Significance Analysis for Pairwise Variable Selection in Classification

The goal of this article is to select important variables that can distinguish one class of data from another. A marginal variable selection method ranks the marginal effects for classification of individual variables, and is a useful and efficient approach for variable selection. Our focus here is to consider the bivariate effect, in addition to the marginal effect. In particular, we are interested in those pairs of variables that can lead to accurate classification predictions when they are viewed jointly. To accomplish this, we propose a permutation test called Significance test of Joint Effect (SigJEff). In the absence of joint effect in the data, SigJEff is similar or equivalent to many marginal methods. However, when joint effects exist, our method can significantly boost the performance of variable selection. Such joint effects can help to provide additional, and sometimes dominating, advantage for classification. We illustrate and validate our approach using both simulated example and a real glioblastoma multiforme data set, which provide promising results.Comment: 28 pages, 7 figure

Numerical Complete Solution for Random Genetic Drift by Energetic Variational Approach

In this paper, we focus on numerical solutions for random genetic drift problem, which is governed by a degenerated convection-dominated parabolic equation. Due to the fixation phenomenon of genes, Dirac delta singularities will develop at boundary points as time evolves. Based on an energetic variational approach (EnVarA), a balance between the maximal dissipation principle (MDP) and least action principle (LAP), we obtain the trajectory equation. In turn, a numerical scheme is proposed using a convex splitting technique, with the unique solvability (on a convex set) and the energy decay property (in time) justified at a theoretical level. Numerical examples are presented for cases of pure drift and drift with semi-selection. The remarkable advantage of this method is its ability to catch the Dirac delta singularity close to machine precision over any equidistant grid.Comment: 22 pages, 11 figures, 2 table

Behavior of different numerical schemes for population genetic drift problems

In this paper, we focus on numerical methods for the genetic drift problems, which is governed by a degenerated convection-dominated parabolic equation. Due to the degeneration and convection, Dirac singularities will always be developed at boundary points as time evolves. In order to find a \emph{complete solution} which should keep the conservation of total probability and expectation, three different schemes based on finite volume methods are used to solve the equation numerically: one is a upwind scheme, the other two are different central schemes. We observed that all the methods are stable and can keep the total probability, but have totally different long-time behaviors concerning with the conservation of expectation. We prove that any extra infinitesimal diffusion leads to a same artificial steady state. So upwind scheme does not work due to its intrinsic numerical viscosity. We find one of the central schemes introduces a numerical viscosity term too, which is beyond the common understanding in the convection-diffusion community. Careful analysis is presented to prove that the other central scheme does work. Our study shows that the numerical methods should be carefully chosen and any method with intrinsic numerical viscosity must be avoided.Comment: 17 pages, 8 figure

The Cumulative Distribution Function Based Method for Random Drift Model

In this paper, we propose a numerical method to uniformly handle the random genetic drift model for pure drift with or without natural selection and mutation. For pure drift and natural selection case, the Dirac $\delta$ singularity will develop at two boundary ends and the mass lumped at the two ends stands for the fixation probability. For the one-way mutation case, known as Muller's ratchet, the accumulation of deleterious mutations leads to the loss of the fittest gene, the Dirac $\delta$ singularity will spike only at one boundary end, which stands for the fixation of the deleterious gene and loss of the fittest one. For two-way mutation case, the singularity with negative power law may emerge near boundary points. We first rewrite the original model on the probability density function (PDF) to one with respect to the cumulative distribution function (CDF). Dirac $\delta$ singularity of the PDF becomes the discontinuity of the CDF. Then we establish a upwind scheme, which keeps the total probability, is positivity preserving and unconditionally stable. For pure drift, the scheme also keeps the conservation of expectation. It can catch the discontinuous jump of the CDF, then predicts accurately the fixation probability for pure drift with or without natural selection and one-way mutation. For two-way mutation case, it can catch the power law of the singularity. %Moreover, some artificial algorithms or additional boundary criteria is not needed in the numerical simulation. The numerical results show the effectiveness of the scheme

Attention based surrogate model to predict load envelope of monopile supporting offshore wind turbines

publishedVersio

Hospital readmission and healthcare utilization following sepsis in community settings

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/108012/1/jhm2197.pd