Xinwei Deng

Sparse linear discriminant analysis by thresholding for high dimensional data

In many social, economical, biological and medical studies, one objective is to classify a subject into one of several classes based on a set of variables observed from the subject. Because the probability distribution of the variables is usually unknown, the rule of classification is constructed using a training sample. The well-known linear discriminant analysis (LDA) works well for the situation where the number of variables used for classification is much smaller than the training sample size. Because of the advance in technologies, modern statistical studies often face classification problems with the number of variables much larger than the sample size, and the LDA may perform poorly. We explore when and why the LDA has poor performance and propose a sparse LDA that is asymptotically optimal under some sparsity conditions on the unknown parameters. For illustration of application, we discuss an example of classifying human cancer into two classes of leukemia based on a set of 7,129 genes and a training sample of size 72. A simulation is also conducted to check the performance of the proposed method.

Statistical approach to quantifying the elastic deformation of nanomaterials

Quantifying the mechanical properties of nanomaterials is challenged by its small size, difficulty of manipulation, lack of reliable measurement techniques, and grossly varying measurement conditions and environment. A recently proposed approach is to estimate the elastic modulus from a force-deflection physical model based on the continuous bridged-deformation of a nanobelt/nanowire using an atomic force microscope tip under different contact forces. However, the nanobelt may have some initial bending, surface roughness and imperfect physical boundary conditions during measurement, leading to large systematic errors and uncertainty in data quantification. In this article, a statistical modeling technique, sequential profile adjustment by regression (SPAR), is proposed to account for and eliminate the various experimental errors and artifacts. SPAR can automatically detect and remove the systematic errors and therefore gives more precise estimation of the elastic modulus. This research presents an innovative approach that can potentially have a broad impact in quantitative nanomechanics and nanoelectronics.

Active Learning Through Sequential Design, With Applications to Detection of Money Laundering

Money laundering is a process designed to conceal the true origin of funds that were originally derived from illegal activities. Because money laundering often involves criminal activities, financial institutions have the responsibility to detect and report it to the appropriate government agencies in a timely manner. But the huge number of transactions occurring each day make detecting money laundering difficult. The usual approach adopted by financial institutions is to extract some summary statistics from the transaction history and conduct a thorough and time-consuming investigation on those suspicious accounts. In this article we propose an active learning through sequential design method for prioritization to improve the process of money laundering detection. The method uses a combination of stochastic approximation and D-optimal designs to judiciously select the accounts for investigation. The sequential nature of the method helps identify the optimal prioritization criterion with minimal time and effort. A case study with real banking data demonstrates the performance of the proposed method. A simulation study shows the method’s efficiency and accuracy, as well as its robustness to model assumptions.

Penalized Covariance Matrix Estimation Using a Matrix-Logarithm Transformation

For statistical inferences that involve covariance matrices, it is desirable to obtain an accurate covariance matrix estimate with a well-structured eigen-system. We propose to estimate the covariance matrix through its matrix logarithm based on an approximate log-likelihood function. We develop a generalization of the Leonard and Hsu log-likelihood approximation that no longer requires a nonsingular sample covariance matrix. The matrix log-transformation provides the ability to impose a convex penalty on the transformed likelihood such that the largest and smallest eigenvalues of the covariance matrix estimate can be regularized simultaneously. The proposed method transforms the problem of estimating the covariance matrix into the problem of estimating a symmetric matrix, which can be solved efficiently by an iterative quadratic programming algorithm. The merits of the proposed method are illustrated by a simulation study and two real applications in classification and portfolio optimization. Supplementary materials for this article are available online.

QQ Models: Joint Modeling for Quantitative and Qualitative Quality Responses in Manufacturing Systems

A manufacturing system with both quantitative and qualitative (QQ) quality responses (as a QQ system) is widely encountered in many cases. For example, in a lapping process of the semiconductor manufacturing, the quality of wafer’s geometrical characteristics is often measured by the total thickness variation as a quantitative response and the conformity of site total indicator reading as a binary qualitative response. The QQ responses are closely associated with each other in a QQ system, but current methodologies often model the two types of quality responses separately. This article presents a novel modeling approach, called “QQ models,” to jointly model the QQ responses through a constrained likelihood estimation. The QQ models can jointly select significant predictors by incorporating inherent features of QQ systems, leading to accurate variable selection and prediction. Both simulation studies and a case study in a lapping process are used to evaluate the performance of the proposed method. Supplementary materials to this article are available online.

