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In many real world problems it is of interest to ascertain which factors are most relevant for determining a given outcome. This is the so-called variable selection problem. The present paper proposes a new regression model for its solution. We show that the proposed model satisfies continuity, sparsity, and unbiasedness properties. A generalized Krylov subspace method for the practical solution of the minimization problem involved is described. This method can be used for the solution of both small-scale and large-scale problems. Several computed examples illustrate the good performance of the proposed model. We place special focus on screening studies using saturated and supersaturated experimental designs. [ABSTRACT FROM AUTHOR]

One of the properties of interest in the analysis of networks is global communicability , i.e., how easy or difficult it is, generally, to reach nodes from other nodes by following edges. Different global communicability measures provide quantitative assessments of this property, emphasizing different aspects of the problem. This paper investigates the sensitivity of global measures of communicability to local changes. In particular, for directed, weighted networks, we study how different global measures of communicability change when the weight of a single edge is changed; or, in the unweighted case, when an edge is added or removed. The measures we study include the total network communicability , based on the matrix exponential of the adjacency matrix, and the Perron network communicability , defined in terms of the Perron root of the adjacency matrix and the associated left and right eigenvectors. Finding what local changes lead to the largest changes in global communicability has many potential applications, including assessing the resilience of a system to failure or attack, guidance for incremental system improvements, and studying the sensitivity of global communicability measures to errors in the network connection data. [ABSTRACT FROM AUTHOR]

Matrix functions play an important role in applied mathematics. In network analysis, in particular, the exponential of the adjacency matrix associated with a network provides valuable information about connectivity, as well as about the relative importance or centrality of nodes. Another popular approach to rank the nodes of a network is to compute the left Perron vector of the adjacency matrix for the network. The present article addresses the problem of evaluating matrix functions, as well as computing an approximation to the left Perron vector, when only some of the columns and/or some of the rows of the adjacency matrix are known. Applications to network analysis are considered, when only some sampled columns and/or rows of the adjacency matrix that defines the network are available. A sampling scheme that takes the connectivity of the network into account is described. Computed examples illustrate the performance of the methods discussed. [ABSTRACT FROM AUTHOR]

We describe a computational method for parameter estimation in linear regression, that is capable of simultaneously producing sparse estimates and dealing with outliers and heavy-tailed error distributions. The method used is based on the image restoration method proposed in Huang et al. (2017) [13]. It can be applied to problems of arbitrary size. The choice of certain parameters is discussed. Results obtained for simulated and real data are presented. [ABSTRACT FROM AUTHOR]

Background: A key barrier to controlling esophageal adenocarcinoma (EAC) is identifying those most likely to benefit from screening and surveillance. We aimed to develop an online educational tool, termed IC-RISC™, for providers and patients to estimate more precisely their absolute risk of developing EAC, interpret this estimate in the context of risk of dying from other causes, and aid in decision-making.Results: U.S. incidence and mortality data and published relative risk estimates from observational studies and clinical trials were used to calculate absolute risk of EAC over 10 years adjusting for competing risks. These input parameters varied depending on presence of the key precursor, Barrett's esophagus. The open source application works across common devices to gather risk factor data and graphically illustrate estimated risk on a single page. Changes to input data are immediately reflected in the colored graphs. We used the calculator to compare the risk distribution between EAC cases and controls from six population-based studies to gain insight into the discrimination metrics of current practice guidelines for screening, observing that current guidelines sacrifice a significant amount of specificity to identify 78-86% of eventual cases in the US population.Conclusions: This educational tool provides a simple and rapid means to graphically communicate risk of EAC in the context of other health risks, facilitates "what-if" scenarios regarding potential preventative actions, and can inform discussions regarding screening, surveillance and treatment options. Its generic architecture lends itself to being easily extended to other cancers with distinct pathways and/or intermediate stages, such as hepatocellular cancer. IC-RISC™ extends current qualitative clinical practice guidelines into a quantitative assessment, which brings the possibility of preventative actions being offered to persons not currently targeted for screening and, conversely, reducing unnecessary procedures in those at low risk. Prospective validation and application to existing well-characterized cohort studies are needed. [ABSTRACT FROM AUTHOR]