{"title":"Maximum Likelihood Estimation Over Directed Acyclic Gaussian Graphs.","authors":"Yiping Yuan, Xiaotong Shen, Wei Pan","doi":"10.1002/sam.11168","DOIUrl":"10.1002/sam.11168","url":null,"abstract":"<p><p>Estimation of multiple directed graphs becomes challenging in the presence of inhomogeneous data, where directed acyclic graphs (DAGs) are used to represent causal relations among random variables. To infer causal relations among variables, we estimate multiple DAGs given a known ordering in Gaussian graphical models. In particular, we propose a constrained maximum likelihood method with nonconvex constraints over elements and element-wise differences of adjacency matrices, for identifying the sparseness structure as well as detecting structural changes over adjacency matrices of the graphs. Computationally, we develop an efficient algorithm based on augmented Lagrange multipliers, the difference convex method, and a novel fast algorithm for solving convex relaxation subproblems. Numerical results suggest that the proposed method performs well against its alternatives for simulated and real data.</p>","PeriodicalId":48684,"journal":{"name":"Statistical Analysis and Data Mining","volume":"5 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3866136/pdf/nihms461070.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"31973834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wonyul Lee, Ying Du, Wei Sun, D Neil Hayes, Yufeng Liu
{"title":"Multiple Response Regression for Gaussian Mixture Models with Known Labels.","authors":"Wonyul Lee, Ying Du, Wei Sun, D Neil Hayes, Yufeng Liu","doi":"10.1002/sam.11158","DOIUrl":"10.1002/sam.11158","url":null,"abstract":"<p><p>Multiple response regression is a useful regression technique to model multiple response variables using the same set of predictor variables. Most existing methods for multiple response regression are designed for modeling homogeneous data. In many applications, however, one may have heterogeneous data where the samples are divided into multiple groups. Our motivating example is a cancer dataset where the samples belong to multiple cancer subtypes. In this paper, we consider modeling the data coming from a mixture of several Gaussian distributions with known group labels. A naive approach is to split the data into several groups according to the labels and model each group separately. Although it is simple, this approach ignores potential common structures across different groups. We propose new penalized methods to model all groups jointly in which the common and unique structures can be identified. The proposed methods estimate the regression coefficient matrix, as well as the conditional inverse covariance matrix of response variables. Asymptotic properties of the proposed methods are explored. Through numerical examples, we demonstrate that both estimation and prediction can be improved by modeling all groups jointly using the proposed methods. An application to a glioblastoma cancer dataset reveals some interesting common and unique gene relationships across different cancer subtypes.</p>","PeriodicalId":48684,"journal":{"name":"Statistical Analysis and Data Mining","volume":"5 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3885347/pdf/nihms539872.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"32023141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonlinear Vertex Discriminant Analysis with Reproducing Kernels.","authors":"Tong Tong Wu, Yichao Wu","doi":"10.1002/sam.11137","DOIUrl":"10.1002/sam.11137","url":null,"abstract":"<p><p>The novel supervised learning method of vertex discriminant analysis (VDA) has been demonstrated for its good performance in multicategory classification. The current paper explores an elaboration of VDA for nonlinear discrimination. By incorporating reproducing kernels, VDA can be generalized from linear discrimination to nonlinear discrimination. Our numerical experiments show that the new reproducing kernel-based method leads to accurate classification for both linear and nonlinear cases.</p>","PeriodicalId":48684,"journal":{"name":"Statistical Analysis and Data Mining","volume":"5 2","pages":"167-176"},"PeriodicalIF":1.3,"publicationDate":"2012-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510707/pdf/nihms419106.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"31092124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Reduced Rank Ridge Regression and Its Kernel Extensions.","authors":"Ashin Mukherjee, Ji Zhu","doi":"10.1002/sam.10138","DOIUrl":"https://doi.org/10.1002/sam.10138","url":null,"abstract":"<p><p>In multivariate linear regression, it is often assumed that the response matrix is intrinsically of lower rank. This could be because of the correlation structure among the prediction variables or the coefficient matrix being lower rank. To accommodate both, we propose a reduced rank ridge regression for multivariate linear regression. Specifically, we combine the ridge penalty with the reduced rank constraint on the coefficient matrix to come up with a computationally straightforward algorithm. Numerical studies indicate that the proposed method consistently outperforms relevant competitors. A novel extension of the proposed method to the reproducing kernel Hilbert space (RKHS) set-up is also developed.</p>","PeriodicalId":48684,"journal":{"name":"Statistical Analysis and Data Mining","volume":"4 6","pages":"612-622"},"PeriodicalIF":1.3,"publicationDate":"2011-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/sam.10138","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"30919516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Anna J Blackstock, Amita K Manatunga, Youngja Park, Dean P Jones, Tianwei Yu
