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Articles 1 - 17 of 17
Full-Text Articles in Entire DC Network
Nonparametric Copula Density Estimation In Sensor Networks, Leming Qu, Hao Chen, Yicheng Tu
Nonparametric Copula Density Estimation In Sensor Networks, Leming Qu, Hao Chen, Yicheng Tu
Leming Qu
Statistical and machine learning is a fundamental task in sensor networks. Real world data almost always exhibit dependence among different features. Copulas are full measures of statistical dependence among random variables. Estimating the underlying copula density function from distributed data is an important aspect of statistical learning in sensor networks. With limited communication capacities or privacy concerns, centralization of the data is often impossible. By only collecting the ranks of the data observed by different sensors, we estimate and evaluate the copula density on an equally spaced grid after binning the standardized ranks at the fusion center. Without assuming any …
Nonparametric Copula Density Estimation In Sensor Networks, Leming Qu, Hao Chen, Yicheng Tu
Nonparametric Copula Density Estimation In Sensor Networks, Leming Qu, Hao Chen, Yicheng Tu
Leming Qu
Statistical and machine learning is a fundamental task in sensor networks. Real world data almost always exhibit dependence among different features. Copulas are full measures of statistical dependence among random variables. Estimating the underlying copula density function from distributed data is an important aspect of statistical learning in sensor networks. With limited communication capacities or privacy concerns, centralization of the data is often impossible. By only collecting the ranks of the data observed by different sensors, we estimate and evaluate the copula density on an equally spaced grid after binning the standardized ranks at the fusion center. Without assuming any …
Nonparametric Copula Density Estimation In Sensor Networks, Leming Qu, Hao Chen, Yicheng Tu
Nonparametric Copula Density Estimation In Sensor Networks, Leming Qu, Hao Chen, Yicheng Tu
Leming Qu
Statistical and machine learning is a fundamental task in sensor networks. Real world data almost always exhibit dependence among different features. Copulas are full measures of statistical dependence among random variables. Estimating the underlying copula density function from distributed data is an important aspect of statistical learning in sensor networks. With limited communication capacities or privacy concerns, centralization of the data is often impossible. By only collecting the ranks of the data observed by different sensors, we estimate and evaluate the copula density on an equally spaced grid after binning the standardized ranks at the fusion center. Without assuming any …
Wavelet Thresholding In Partially Linear Models: A Computation And Simulation, Leming Qu
Wavelet Thresholding In Partially Linear Models: A Computation And Simulation, Leming Qu
Leming Qu
Partially linear models have a linear part as in the linear regression and a non-linear part similar to that in the non-parametric regression. The estimates in Partially Linear Models have been studied previously using traditional smoothing methods such as smoothing spline, kernel and piecewise polynomial smoothers. In this paper, a wavelet thresholding method for estimating the corresponding parameters in Partially Linear Models is presented. Extensive simulation results shows that wavelet smoothing approach is comparable to traditional smoothing methods when their assumptions are satisfied. But wavelet smoothing is often superior when assumptions about the smoothness of the underlying function of non-parametric …
Change Point Estimation Of Bilevel Functions, Leming Qu, Yi-Cheng Tu
Change Point Estimation Of Bilevel Functions, Leming Qu, Yi-Cheng Tu
Leming Qu
Reconstruction of a bilevel function such as a bar code signal in a partially blind deconvolution problem is an important task in industrial processes. Existing methods are based on either the local approach or the regularization approach with a total variation penalty. This article reformulated the problem explicitly in terms of change points of the 0-1 step function. The bilevel function is then reconstructed by solving the nonlinear least squares problem subject to linear inequality constraints, with starting values provided by the local extremas of the derivative of the convolved signal from discrete noisy data. Simulation results show a considerable …
Inversion For Non-Smooth Models With Physical Bounds, Partha S. Routh, Leming Qu, Mrinal K. Sen, Phil D. Anno
