Query: Variable Selection Under Missing Values and Unlabeled Data in Semiconductor Processes

Candidate papers:

abstract: Manufacturing semiconductor wafers involves many sequential processes, and each process has various equipment related variables or factors, which results in high dimensional data. However, measuring the quality of all wafers is time and cost intensive, and only a small proportion of the wafers is labeled. Further, equipment factors are not always measured by sensors due to the complicated process. Variable selection, which is performed to reduce the dimensionality of the input variable space while improving or preserving regression performance by selecting important input factors, plays an important role in regression problems. We propose a variable selection procedure to find the main equipment factors that affect in process wafer quality in consideration of the following issues: 1) imputation for missing values; 2) semi supervised regression for unlabeled data; and 3) redundancy among variables. In the proposed procedure, partial least squares and least absolute shrinkage and selection operator regression are utilized as prediction models. Experiments using two semiconductor equipment datasets were conducted to evaluate the performance of the proposed procedure.
author_names: Kyung-jun Kim

Kyu-Jin Kim

Chi-Hyuck Jun

Il-Gyo Chong

Geun-Young Song
title: Variable Selection Under Missing Values and Unlabeled Data in Semiconductor Processes
venue: IEEE Transactions on Semiconductor Manufacturing
year: 2019

abstract: SUMMARY VarSelLCM allows a full model selection (detection of the relevant features for clustering and selection of the number of clusters) in model based clustering, according to classical information criteria. Data to be analyzed can be composed of continuous, integer and/or categorical features. Moreover, missing values are managed, without any pre processing, by the model used to cluster with the assumption that values are missing completely at random. Thus, VarSelLCM also allows data imputation by using mixture models. A Shiny application is implemented to easily interpret the clustering results. AVAILABILITY AND IMPLEMENTATION VarSelLCM is available to download at https:/CRAN.R project.org/package=VarSelLCM/ TUTORIAL vignette is available online at http:/varsellcm.r forge.r project.org/ SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
author_names: Matthieu Marbac

Mohammed Sedki
title: VarSelLCM: an R/C+ package for variable selection in model based clustering of mixed data with missing values
venue: Bioinform.
year: 2019

abstract: Abstract Longitudinal data with multilevel structures are commonly collected when following up subjects in clusters over a period of time. Missing values and variable selection issues are common for such data. Biased results may be produced if incompleteness of data is ignored in the analysis. On the other hand, incorporating a large number of irrelevant covariates into inferential procedures may lead to difficulty in computation and interpretation. A unified penalized composite likelihood framework is developed to handle data with missingness and variable selection issues. It is flexible to handle the situation where responses and covariates are missing not simultaneously under the assumption of missing not at random. The method is justified both rigorously with theoretical results and numerically with simulation studies. The method is also applied to the Waterloo Smoking Prevention Project data.
author_names: Haocheng Li

Di Shu

Wenqing He

Grace Y Yi
title: Variable selection via the composite likelihood method for multilevel longitudinal data with missing responses and covariates
venue: Comput. Stat. Data Anal.
year: 2019

abstract: We consider the problem of model based clustering in the presence of many correlated, mixed continuous, and discrete variables, some of which may have missing values. Discrete variables are treated with a latent continuous variable approach, and the Dirichlet process is used to construct a mixture model with an unknown number of components. Variable selection is also performed to identify the variables that are most influential for determining cluster membership. The work is motivated by the need to cluster patients thought to potentially have autism spectrum disorder on the basis of many cognitive and/or behavioral test scores. There are a modest number of patients (486) in the data set along with many (55) test score variables (many of which are discrete valued and/or missing) The goal of the work is to (1) cluster these patients into similar groups to help identify those with similar clinical presentation and (2) identify a sparse subset of tests that inform the clusters in order to eliminate unnecessary testing. The proposed approach compares very favorably with other methods via simulation of problems of this type. The results of the autism spectrum disorder analysis suggested 3 clusters to be most likely, while only 4 test scores had high >0.5) posterior probability of being informative. This will result in much more efficient and informative testing. The need to cluster observations on the basis of many correlated, continuous/discrete variables with missing values is a common problem in the health sciences as well as in many other disciplines.
author_names: Curtis B Storlie

