Sparse Multinomial Regression Research Articles

Discriminating chert origins using machine‐learning approaches

Automatic techniques have not been applied in the geochemical discrimination of marine, terrestrial and hydrothermal cherts, which is critical to retrieving the paleoenvironmental information of ancient sedimentary basins. Here, we applied three supervised machine‐learning methods to analyse the labelled geochemical compositional data (32 major and trace elements) of cherts, including the support vector machine (SVM), sparse multinomial regression and linear discrimination analysis. Our results show that these machine‐learning methods can successfully discriminate different chert types, as the lowest classification score is 79%. Among the methods, the SVM is the most powerful approach (classification score 88%, on average), even though it is hard to be geochemically interpreted. Sparse multinomial regression and linear discrimination analysis are also efficient approaches (mean classification score 84%), which can be used to extract the important elements and the most representative sample for each chert type. Especially, the linear discrimination analysis can construct binary discrimination diagram superposed with biplot rays and posterior probability‐based decision boundaries, which could be quickly applied and explained by other researchers. Furthermore, the successful discrimination of different chert types indicates that cherts derived from different silica sources have different geochemical signatures, albeit mixing between different sources of silica during chert formation is common. Last, the general geochemical features of each chert type were summarised based on geochemical information extracted by machine‐learning methods and previous geochemical studies.

Risk Indicators for Noncavitated and Cavitated Carious Lesions in Preschool Children

ObjectiveThe aim of this study was to evaluate the risk indicators associated with noncavitated and cavitated lesions in preschool children. MethodsThe cross-sectional study included 3- to 4-year-old healthy children (N = 741) recruited in a randomised controlled clinical trial. After obtaining written informed consent, parents completed a questionnaire about their child's sociodemographic background and oral health–related behaviours and parents' oral health–related knowledge and attitude. Caries and plaque were evaluated using International Caries Detection and Assessment System-II and Visible Plaque Index (VPI), respectively. Children were grouped according to their oral health status as being caries-free (CF), having only noncavitated lesions (NC), or having cavitated lesions (CL). The least absolute shrinkage and selection operator (LASSO) sparse multinomial regression was used to study the variables using 1 standard error above the minimum criterion set at P < .05. ResultsThe prevalence of children with NC and CL was 29.1% and 49.4%, respectively, with a prevalence of early childhood caries being 78.5%. The proportion of children who brushed twice or more than twice a day was highest in CF (71.7%), followed by NC (58.3%), and was least in CL (57.7%). A higher percentage of CL children (56.2%) had twice or more than twice the frequency of between-meal snacking than CF (41.7%) and NC (41.1%) (P < .001) children. The variables included with non-zero coefficients in the model were mean parental oral health knowledge, attitude score, and children's mean VPI score, and all were significant for CL; however, in NC, only VPI score was found to be significant. ConclusionsPoor oral hygiene is the risk indicator associated with the presence of NC in preschool children, whilst poor oral hygiene and poor parental oral health knowledge and attitude are associated with the presence of cavitated lesions.

Cancer Diagnosis and Disease Gene Identification via Statistical Machine Learning

Diagnosing cancer and identifying the disease gene by using DNA microarray gene expression data are the hot topics in current bioinformatics. This paper is devoted to the latest development in cancer diagnosis and gene selection via statistical machine learning. A support vector machine is firstly introduced for the binary cancer diagnosis. Then, 1-norm support vector machine, doubly regularized support vector machine, adaptive huberized support vector machine and other extensions are presented to improve the performance of gene selection. Lasso, elastic net, partly adaptive elastic net, group lasso, sparse group lasso, adaptive sparse group lasso and other sparse regression methods are also introduced for performing simultaneous binary cancer classification and gene selection. In addition to introducing three strategies for reducing multiclass to binary, methods of directly considering all classes of data in a learning model (multi_class support vector, sparse multinomial regression, adaptive multinomial regression and so on) are presented for performing multiple cancer diagnosis. Limitations and promising directions are also discussed.

Geochemical Discrimination and Characteristics of Magmatic Tectonic Settings: A Machine‐Learning‐Based Approach

AbstractGeochemically discriminating between magmatism in different tectonic settings remains a fundamental part of understanding the processes of magma generation within the Earth's mantle. Here we present an approach where machine learning (ML) methods are used for quantitative tectonic discrimination and feature selection using global geochemical data sets containing data for volcanic rocks generated in eight different tectonic settings. This study uses support vector machine, random forest, and sparse multinomial regression (SMR) approaches. All these ML methods with data for 24 elements and five isotopic ratios allowed the successful geochemical discrimination between igneous rocks formed in eight different tectonic settings with a discriminant ratio better than 83% for all settings barring oceanic plateaus and back‐arc basins. SMR is a particularly powerful and interpretable ML method because it quantitatively identifies geochemical signatures that characterize the tectonic settings of interest and the characteristics of each sample as a probability of the membership of the sample for each setting. We also present the most representative basalt composition for each tectonic setting. The new data provide reference points for future geochemical discussions. Our results indicate that at least 17 elements and isotopic ratios are required to characterize each tectonic setting, suggesting that geochemical tectonic discrimination cannot be achieved using only a small number of elemental compositions and/or isotopic ratios. The results show that volcanic rocks formed in different tectonic settings have unique geochemical signatures, indicating that both volcanic rock geochemistry and magma generation processes are closely connected to the tectonic setting.