Ensemble modeling for data fusion in manufacturing process scale-up

In modern manufacturing process scale-up, design of experiments is widely used to identify optimal process settings, followed by production runs to validate these process settings. Both experimental data and observational data are collected in the manufacturing process. However, current methodologies often use a single type of data to model the process. This work presents an innovative method to efficiently model a manufacturing process by integrating the two types of data. An ensemble modeling strategy is proposed that utilizes the constrained likelihood approach, where the constraints incorporate the sequential nature and inherent features of the two types of data. It therefore achieves better estimation and prediction than conventional methods. Simulations and a case study in wafer manufacturing are provided to illustrate the merits of the proposed method.

Modeling maximum daily temperature using a varying coefficient regression model

Relationships between stream water and air temperatures are often modeled using linear or nonlinear regression methods. Despite a strong relationship between water and air temperatures and a variety of models that are effective for data summarized on a weekly basis, such models did not yield consistently good predictions for summaries such as daily maximum temperature. A good predictive model for daily maximum temperature is required because daily maximum temperature is an important measure for predicting survival of temperature sensitive fish. To appropriately model the strong relationship between water and air temperatures at a daily time step, it is important to incorporate information related to the time of the year into the modeling. In this work, a time-varying coefficient model is used to study the relationship between air temperature and water temperature. The time-varying coefficient model enables dynamic modeling of the relationship, and can be used to understand how the air-water temperature relationship varies over time. The proposed model is applied to 10 streams in Maryland, West Virginia, Virginia, North Carolina, and Georgia using daily maximum temperatures. It provides a better fit and better predictions than those produced by a simple linear regression model or a nonlinear logistic model.

Constrained hierarchical modeling of degradation data in tissue-engineered scaffold fabrication

ABSTRACT In tissue-engineered scaffold fabrication, the degradation of scaffolds is a critical issue because it needs to match with the rate of new tissue formation in the human body. However, scaffold degradation is a very complicated process, making degradation regulation a challenging task. To provide a scientific understanding on the degradation of scaffolds, we propose a novel constrained hierarchical model (CHM) for the degradation data. The proposed model has two levels, with the first level characterizing scaffold degradation profiles and the second level characterizing the effect of process parameters on the degradation. Moreover, it can incorporate expert knowledge in the modeling through meaningful constraints, leading to insightful inference on scaffold degradation. Bayesian methods are used for parameter estimation and model comparison. In the case study, the proposed method is illustrated and compared with existing methods using data from a novel tissue-engineered scaffold fabrication process. A numerical study is conducted to examine the effect of sample size on model estimation.

Logistic regression for crystal growth process modeling through hierarchical nonnegative garrote-based variable selection

ABSTRACT Single-crystal silicon ingots are produced from a complex crystal growth process. Such a process is sensitive to subtle process condition changes, which may easily become failed and lead to the growth of a polycrystalline ingot instead of the desired monocrystalline ingot. Therefore, it is important to model this polycrystalline defect in the crystal growth process and identify key process variables and their features. However, to model the crystal growth process poses great challenges due to complicated engineering mechanisms and a large amount of functional process variables. In this article, we focus on modeling the relationship between a binary quality indicator for polycrystalline defect and functional process variables. We propose a logistic regression model with hierarchical nonnegative garrote-based variable selection method that can accurately estimate the model, identify key process variables, and capture important features. Simulations and a case study are conducted to illustrate the merits of the proposed method in prediction and variable selection.

Additive Gaussian Process for Computer Models With Qualitative and Quantitative Factors

ABSTRACT Computer experiments with qualitative and quantitative factors occur frequently in various applications in science and engineering. Analysis of such experiments is not yet completely resolved. In this work, we propose an additive Gaussian process model for computer experiments with qualitative and quantitative factors. The proposed method considers an additive correlation structure for qualitative factors, and assumes that the correlation function for each qualitative factor and the correlation function of quantitative factors are multiplicative. It inherits the flexibility of unrestrictive correlation structure for qualitative factors by using the hypersphere decomposition, embracing more flexibility in modeling the complex systems of computer experiments. The merits of the proposed method are illustrated by several numerical examples and a real data application. Supplementary materials for this article are available online.