Scott M Myers

Slavica K Katusic

Amy L Weaver

Robert G Voigt

Paul E Croarkin

Ruth E Stoeckel

J David Port
title: Clustering and variable selection in the presence of mixed variable types and missing data.
venue: Statistics in medicine
year: 2018

abstract: Abstract Semiconductor wafers are fabricated through sequential process steps. Some process steps have a strong relationship with wafer yield, and these are called critical process steps. Because wafer yield is a key performance index in wafer fabrication, the critical process steps should be carefully selected and managed. This paper proposes a systematic and data driven approach for identifying the critical process steps. The proposed method considers troublesome properties of the data from the process steps such as imbalanced data, missing values, and random sampling. As a case study, we analyzed hypothetical operational data and confirmed that the proposed method works well.
author_names: Dong-Hee Lee

Jin Kyung Yang

Cho Heui Lee

Kwang-Jae Kim
title: A data driven approach to selection of critical process steps in the semiconductor manufacturing process considering missing and imbalanced data
venue: Journal of Manufacturing Systems
year: 2019

abstract: The regularization approach for variable selection was well developed for a completely observed data set in the past two decades. In the presence of missing values, this approach needs to be tailored to different missing data mechanisms. In this paper, we focus on a flexible and generally applicable missing data mechanism, which contains both ignorable and nonignorable missing data mechanism assumptions. We show how the regularization approach for variable selection can be adapted to the situation under this missing data mechanism. The computational and theoretical properties for variable selection consistency are established. The proposed method is further illustrated by comprehensive simulation studies and real data analyses, for both low and high dimensional settings.
author_names: Jiwei Zhao

Yongxiang Yang

Yang Ning
title: Penalized pairwise pseudo likelihood for variable selection with nonignorable missing data
year: 2017

abstract: Introduction In many studies, covariates are not always fully observed because of missing data process. Usually, subjects with missing data are excluded from the analysis but the number of covariates can be greater than the size of the sample when the number of removed subjects is high. Subjective selection or imputation procedures are used but this leads to biased or powerless models. The aim of our study was to develop a method based on the selection of the nearest covariate to the centroid of a homogeneous cluster of covariates. We applied this method to a forensic medicine data set to estimate the age of aborted fetuses. Analysis Methods We measured 46 biometric covariates on 50 aborted fetuses. But the covariates were complete for only 18 fetuses. First, to obtain homogeneous clusters of covariates we used a hierarchical cluster analysis. Second, for each obtained cluster we selected the nearest covariate to the centroid of the cluster, maximizing the sum of correlations (the centroid criterion) Third, with the covariate selected this way, the sample size was sufficient to compute a classical linear regression model. We have shown the almost sure convergence of the centroid criterion and simulations were performed to build its empirical distribution. We compared our method to a subjective deletion method, two simple imputation methods and to the multiple imputation method. Results The hierarchical cluster analysis built 2 clusters of covariates and 6 remaining covariates. After the selection of the nearest covariate to the centroid of each cluster, we computed a stepwise linear regression model. The model was adequate (R2=90.02% and the cross validation showed low prediction errors (2.23 10 3) The empirical distribution of the criterion provided empirical mean (31.91) and median (32.07) close to the theoretical value (32.03) The comparisons showed that deletion and simple imputation methods provided models of inferior quality than the multiple imputation method and the centroid method. Conclusion When the number of continuous covariates is greater than the sample size because of missing process, the usual procedures are biased. Our selection procedure based on the centroid criterion is a valid alternative to compose a set of predictors.
author_names: Jean Gaudart

Pascal Adalian

Georges Leonetti
title: Predictive model in the presence of missing data: the centroid criterion for variable selection
year: 2018

