Scoring Functions for Multivariate Distributions and Level Sets

Interest in predicting multivariate probability distributions is growing due to the increasing availability of rich datasets and computational developments. Scoring functions enable the comparison of forecast accuracy, and can potentially be used for estimation. A scoring function for multivariate distributions that has gained some popularity is the energy score. This is a generalization of the continuous ranked probability score (CRPS), which is widely used for univariate distributions. A little-known, alternative generalization is the multivariate CRPS (MCRPS). We propose a theoretical framework for scoring functions for multivariate distributions, which encompasses the energy score and MCRPS, as well as the quadratic score, which has also received little attention. We demonstrate how this framework can be used to generate new scores. For univariate distributions, it is well-established that the CRPS can be expressed as the integral over a quantile score. We show that, in a similar way, scoring functions for multivariate distributions can be "disintegrated" to obtain scoring functions for level sets. Using this, we present scoring functions for different types of level set, including those for densities and cumulative distributions. To compute the scoring functions, we propose a simple numerical algorithm. We illustrate our proposals using simulated and stock returns data

Peer relationship and adolescent smartphone addiction: The mediating role of self-esteem and the moderating role of the need to belong

Adolescent smartphone addiction has received increased attention in recent years, and peer relationship has been found to be a protective factor in adolescent smartphone. However, little is known about the mediating and moderating mechanisms underlying this relation. The aim of this study was to investigate (a) the mediating role of self-esteem in the association between student–student relationship and smartphone addiction, and (b) the moderating role of the need to belong in the indirect relationship between student–student relationship and adolescent smartphone addiction. Methods This model was examined with 768 Chinese adolescents (mean age = 16.81 years, SD = 0.73); the participants completed measurements regarding student–student relationship, self-esteem, the need to belong, and smartphone addiction. Results The correlation analyses indicated that student–student relationship was significantly negatively associated with adolescent smartphone addiction, and the need to belong was significantly positively associated with adolescent smartphone addiction. Mediation analyses revealed that self-esteem partially mediated the link between student-student relationship and adolescent smartphone addiction. Moderated mediation further indicated that the mediated path was weaker for adolescents with lower levels of the need to belong. Discussion and conclusion High self-esteem could be a protective factor against smartphone addiction for adolescents with a strong need to belong as these students appeared to be at elevated risk of developing smartphone addiction

Exploring the roles of cannot-link constraint in community detection via multi-variance mixed Gaussian generative model

Due to the demand for performance improvement and the existence of prior information, semi-supervised community detection with pairwise constraints becomes a hot topic. Most existing methods have been successfully encoding the must-link constraints, but neglect the opposite ones, i.e., the cannot-link constraints, which can force the exclusion between nodes. In this paper, we are interested in understanding the role of cannot-link constraints and effectively encoding pairwise constraints. Towards these goals, we define an integral generative process jointly considering the network topology, must-link and cannot-link constraints. We propose to characterize this process as a Multi-variance Mixed Gaussian Generative (MMGG) Model to address diverse degrees of confidences that exist in network topology and pairwise constraints and formulate it as a weighted nonnegative matrix factorization problem. The experiments on artificial and real-world networks not only illustrate the superiority of our proposed MMGG, but also, most importantly, reveal the roles of pairwise constraints. That is, though the must-link is more important than cannot-link when either of them is available, both must-link and cannot-link are equally important when both of them are available. To the best of our knowledge, this is the first work on discovering and exploring the importance of cannot-link constraints in semi-supervised community detection

Potential effective diagnostic biomarker in patients with primary and metastatic small intestinal neuroendocrine tumors

Background: Small intestinal neuroendocrine tumors (SI-NETs) are the most common malignant tumors of the small intestine, with many patients presenting with metastases and their incidence increasing. We aimed to find effective diagnostic biomarkers for patients with primary and metastatic SI-NETs that could be applied for clinical diagnosis.Methods: We downloaded GSE65286 (training set) and GSE98894 (test set) from the GEO database and performed differential gene expression analysis to obtain differentially expressed genes (DEGs) and differentially expressed long non-coding RNAs (DElncRNAs). The functions and pathways involved in these genes were further explored by Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analyses. In addition, a global regulatory network involving dysregulated genes in SI-NETs was constructed based on RNAInter and TRRUST v2 databases, and the diagnostic power of hub genes was identified by receiver operating characteristic curve (ROC).Results: A total of 2,969 DEGs and DElncRNAs were obtained in the training set. Enrichment analysis revealed that biological processes (BPs) and KEGG pathways were mainly associated with cancer. Based on gene set enrichment analysis (GSEA), we obtained five BPs (cytokinesis, iron ion homeostasis, mucopolysaccharide metabolic process, platelet degranulation and triglyceride metabolic process) and one KEGG pathway (ppar signaling pathway). In addition, the core set of dysregulated genes obtained included MYL9, ITGV8, FGF2, FZD7, and FLNC. The hub genes were upregulated in patients with primary SI-NETs compared to patients with metastatic SI-NETs, which is consistent with the training set. Significantly, the results of ROC analysis showed that the diagnostic power of the hub genes was strong in both the training and test sets.Conclusion: In summary, we constructed a global regulatory network in SI-NETs. In addition, we obtained the hub genes including MYL9, ITGV8, FGF2, FZD7, and FLNC, which may be useful for the diagnosis of patients with primary and metastatic SI-NETs

Hepatitis E Virus Genotype Diversity in Eastern China

We studied 47 hepatitis E virus (HEV) isolates from hospitalized patients in Nanjing and Taizhou, eastern China. Genotypes 1, 3, and 4 were prevalent; genotype 3 and subgenotype 4b showed a close relationship with the swine strains in eastern China, thus indicating that HEV genotype 3 had infected humans in China