Showing papers in "Technometrics in 2018"
TL;DR: In this paper, a systematic study of how ordering affects the accuracy of Vecchia's approximation of Gaussian process parameters is presented, showing that random orderings can give dramatically sharper approximations than default coordinate-based orderings.
Abstract: Vecchia’s approximate likelihood for Gaussian process parameters depends on how the observations are ordered, which has been cited as a deficiency. This article takes the alternative standpoint that the ordering can be tuned to sharpen the approximations. Indeed, the first part of the article includes a systematic study of how ordering affects the accuracy of Vecchia’s approximation. We demonstrate the surprising result that random orderings can give dramatically sharper approximations than default coordinate-based orderings. Additional ordering schemes are described and analyzed numerically, including orderings capable of improving on random orderings. The second contribution of this article is a new automatic method for grouping calculations of components of the approximation. The grouping methods simultaneously improve approximation accuracy and reduce computational burden. In common settings, reordering combined with grouping reduces Kullback–Leibler divergence from the target model by more th...
95 citations
TL;DR: S spatio-temporal smooth sparse decomposition (ST-SSD) is introduced, which serves as a dimension reduction and denoising technique by decomposing the original tensor into the functional mean, sparse anomalies, and random noises.
Abstract: High-dimensional data monitoring and diagnosis has recently attracted increasing attention among researchers as well as practitioners. However, existing process monitoring methods fail to fully use...
79 citations
TL;DR: The first method to detect deviating data cells in a multivariate sample which takes the correlations between the variables into account is proposed, which has no restriction on the number of clean rows, and can deal with high dimensions.
Abstract: A multivariate dataset consists of n cases in d dimensions, and is often stored in an n by d data matrix. It is well-known that real data may contain outliers. Depending on the situation, outliers ...
71 citations
TL;DR: This work introduces fast alternating direction method of multipliers (ADMM) algorithms for computing the sparse penalized quantile regression and demonstrates the competitive performance of this algorithm: it significantly outperforms several other fast solvers for high-dimensional penalizedquantile regression.
Abstract: Sparse penalized quantile regression is a useful tool for variable selection, robust estimation and heteroscedasticity detection in high-dimensional data analysis. The computational issue of the sparse penalized quantile regression has not yet been fully resolved in the literature, due to non-smoothness of the quantile regression loss function. We introduce fast alternating direction method of multipliers (ADMM) algorithms for computing the sparse penalized quantile regression. The convergence properties of the proposed algorithms are established. Numerical examples demonstrate the competitive performance of our algorithm: it significantly outperforms several other fast solvers for high-dimensional penalized quantile regression. Supplementary materials for this article are available online.
71 citations
TL;DR: This work proposes an extension of the adaptive lasso named the Tukey-lasso, implemented with the APG algorithm, which is resistant to outliers in both the response and covariates and enjoys the oracle property.
Abstract: The adaptive lasso is a method for performing simultaneous parameter estimation and variable selection. The adaptive weights used in its penalty term mean that the adaptive lasso achieves the oracle property. In this work, we propose an extension of the adaptive lasso named the Tukey-lasso. By using Tukey's biweight criterion, instead of squared loss, the Tukey-lasso is resistant to outliers in both the response and covariates. Importantly, we demonstrate that the Tukey-lasso also enjoys the oracle property. A fast accelerated proximal gradient (APG) algorithm is proposed and implemented for computing the Tukey-lasso. Our extensive simulations show that the Tukey-lasso, implemented with the APG algorithm, achieves very reliable results, including for high-dimensional data where p > n. In the presence of outliers, the Tukey-lasso is shown to offer substantial improvements in performance compared to the adaptive lasso and other robust implementations of the lasso. Real-data examples further demonstr...
55 citations
TL;DR: In this paper, the authors propose a spatial process model for analyzing geostatistical data, which involves computations that become prohibitive as the number of spatial locations becomes large.
Abstract: Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations becomes large. There is a burgeoning literature on approaches...
51 citations
TL;DR: The Wiener process is used to model product degradation, and the group-specific random environments are captured using a stochastic time scale and both semiparametric and parametric estimation procedures are developed for the model.