abstract: Abstract Motivation Recent advances in high dimensional phenotyping bring time as an extra dimension into the phenotypes. This promotes the quantitative trait locus (QTL) studies of function valued traits such as those related to growth and development. Existing approaches for analyzing functional traits utilize either parametric methods or semi parametric approaches based on splines and wavelets. However, very limited choices of software tools are currently available for practical implementation of functional QTL mapping and variable selection. Results We propose a Bayesian Gaussian process (GP) approach for functional QTL mapping. We use GPs to model the continuously varying coefficients which describe how the effects of molecular markers on the quantitative trait are changing over time. We use an efficient gradient based algorithm to estimate the tuning parameters of GPs. Notably, the GP approach is directly applicable to the incomplete datasets having even larger than 50% missing data rate (among phenotypes) We further develop a stepwise algorithm to search through the model space in terms of genetic variants, and use a minimal increase of Bayesian posterior probability as a stopping rule to focus on only a small set of putative QTL. We also discuss the connection between GP and penalized B splines and wavelets. On two simulated and three real datasets, our GP approach demonstrates great flexibility for modeling different types of phenotypic trajectories with low computational cost. The proposed model selection approach finds the most likely QTL reliably in tested datasets. Availability and implementation Software and simulated data are available as a MATLAB package 'GPQTLmapping' and they can be downloaded from GitHub (https:/github.com/jpvanhat/GPQTLmapping) Real datasets used in case studies are publicly available at QTL Archive. Supplementary information Supplementary data are available at Bioinformatics online.
author_names: Jarno Vanhatalo

Zitong Li

Mikko J Sillanpaa
title: A Gaussian process model and Bayesian variable selection for mapping function valued quantitative traits with incomplete phenotypic data
venue: Bioinform.
year: 2019

abstract: The selection of variables with high dimensional and missing data is a major challenge and very few methods are available to solve this problem. Here we propose a new method adaptive Bayesian SLOPE which is an extension of the SLOPE method of sorted $l_1$ regularization within a Bayesian framework and which allows to simultaneously estimate the parameters and select variables for large data despite missing values. The method follows the idea of the Spike and Slab LASSO, but replaces the Laplace mixture prior with the frequentist motivated "SLOPE" prior, which targets control of the False Discovery Rate. The regression parameters and the noise variance are estimated using stochastic approximation EM algorithm, which allows to incorporate missing values as well as latent model parameters, like the signal magnitude and its sparsity. Extensive simulations highlight the good behavior in terms of power, FDR and estimation bias under a wide range of simulation scenarios. Finally, we consider an application of severely traumatized patients from Paris hospitals to predict the level of platelet, and demonstrate, beyond the advantage of selecting relevant variables, which is crucial for interpretation, excellent predictive capabilities. The methodology is implemented in the R package ABSLOPE, which incorporates C+ code to improve the efficiency of the proposed method.
author_names: Wei Jiang

Malgorzata Bogdan

Julie Josse

Blazej Miasojedow

Veronika Rockova

Traumabase Group
title: Adaptive Bayesian SLOPE High dimensional Model Selection with Missing Values
year: 2019

abstract: Longitudinal data are common in various sectors where repeated measurements on a dependent variable are collected for all subjects. Missing data pattern are caused when most planned measurements are unavailable for some subjects. The dropout process may cause three missing values mechanism, namely: Missing Completely at Random (MCAR) Missing at Random (MAR) and Missing Not at Random (MNAR) The missing values have influence on quantitative study that can be serious, leading to biased estimates of parameters, information loss, reduced statistical power, increased standard errors, and weakened generalization of findings. This thesis compared the performance of seven (7) techniques of imputing missing values under the assumptions of MCAR and MAR mechanisms. The study adopted the little's test to check whether a dataset with missing values is MCAR or MAR. The techniques for solving missing values problems were compared using the Generalized Estimating Equation (GEE) model for the complete dataset, the coefficient of determination and root mean squared error (RMSE) The study discovered that when large (above 10% or small (below 10% values are missing at random (MAR) it is important to use multiple imputation or expectation maximization to replace missing values in the dataset. The pairwise deletion is the best under MCAR mechanism. Listwise deletion and the hot deck imputation methods performed poorly under the MCAR mechanism. It is recommended that researchers should understand the patterns of missing values in dataset and clearly recognize missing data problems and the situations under which they occurred. However, further research is needed to find a better method for imputing missing not at random (MNAR) with multiple imputation. This thesis focused on missing values in a longitudinal dataset. However, future research using categorical data is a step in right the direction. iii University of Ghana http:/ugspace.ug.edu.gh
author_names: Lotsi Anani

Louis Asiedu

Johnson Katsekpor
title: Comparison of Imputation Methods for Missing Values in Longitudinal Data Under Missing Completely at Random (mcar) mechanism
year: 2017