methods of cardiovascular physics and show their potentials to clinically relevant problems in cardiology. The first part describes methods of cardiovascular physics, especially data analysis and modeling of noninvasively measured biosignals, ..."
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Cited by 3 (2 self)
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In this tutorial we present recently developed nonlinear methods of cardiovascular physics and show their potentials to clinically relevant problems in cardiology. The first part describes methods of cardiovascular physics, especially data analysis and modeling of noninvasively measured biosignals, with the aim to improve clinical diagnostics and to improve the understanding of cardiovascular regulation. Applications of nonlinear data analysis and modeling tools are various and outlined in the second part of this tutorial: monitoring, diagnosis, course and mortality prognoses as well as early detection of heart diseases. We show, that these data analyses and modeling methods lead to significant improvements in different medical fields.
Estimating Structural Exchange Rate Models By Artificial Neural Networks
, 1998
"... this paper. During the past few years there has been a noticeable increase of ANN applications in economics and finance (Trippi and Turban, 1993; Rehkugler and Zimmermann, 1994). However, no paper has been published on the application of ANNs to structural exchange rate modelling. Recently, some pap ..."
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Cited by 3 (1 self)
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this paper. During the past few years there has been a noticeable increase of ANN applications in economics and finance (Trippi and Turban, 1993; Rehkugler and Zimmermann, 1994). However, no paper has been published on the application of ANNs to structural exchange rate modelling. Recently, some papers have attempted to forecast currency exchange rates by ANNs, but they are not based on specific structural exchange rate (determination) models and are either based on nonlinear and nonparametric trading issues (Baestaens et al., 1994; Deboeck, 1994; Dunis, 1995) or are of a purely empirical nature (Refenes et al., 1993; Kuan andLiu,1995).Hencethereisaneedforaneconometric
Penalized Multivariate Logistic Regression With A Large Data Set
, 1999
"... We combine a smoothing spline ANOVA model and a loglinear model to build a partly exible model for multivariate Bernoulli data. The joint distribution conditioning on the predictor variables is estimated. The conditional log odds ratio is used to measure the association between outcome variables. A ..."
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Cited by 2 (1 self)
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We combine a smoothing spline ANOVA model and a loglinear model to build a partly exible model for multivariate Bernoulli data. The joint distribution conditioning on the predictor variables is estimated. The conditional log odds ratio is used to measure the association between outcome variables. A numerical scheme based on the block onestep SORNewtonRalphson algorithm is proposed to obtain an approximate solution for the variational problem. It is proved for a special case that the approximate solution can achieve the same statistical convergence rate as the exact solution, but is much more computing ecient. We extend GACV (Generalized Approximate Cross Validation) to the case of multivariate Bernoulli responses. Its randomized version is fast and stable to compute. Simulation studies show that it is an excellent computational proxy for the CKL (Comparative KullbackLeibler) distance. It is used to adaptively select smoothing parameters in each block onestep SOR iteration. Approximate Bayesian condence intervals are obtained for the exible estimates of the conditional logit functions. Simulation studies are conducted to check the performance of the proposed method. Finally, the model is applied to twoeye observational data from the Beaver Dam Eye Study to examine the association of pigmentary abnormalities and various covariates. ii Acknowledgements I would like to express my deepest gratitude to my advisor, Professor Grace Wahba. She initiated the research described in this dissertation and her dedication to statistics has been a tremendous inspiration to me. During the course of this study we had many fruitful discussions and she provided me numerous insightful suggestions. I shall always appreciate her guidance which led me into the wonderful world of smo...
A Brief Introduction to Neural Networks
"... Arti#cial neural networks are being used with increasing frequency for high dimensional problems of regression or classi#cation. This article provides a tutorial overview of neural networks, focusing on back propagation networks as a method for approximating nonlinear multivariable functions. We ..."
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Cited by 1 (0 self)
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Arti#cial neural networks are being used with increasing frequency for high dimensional problems of regression or classi#cation. This article provides a tutorial overview of neural networks, focusing on back propagation networks as a method for approximating nonlinear multivariable functions. We explain, from a statistician's vantage point, why neural networks might be attractive and how they compare to other modern regression techniques. KEYWORDS: nonparametric regression; function approximation; backpropagation. 1 Introduction Networks that mimic the way the brain works; computer programs that actually LEARN patterns; forecasting without having to know statistics. These are just some of the many claims and attractions of arti#cial neural networks. Neural networks #we will henceforth drop the term arti#cial, unless we need to distinguish them from biological neural networks# seem to be everywhere these days, and at least in their advertising, are able to do all that statistics...