Abstract: Degradation studies are often used to assess reliability of products subject to degradation-induced soft failures. Because of limited test resources, several test subjects may have to share a test rig and have their degradation measured by the same operator. The common environments experienced by subjects in the same group introduce significant interindividual correlations in their degradation, which is known as the block effect. In the present article, the Wiener process is used to model product degradation, and the group-specific random environments are captured using a stochastic time scale. Both semiparametric and parametric estimation procedures are developed for the model. Maximum likelihood estimations of the model parameters for both the semiparametric and parametric models are obtained with the help of the EM algorithm. Performance of the maximum likelihood estimators is validated through large sample asymptotics and small sample simulations. The proposed models are illustrated by an appl...
49 citations
TL;DR: This research proposes a class of basis functions extracted from thin-plate splines that are ordered in terms of their degrees of smoothness with higher-order functions corresponding to larger-scale features and lower-order ones corresponding to smaller-scale details, leading to a parsimonious representation of a (nonstationary) spatial covariance function.
Abstract: The spatial random effects model is flexible in modeling spatial covariance functions and is computationally efficient for spatial prediction via fixed rank kriging (FRK). However, the model depend...
46 citations
TL;DR: In this article, the authors focus on industrial environments, where large amounts of data are potentially available and the advance of sensor and information technologies is leading to data-rich industrial environments.
Abstract: The advance of sensor and information technologies is leading to data-rich industrial environments, where large amounts of data are potentially available. This study focuses on industrial a...
38 citations
TL;DR: An adaptive Bayesian methodology is presented that effectively combines in-plane deviation data and models for a small sample of previously manufactured, disparate shapes to aid in the model specification of in-planes deviation for a broad class of new shapes.
Abstract: Quality control of geometric shape deviation in additive manufacturing relies on statistical deviation models. However, resource constraints limit the manufacture of test shapes, and consequently i...
37 citations
TL;DR: A nonparametric adaptive sampling strategy to online monitor nonnormal big data streams in the context of limited resources, where only a subset of observations are available at each acquisition time is proposed.
Abstract: With the rapid advancement of sensor technology, a huge amount of data is generated in various applications, which poses new and unique challenges for statistical process control (SPC). In this art...
TL;DR: An alternative view on modeling CM signals is proposed, based on treating each CM signal as an individual task, which can account for heterogeneity in the data and automatically infer the commonalities between the new testing observations and CM signals in the historical dataset.
Abstract: Condition monitoring (CM) signals play a critical role in assessing the remaining useful life of in-service components. In this article, an alternative view on modeling CM signals is proposed. This...
TL;DR: This article proposes a Phase I control chart for monitoring products from 3D printing that addresses all the challenges of quality control and shows that it works well in practice.
Abstract: In recent years, 3D printing gets more and more popular in manufacturing industries. Quality control of 3D printing products thus becomes an important research problem. However, this problem is cha...
Journal Article•
TL;DR: ADMM for High-Dimensional Sparse Penalized Quantile Regression (ADMM-QR) as mentioned in this paper is a high-dimensional sparse penalized quantile regression method.
Abstract: Supplemental material for "ADMM for High-Dimensional Sparse Penalized Quantile Regression."..
TL;DR: In this article, a supervised learning-based approach for monitoring and diagnosing texture-related defects in manufactured products characterized by stochastic textured surfaces that satisfy the local conditions is presented.
Abstract: We develop a supervised-learning-based approach for monitoring and diagnosing texture-related defects in manufactured products characterized by stochastic textured surfaces that satisfy the localit...
TL;DR: A dynamic monitoring procedure is developed after connecting the curve monitoring problem to curve comparison, and under the framework of generalized likelihood ratio testing a new exponentially weighted moving average (EWMA) control chart is suggested that can accommodate unequally spaced design points.
Abstract: Rapid sequential comparison between the longitudinal pattern of a given subject and a target pattern has become increasingly important in modern scientific research for detecting abnormal activitie...
TL;DR: The multivariate Gaussian process model is proposed, which offers a natural way to accommodate both within-profile and between-profile correlations and to mitigate the prohibitively high computation in building such models, a pairwise estimation strategy is adopted.
Abstract: Profile monitoring is often conducted when the product quality is characterized by profiles. Although existing methods almost exclusively deal with univariate profiles, observations of multivariate profile data are increasingly encountered in practice. These data are seldom analyzed in the area of statistical process control due to lack of effective modeling tools. In this article, we propose to analyze them using the multivariate Gaussian process model, which offers a natural way to accommodate both within-profile and between-profile correlations. To mitigate the prohibitively high computation in building such models, a pairwise estimation strategy is adopted. Asymptotic normality of the parameter estimates from this approach has been established. Comprehensive simulation studies are conducted. In the case study, the method has been demonstrated using transmittance profiles from low-emittance glass. Supplementary materials for this article are available online.