Inversion For Non-Smooth Models With Physical Bounds, Partha S. Routh, Leming Qu, Mrinal K. Sen, Phil D. Anno
Leming Qu
Geological processes produce structures at multiple scales. A discontinuity in the subsurface can occur due to layering, tectonic activities such as faulting, folding and fractures. Traditional approaches to invert geophysical data employ smoothness constraints. Such methods produce smooth models and thefore sharp contrasts in the medium such as lithological boundaries are not easily discernible. The methods that are able to produce non-smooth models, can help interpret the geological discontinuity. In this paper we examine various approaches to obtain non-smooth models from a finite set of noisy data. Broadly they can be categorized into approaches: (1) imposing non-smooth regularization in the …
Rayleigh Wave Dispersion Curve Inversion: Occam Versus The L1-Norm, Matthew M. Haney, Leming Qu
Rayleigh Wave Dispersion Curve Inversion: Occam Versus The L1-Norm, Matthew M. Haney, Leming Qu
Leming Qu
We compare inversions of Rayleigh wave dispersion curves for shear wave velocity depth profiles based on the L2-norm (Occam's Inversion) and L1-norm (TV Regularization). We forward model Rayleigh waves using a finite-element method instead of the conventional technique based on a recursion formula and root-finding. The forward modeling naturally leads to an inverse problem that is overparameterized in depth. Solving the inverse problem with Occam's Inversion gives the smoothest subsurface model that satisfies the data. However, the subsurface need not be smooth and we therefore also solve the inverse problem with TV Regularization, a procedure that does not penalize discontinuities. …
Bayesian Wavelet Estimation Of Long Memory Parameter, Leming Qu
Bayesian Wavelet Estimation Of Long Memory Parameter, Leming Qu
Leming Qu
A Bayesian wavelet estimation method for estimating parameters of a stationary I(d) process is represented as an useful alternative to the existing frequentist wavelet estimation methods. The effectiveness of the proposed method is demonstrated through Monte Carlo simulations. The sampling from the posterior distribution is through the Markov Chain Monte Carlo (MCMC) easily implemented in the WinBUGS software package.
Copula Density Estimation By Total Variation Penalized Likelihood With Linear Equality Constraints, Leming Qu, Wotao Yin
Copula Density Estimation By Total Variation Penalized Likelihood With Linear Equality Constraints, Leming Qu, Wotao Yin
Leming Qu
A copula density is the joint probability density function (PDF) of a random vector with uniform marginals. An approach to bivariate copula density estimation is introduced that is based on a maximum penalized likelihood estimation (MPLE) with a total variation (TV) penalty term. The marginal unity and symmetry constraints for copula density are enforced by linear equality constraints. The TV-MPLE subject to linear equality constraints is solved by an augmented Lagrangian and operator-splitting algorithm. It offers an order of magnitude improvement in computational efficiency over another TV-MPLE method without constraints solved by log-barrier method for second order cone program. A …
Wavelet Image Restoration And Regularization Parameters Selection, Leming Qu
Wavelet Image Restoration And Regularization Parameters Selection, Leming Qu
Leming Qu
For the restoration of an image based on its noisy distorted observations, we propose wavelet domain restoration by scale-dependent ∫1 penalized regularization method (WaveRSL1). The data adaptive choice of the regularization parameters is based on the Akaike Information Criterion (AIC) and the degrees of freedom (df) is estimated by the number of nonzero elements in the solution. Experiments on some commonly used testing images illustrate that the proposed method possesses good empirical properties.
Wavelet Reconstruction Of Nonuniformly Sampled Signals, Leming Qu, Partha S. Routh, Phil D. Anno
Wavelet Reconstruction Of Nonuniformly Sampled Signals, Leming Qu, Partha S. Routh, Phil D. Anno
Leming Qu
For the reconstruction of a nonuniformly sampled signal based on its noisy observations, we propose a level dependent l1 penalized wavelet reconstruction method. The LARS/Lasso algorithm is applied to solve the Lasso problem. The data adaptive choice of the regularization parameters is based on the AIC and the degrees of freedom is estimated by the number of nonzero elements in the Lasso solution. Simulation results conducted on some commonly used 1_D test signals illustrate that the proposed method possesses good empirical properties.
