Building Support Vector Machines in the Context of Regularised Least Squares

This paper formulates a linear kernel support vector machine (SVM) as a regularized least-squares (RLS) problem. By defining a set of indicator variables of the errors, the solution to the RLS problem is represented as an equation that relates the error vector to the indicator variables. Through partitioning the training set, the SVM weights and bias are expressed analytically using the support vectors. It is also shown how this approach naturally extends to Sums with nonlinear kernels whilst avoiding the need to make use of Lagrange multipliers and duality theory. A fast iterative solution algorithm based on Cholesky decomposition with permutation of the support vectors is suggested as a solution method. The properties of our SVM formulation are analyzed and compared with standard SVMs using a simple example that can be illustrated graphically. The correctness and behavior of our solution (merely derived in the primal context of RLS) is demonstrated using a set of public benchmarking problems for both linear and nonlinear SVMs.

Efficacy and safety of lumacaftor/ivacaftor combination therapy in patients with cystic fibrosis homozygous for Phe508del CFTR by pulmonary function subgroup

Background Lumacaftor/ivacaftor combination therapy demonstrated clinical benefits inpatients with cystic fibrosis homozygous for the Phe508del CFTR mutation.Pretreatment lung function is a confounding factor that potentially impacts the efficacyand safety of lumacaftor/ivacaftor therapy. Methods Two multinational, randomised, double-blind, placebo-controlled, parallelgroupPhase 3 studies randomised patients to receive placebo or lumacaftor (600 mgonce daily [qd] or 400 mg every 12 hours [q12h]) in combination with ivacaftor (250 mgq12h) for 24 weeks. Prespecified analyses of pooled efficacy and safety data by lungfunction, as measured by percent predicted forced expiratory volume in 1 second(ppFEV1), were performed for patients with baseline ppFEV1 <40 (n=81) and ≥40(n=1016) and screening ppFEV1 <70 (n=730) and ≥70 (n=342). These studies wereregistered with ClinicalTrials.gov (NCT01807923 and NCT01807949). Findings The studies were conducted from April 2013 through April 2014.Improvements in the primary endpoint, absolute change from baseline at week 24 inppFEV1, were observed with both lumacaftor/ivacaftor doses in the subgroup withbaseline ppFEV1 <40 (least-squares mean difference versus placebo was 3∙7 and 3.3percentage points for lumacaftor 600 mg qd/ivacaftor 250 mg q12h and lumacaftor 400mg q12h/ivacaftor 250 mg q12h, respectively [p<0∙05] and in the subgroup with baselineppFEV1 ≥40 (3∙3 and 2∙8 percentage points, respectively [p<0∙001]). Similar absoluteimprovements versus placebo in ppFEV1 were observed in subgroups with screening 4ppFEV1 <70 (3∙3 and 3∙3 percentage points for lumacaftor 600 mg qd/ivacaftor 250 mgq12h and lumacaftor 400 mg q12h/ivacaftor 250 mg q12h, respectively [p<0∙001]) and≥70 (3∙3 and 1∙9 percentage points, respectively [p=0.002] and [p=0∙079]). Increases inBMI and reduction in number of pulmonary exacerbation events were observed in bothLUM/IVA dose groups vs placebo across all lung function subgroups. Treatment wasgenerally well tolerated, although the incidence of some respiratory adverse events washigher with active treatment than with placebo. Interpretation Lumacaftor/ivacaftor combination therapy benefits patients homozygousfor Phe508del CFTR who have varying degrees of lung function impairment. Funding Vertex Pharmaceuticals Incorporated.

Compositional data analysis of Holocene sediments from the West Bengal Sundarbans, India: Geochemical proxies for grain-size variability in a delta environment

This paper is part of a special issue of Applied Geochemistry focusing on reliable applications of compositional multivariate statistical methods. This study outlines the application of compositional data analysis (CoDa) to calibration of geochemical data and multivariate statistical modelling of geochemistry and grain-size data from a set of Holocene sedimentary cores from the Ganges-Brahmaputra (G-B) delta. Over the last two decades, understanding near-continuous records of sedimentary sequences has required the use of core-scanning X-ray fluorescence (XRF) spectrometry, for both terrestrial and marine sedimentary sequences. Initial XRF data are generally unusable in ‘raw-format’, requiring data processing in order to remove instrument bias, as well as informed sequence interpretation. The applicability of these conventional calibration equations to core-scanning XRF data are further limited by the constraints posed by unknown measurement geometry and specimen homogeneity, as well as matrix effects. Log-ratio based calibration schemes have been developed and applied to clastic sedimentary sequences focusing mainly on energy dispersive-XRF (ED-XRF) core-scanning. This study has applied high resolution core-scanning XRF to Holocene sedimentary sequences from the tidal-dominated Indian Sundarbans, (Ganges-Brahmaputra delta plain). The Log-Ratio Calibration Equation (LRCE) was applied to a sub-set of core-scan and conventional ED-XRF data to quantify elemental composition. This provides a robust calibration scheme using reduced major axis regression of log-ratio transformed geochemical data. Through partial least squares (PLS) modelling of geochemical and grain-size data, it is possible to derive robust proxy information for the Sundarbans depositional environment. The application of these techniques to Holocene sedimentary data offers an improved methodological framework for unravelling Holocene sedimentation patterns.