TL;DR: In this article, a nonparametric multiple linear expectile regression in a reproducing kernel Hilbert space (KERE) is proposed, which has multiple advantages over the classical multiple linear Expectile regression by incorporating nonlinearity, nonadditivity, and complex interactions in the final estimator.
Abstract: Expectile, first introduced by Newey and Powell in 1987 in the econometrics literature, has recently become increasingly popular in risk management and capital allocation for financial institutions due to its desirable properties such as coherence and elicitability. The current standard tool for expectile regression analysis is the multiple linear expectile regression proposed by Newey and Powell in 1987. The growing applications of expectile regression motivate us to develop a much more flexible nonparametric multiple expectile regression in a reproducing kernel Hilbert space. The resulting estimator is called KERE, which has multiple advantages over the classical multiple linear expectile regression by incorporating nonlinearity, nonadditivity, and complex interactions in the final estimator. The kernel learning theory of KERE is established. We develop an efficient algorithm inspired by majorization-minimization principle for solving the entire solution path of KERE. It is shown that the algori...
TL;DR: This work proposes a sequential Bayesian strategy for planning of ALTs and a Bayesian estimation procedure for updating the parameter estimates sequentially, which is more robust and efficient, as compared to existing non-sequential optimum designs.
Abstract: Most of the recently developed methods on optimum planning for accelerated life tests (ALT) involve “guessing” values of parameters to be estimated, and substituting such guesses in the proposed solution to obtain the final testing plan. In reality, such guesses may be very different from true values of the parameters, leading to inefficient test plans. To address this problem, we propose a sequential Bayesian strategy for planning of ALTs and a Bayesian estimation procedure for updating the parameter estimates sequentially. The proposed approach is motivated by ALT for polymer composite materials, but are generally applicable to a wide range of testing scenarios. Through the proposed sequential Bayesian design, one can efficiently collect data and then make predictions for the field performance. We use extensive simulations to evaluate the properties of the proposed sequential test planning strategy. We compare the proposed method to various traditional non-sequential optimum designs. Our results...
TL;DR: In this paper, a semiparametric model is proposed to describe ADDT data, which not only provides flexible models with few assumptions but also retains the physical meaning of degradation mechanisms (e.g., the degradation path is monotonic).
Abstract: Accelerated destructive degradation tests (ADDT) are widely used in industry to evaluate materials’ long-term properties. Even though there has been tremendous statistical research in nonparametric methods, the current industrial practice is still to use application-specific parametric models to describe ADDT data. The challenge of using a nonparametric approach comes from the need to retain the physical meaning of degradation mechanisms and also perform extrapolation for predictions at the use condition. Motivated by this challenge, we propose a semiparametric model to describe ADDT data. We use monotonic B-splines to model the degradation path, which not only provides flexible models with few assumptions, but also retains the physical meaning of degradation mechanisms (e.g., the degradation path is monotonic). Parametric models, such as the Arrhenius model, are used for modeling the relationship between the degradation and the accelerating variable, allowing for extrapolation to the use conditio...
TL;DR: Experimental investigations suggest that the DPGSM approach can consistently detect incipient, critical changes in intermittent signals some 50–2000 ms ahead of competing methods in benchmark test cases as well as a variety of real-world applications, such as in alternation patterns in a music piece and in the vibration signals capturing the initiation of product defects in an ultraprecision manufacturing process.
Abstract: The ability to detect incipient and critical changes in real world process—esessential for system integrity assurance—is currently impeded by the mismatch between the key assumption of stationarity...
TL;DR: The proposed generalized inferential procedures are extended to construct prediction limits for a single future measurement and for at least p of m measurements at each of r locations.
Abstract: This study develops inferential procedures for a gamma distribution. Based on the Cornish–Fisher expansion and pivoting the cumulative distribution function, an approximate confidence interval for ...
TL;DR: Different sequential design approaches are investigated and it is shown that the simple separate design approach has its merit in practical use when designing for functional calibration.