{"title":"Clustering Based on Periodicity in High-Throughput Time Course Data.","authors":"Anna J Blackstock, Amita K Manatunga, Youngja Park, Dean P Jones, Tianwei Yu","doi":"10.1002/sam.10137","DOIUrl":"https://doi.org/10.1002/sam.10137","url":null,"abstract":"<p><p>Nuclear magnetic resonance (NMR) spectroscopy, traditionally used in analytical chemistry, has recently been introduced to studies of metabolite composition of biological fluids and tissues. Metabolite levels change over time, and providing a tool for better extraction of NMR peaks exhibiting periodic behavior is of interest. We propose a method in which NMR peaks are clustered based on periodic behavior. Periodic regression is used to obtain estimates of the parameter corresponding to period for individual NMR peaks. A mixture model is then used to develop clusters of peaks, taking into account the variability of the regression parameter estimates. Methods are applied to NMR data collected from human blood plasma over a 24-hour period. Simulation studies show that the extra variance component due to the estimation of the parameter estimate should be accounted for in the clustering procedure.</p>","PeriodicalId":48684,"journal":{"name":"Statistical Analysis and Data Mining","volume":"4 6","pages":"579-589"},"PeriodicalIF":1.3,"publicationDate":"2011-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/sam.10137","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"31503030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Novel Support Vector Classifier for Longitudinal High-dimensional Data and Its Application to Neuroimaging Data.","authors":"Shuo Chen, F DuBois Bowman","doi":"10.1002/sam.10141","DOIUrl":"10.1002/sam.10141","url":null,"abstract":"<p><p>Recent technological advances have made it possible for many studies to collect high dimensional data (HDD) longitudinally, for example images collected during different scanning sessions. Such studies may yield temporal changes of selected features that, when incorporated with machine learning methods, are able to predict disease status or responses to a therapeutic treatment. Support vector machine (SVM) techniques are robust and effective tools well-suited for the classification and prediction of HDD. However, current SVM methods for HDD analysis typically consider cross-sectional data collected during one time period or session (e.g. baseline). We propose a novel support vector classifier (SVC) for longitudinal HDD that allows simultaneous estimation of the SVM separating hyperplane parameters and temporal trend parameters, which determine the optimal means to combine the longitudinal data for classification and prediction. Our approach is based on an augmented reproducing kernel function and uses quadratic programming for optimization. We demonstrate the use and potential advantages of our proposed methodology using a simulation study and a data example from the Alzheimer's disease Neuroimaging Initiative. The results indicate that our proposed method leverages the additional longitudinal information to achieve higher accuracy than methods using only cross-sectional data and methods that combine longitudinal data by naively expanding the feature space.</p>","PeriodicalId":48684,"journal":{"name":"Statistical Analysis and Data Mining","volume":"4 6","pages":"604-611"},"PeriodicalIF":1.3,"publicationDate":"2011-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4189187/pdf/nihms-629358.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"32742225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Space-efficient tracking of persistent items in a massive data stream","authors":"Bibudh Lahiri, S. Tirthapura, J. Chandrashekar","doi":"10.1145/2002259.2002294","DOIUrl":"https://doi.org/10.1145/2002259.2002294","url":null,"abstract":"Motivated by scenarios in network anomaly detection, we consider the problem of detecting persistent items in a data stream, which are items that occur \"regularly\" in the stream. In contrast with heavy-hitters, persistent items do not necessarily contribute significantly to the volume of a stream, and may escape detection by traditional volume-based anomaly detectors.