Wavelet Deconvolution In A Periodic Setting Using Cross-Validation, Leming Qu, Partha S. Routh, Kyungduk Ko
Wavelet Deconvolution In A Periodic Setting Using Cross-Validation, Leming Qu, Partha S. Routh, Kyungduk Ko
Leming Qu
The wavelet deconvolution method WaveD using band-limited wavelets offers both theoretical and computational advantages over traditional compactly supported wavelets. The translation-invariant WaveD with a fast algorithm improves further. The twofold cross-validation method for choosing the threshold parameter and the finest resolution level in WaveD is introduced. The algorithm’s performance is compared with the fixed constant tuning and the default tuning in WaveD.
Wavelet-Based Bayesian Estimation Of Partially Linear Regression Models With Long Memory Errors, Kyungduk Ko, Leming Qu, Marina Vannucci
Wavelet-Based Bayesian Estimation Of Partially Linear Regression Models With Long Memory Errors, Kyungduk Ko, Leming Qu, Marina Vannucci
Leming Qu
In this paper we focus on partially linear regression models with long memory errors, and propose a wavelet-based Bayesian procedure that allows the simultaneous estimation of the model parameters and the nonparametric part of the model. Employing discrete wavelet transforms is crucial in order to simplify the dense variance-covariance matrix of the long memory error. We achieve a fully Bayesian inference by adopting a Metropolis algorithm within a Gibbs sampler. We evaluate the performances of the proposed method on simulated data. In addition, we present an application to Northern hemisphere temperature data, a benchmark in the long memory literature.
On Semiparametric Regression Via Wavelets, Leming Qu
On Semiparametric Regression Via Wavelets, Leming Qu
Leming Qu
Semiparametric regression models have a linear part as in the linear regression and a nonlinear part similar to that in the nonparametric regression. The estimates in semiparametric regression models have been studied previously in traditional smoothing methods such as smoothing spline, kernel and piecewise polynomial smoothers. In this thesis, we apply the regularized wavelet estimators by penalizing the l1 norm of the wavelet coefficients of the nonparametric function. The regularization parameter is chosen by universal threshold or cross-validation. When there is only one explanatory variable in the linear part, we directly solve the linear coefficient. When the linear part has …
Copula Density Estimation By Total Variation Penalized Likelihood, Leming Qu, Yi Qian, Hui Xie
Copula Density Estimation By Total Variation Penalized Likelihood, Leming Qu, Yi Qian, Hui Xie
Leming Qu
Copulas are full measures of dependence among random variables. They are increasingly popular among academics and practitioners in financial econometrics for modeling comovements between markets, risk factors, and other relevant variables. A copula's hidden dependence structure that couples a joint distribution with its marginals makes a parametric copula non-trivial. An approach to bivariate copula density estimation is introduced that is based on a penalized likelihood with a total variation penalty term. Adaptive choice of the amount of regularization is based on approximate Bayesian Information Criterion (BIC) type scores. Performance are evaluated through the Monte Carlo simulation.
Bayesian Wavelet Estimation Of Partially Linear Models, Leming Qu
Bayesian Wavelet Estimation Of Partially Linear Models, Leming Qu
Leming Qu
A Bayesian wavelet approach is presented for estimating a partially linear model (PLM). A PLM consists of a linear part and a nonparametric component. The nonparametric component is represented with a wavelet series where the wavelet coefficients have assumed prior distributions. The prior for each coefficient consists of a mixture of a normal distribution and a point mass at 0. The linear parameters are assumed to have a normal prior. The hyperparameters are estimated by the marginal maximum likelihood estimator using the direct maximization. The model selection and model averaging methods give different estimates of the model parameters. MCMC computation …
Wavelet Estimation Of Partially Linear Models, Xiao-Wen Chang, Leming Qu
Wavelet Estimation Of Partially Linear Models, Xiao-Wen Chang, Leming Qu
Leming Qu
A wavelet approach is presented for estimating a partially linear model (PLM). We find an estimator of the PLM by minimizing the square of the l2 norm of the residual vector while penalizing the l1 norm of the wavelet coefficients of the nonparametric component. This approach, an extension of the wavelet approach for nonparametric regression problems, avoids the restrictive smoothness requirements for the nonparametric function of the traditional smoothing approaches for PLM, such as smoothing spline, kernel and piecewise polynomial methods. To solve the optimization problem, an efficient descent algorithm with an exact line search is presented. Simulation …