Abstract: The calibration of computer models using physical experimental data has received a compelling interest in the last decade. Recently, multiple works have addressed the functional calibration of computer models, where the calibration parameters are functions of the observable inputs rather than taking a set of fixed values as traditionally treated in the literature. While much of the recent works on functional calibration was focused on estimation, the issue of sequential design for functional calibration still presents itself as an open question. Addressing the sequential design issue is thus the focus of this paper. We investigate different sequential design approaches and show that the simple separate design approach has its merit in practical use when designing for functional calibration. Analysis is carried out on multiple simulated and real world examples.
TL;DR: In this article, the authors explore the behavior of wind speed over time, using a subset of the Eastern Wind Dataset published by the National Renewable Energy Laboratory (NERL).
Abstract: We explore the behavior of wind speed over time, using a subset of the Eastern Wind Dataset published by the National Renewable Energy Laboratory. This dataset gives modeled wind speeds over three ...
TL;DR: This work proposes a novel thresholded multivariate principal component analysis (PCA) method for multichannel profile monitoring that applies the functional PCA to extract a reasonably large number of features under the in-control state and uses the soft-thresholding techniques to further select significant features capturing profile information under the out-of- control state.
Abstract: Monitoring multichannel profiles has important applications in manufacturing systems improvement, but it is nontrivial to develop efficient statistical methods because profiles are high-dim...
TL;DR: A Karhunen–Loève (KL) expansion-based GP model is proposed that satisfies the Dirichlet boundary and initial conditions almost surely, and effectively uses information from analytical approximations to the PDE solution.
Abstract: A partial differential equation (PDE) models a physical quantity as a function of space and time. These models are often solved numerically with the finite element (FE) method and the computer outp...
TL;DR: This article proposes some tests based on ranks of nearest neighbors, which can be conveniently used in high dimension, low sample size situations.
Abstract: Several parametric and nonparametric tests of independence between two random vectors are available in the literature. But, many of them perform poorly for high dimensional data and are not applicable when the dimension exceeds the sample size. In this article, we propose some tests based on ranks of nearest neighbors, which can be conveniently used in high dimension, low sample size situations. Several simulated and real data sets are analyzed to show the utility of the proposed tests. Codes for implementation of the proposed tests are available as supplementary materials.
Journal Article•
TL;DR: In this paper, nonparametric modeling and prediction of condition monitoring signals using multivariate Gaussian convolution processes is presented for condition monitoring signal using multi-dimensional Gaussian Convolution Processes.
Abstract: Supplemental material for Nonparametric Modeling and Prognosis of Condition Monitoring Signals Using Multivariate Gaussian Convolution Processes...
TL;DR: This work proposes a method to incorporate the censoring information when performing model calibration, and the results show significant improvement over the traditional calibration methods, especially when the number of censored observations is large.
Abstract: The purpose of model calibration is to make the model predictions closer to reality. The classical Kennedy-O'Hagan approach is widely used for model calibration, which can account for the inadequacy of the computer model while simultaneously estimating the unknown calibration parameters. In many applications, the phenomenon of censoring occurs when the exact outcome of the physical experiment is not observed, but is only known to fall within a certain region. In such cases, the Kennedy-O'Hagan approach cannot be used directly, and we propose a method to incorporate the censoring information when performing model calibration. The method is applied to study the compression phenomenon of liquid inside a bottle. The results show significant improvement over the traditional calibration methods, especially when the number of censored observations is large.
TL;DR: A unified penalized likelihood approach to effectively estimate nonparametric functional parameters and heterogeneous graphical parameters is proposed and an efficient generalized effective expectation-maximization (EM) algorithm is designed to address three significant challenges: high-dimensionality, nonconvexity, and label switching.
Abstract: Graphical models have been widely used to investigate the complex dependence structure of high-dimensional data, and it is common to assume that observed data follow a homogeneous graphical model. However, observations usually come from different resources and have heterogeneous hidden commonality in real-world applications. Thus, it is of great importance to estimate heterogeneous dependencies and discover a subpopulation with certain commonality across the whole population. In this work, we introduce a novel regularized estimation scheme for learning nonparametric finite mixture of Gaussian graphical models, which extends the methodology and applicability of Gaussian graphical models and mixture models. We propose a unified penalized likelihood approach to effectively estimate nonparametric functional parameters and heterogeneous graphical parameters. We further design an efficient generalized effective expectation-maximization (EM) algorithm to address three significant challenges: high-dimensi...