\u0000 We first show that any online algorithm that tracks persistent items exactly must necessarily use a large workspace, and is infeasible to run on a traffic monitoring node. In light of this lower bound, we introduce an approximate formulation of the problem and present a small-space algorithm to approximately track persistent items over a large data stream. Our experiments on a real traffic dataset shows that in typical cases, the algorithm achieves a physical space compression of 5x-7x, while incurring very few false positives (< 1%) and false negatives (< 4%). To our knowledge, this is the first systematic study of the problem of detecting persistent items in a data stream, and our work can help detect anomalies that are temporal, rather than volume based.","PeriodicalId":48684,"journal":{"name":"Statistical Analysis and Data Mining","volume":"45 1 1","pages":"70-92"},"PeriodicalIF":1.3,"publicationDate":"2011-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77904624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sequential Support Vector Regression with Embedded Entropy for SNP Selection and Disease Classification.","authors":"Yulan Liang, Arpad Kelemen","doi":"10.1002/sam.10110","DOIUrl":"10.1002/sam.10110","url":null,"abstract":"<p><p>Comprehensive evaluation of common genetic variations through association of SNP structure with common diseases on the genome-wide scale is currently a hot area in human genome research. For less costly and faster diagnostics, advanced computational approaches are needed to select the minimum SNPs with the highest prediction accuracy for common complex diseases. In this paper, we present a sequential support vector regression model with embedded entropy algorithm to deal with the redundancy for the selection of the SNPs that have best prediction performance of diseases. We implemented our proposed method for both SNP selection and disease classification, and applied it to simulation data sets and two real disease data sets. Results show that on the average, our proposed method outperforms the well known methods of Support Vector Machine Recursive Feature Elimination, logistic regression, CART, and logic regression based SNP selections for disease classification.</p>","PeriodicalId":48684,"journal":{"name":"Statistical Analysis and Data Mining","volume":"4 3","pages":"301-312"},"PeriodicalIF":2.1,"publicationDate":"2011-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3110013/pdf/nihms266558.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"29930336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ferit Akova, Murat Dundar, V Jo Davisson, E Daniel Hirleman, Arun K Bhunia, J Paul Robinson, Bartek Rajwa
{"title":"A Machine-Learning Approach to Detecting Unknown Bacterial Serovars.","authors":"Ferit Akova, Murat Dundar, V Jo Davisson, E Daniel Hirleman, Arun K Bhunia, J Paul Robinson, Bartek Rajwa","doi":"10.1002/sam.10085","DOIUrl":"10.1002/sam.10085","url":null,"abstract":"<p><p>Technologies for rapid detection of bacterial pathogens are crucial for securing the food supply. A light-scattering sensor recently developed for real-time identification of multiple colonies has shown great promise for distinguishing bacteria cultures. The classification approach currently used with this system relies on supervised learning. For accurate classification of bacterial pathogens, the training library should be exhaustive, i.e., should consist of samples of all possible pathogens. Yet, the sheer number of existing bacterial serovars and more importantly the effect of their high mutation rate would not allow for a practical and manageable training. In this study, we propose a Bayesian approach to learning with a nonexhaustive training dataset for automated detection of unmatched bacterial serovars, i.e., serovars for which no samples exist in the training library. The main contribution of our work is the Wishart conjugate priors defined over class distributions. This allows us to employ the prior information obtained from known classes to make inferences about unknown classes as well. By this means, we identify new classes of informational value and dynamically update the training dataset with these classes to make it increasingly more representative of the sample population. This results in a classifier with improved predictive performance for future samples. We evaluated our approach on a 28-class bacteria dataset and also on the benchmark 26-class letter recognition dataset for further validation. The proposed approach is compared against state-of-the-art involving density-based approaches and support vector domain description, as well as a recently introduced Bayesian approach based on simulated classes.</p>","PeriodicalId":48684,"journal":{"name":"Statistical Analysis and Data Mining","volume":"3 5","pages":"289-301"},"PeriodicalIF":2.1,"publicationDate":"2010-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3230886/pdf/nihms242307.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"30319662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}