Stochastic Partitioning for Variable Selection in Multivariate Mixture of Regression Models

Plane waves and response matrices

In this novel forecasting algorithm to calculate the unit‐impulse response matrix of an unbounded medium to analyse dynamic medium‐structure interaction in the time domain based on the substructure method, a finite‐element region adjacent to the structure–medium interface consisting of two or three rows only is introduced. Its exterior boundary is chosen to be similar to the interior boundary which coincides with the structure–medium interface. At similar boundaries of the unbounded medium the unit‐impulse response matrices are a function of the dimensionless time. The unit‐impulse response matrix at the exterior boundary can be forecasted from that at the interior boundary via this dimensionless time by taking advantage of the time delay of waves propagating between these two boundaries. The forecasting algorithm based solely on the finite‐element method is exact in the finite‐element sense in modelling the unbounded medium.

Numerical methods based on transformation of variables are developed to improve the computational efficiency of the variational nodal method (VNM). Reordering and orthogonal transformations of the nodal unknowns are found to reduce the coefficient matrices of VNM into block-diagonal forms. These forms make it possible to reduce greatly the number of floating-point operations in matrix manipulations and hence to reduce the computational times. The red-black response matrix acceleration by transformation of interface partial-current variables has been extended to three-dimensional geometries and higher orders of spatial and angular approximations. These combined methods are incorporated within the algorithms currently used in the variational nodal code VARIANT at Argonne National Laboratory. All primary algorithms ranging from the generation of response matrices to the iterative solution method for the response matrix equations are modified to implement the new formulation. The efficiency of the new methods is tested on eigenvalue problems by comparing the computation times of the new and existing methods. Three-dimensional calculations are performed in hexagonal and Cartesian geometry for various spatial and angular approximations. The test results show that very significant gains can be obtained especially for the coupling coefficient calculations in higher angular approximations. More than an order of magnitude reduction of the total computing time is achieved in the best case.

Our aim is to characterize those matrices that are the response matrix of a semi-positive definite Schr?dinger operator on a circular planar network. Our findings generalize the known results and allow us to consider both nonsingular and non diagonally dominant matrices as response matrices. To this end, we define the Dirichlet-to-Robin map associated with a Schr?dinger operator on general networks, and we prove that it satisfies the alternating property which is essential to characterize the response matrices.

In this paper we are concerned with the problems of variable selection and estimation in double generalized linear models in which both the mean and the dispersion are allowed to depend on explanatory variables. We propose a maximum penalized pseudo-likelihood method when the number of parameters diverges with the sample size. With appropriate selection of the tuning parameters, the consistency of the variable selection procedure and asymptotic properties of the resulting estimators are established. We also carry out simulation studies and a real data analysis to assess the finite sample performance of the proposed variable selection procedure, showing that the proposed variable selection method works satisfactorily.

In this paper we develop statistical models for bankruptcy prediction of Italian firms in the limited liability sector, using annual balance sheet information. Several issues involved in default risk analysis are investigated, such as the structure of the data-base, the sampling procedure and the influence of predictors. In particular we focus on the variable selection problem, comparing innovative techniques based on shrinkage with traditional stepwise methods. The predictive performance of the proposed default risk model has been evaluated by means of different accuracy measures. The results of the analysis, carried out on a data-set of financial ratios expressly created from a sample of industrial firms annual reports, give evidence in favor of the proposed model over traditional ones.

We consider the problem of simultaneous variable selection and parameter estimation in an ultra-high dimensional linear regression model. The adaptive penalty functions are used in this regard to achieve the oracle variable selection property with simpler assumptions and lesser computational burden. Noting the non-robust nature of the usual adaptive procedures (e.g. adaptive LASSO) based on the squared error loss function against data contamination, quite frequent with modern large-scale data sets (e.g. noisy gene expression data, spectra and spectral data), in this paper, we present a new adaptive regularization procedure using a robust loss function based on the density power divergence (DPD) measure under a general class of error distributions. We theoretically prove that the proposed adaptive DPD-LASSO estimator of the regression coefficients is highly robust, consistent, asymptotically normal and leads to robust oracle-consistent variable selection under easily verifiable assumptions. Numerical illustrations are provided for the mostly used normal and heavy-tailed error densities. Finally, the proposal is applied to analyse an interesting spectral dataset, in the field of chemometrics, regarding the electron-probe X-ray microanalysis (EPXMA) of archaeological glass vessels from the 16th and 17th centuries.

We consider the problem of variable selection in regression models. In particular, we are interested in selecting explanatory covariates linked with the response variable and we want to determine which covariates are relevant, that is which covariates are involved in the model. In this framework, we deal with L 1-penalized regression models. To handle the choice of the penalty parameter to perform variable selection, we develop a new method based on the knockoffs idea. This revisited knockoffs method is general, suitable for a wide range of regressions with various types of response variables. Besides, it also works when the number of observations is smaller than the number of covariates and gives an order of importance of the covariates. Finally, we provide many experimental results to corroborate our method and compare it with other variable selection methods.

In this paper, the general linear hypothesis testing and variable selection problems in functional response model are considered. The globalizing pointwise F test and the -test as well as the variable selection methods based on multiple hypothesis testing are adapted to this model. The asymptotic null distributions and consistency under local alternatives of test statistics are established under some standard regularity conditions. Based on these results and nonparametric bootstrap approach, different methods are proposed to approximate the null distribution of test statistics. The performance of the new testing and variable selection procedures is compared with that of the known methods in numerical experiments based on real data set. The results suggest that the new methods often outperform the known ones in terms of size control, power and ability to detect significant variables.

The Lasso and Ridge estimators are effective variable selection methods for a simple linear model. While the multiple linear model is often used in practice, only few studies have examined its problem of variable selection. To address this gap, we study such problem by taking advantage of the Lasso and Ridge estimate. We propose two variable selection methods in the multiple linear model and introduce the multiple random simulation (MRS) algorithm, whose efficiency is similar to that of the least angle regression (LARS) algorithm in a simple linear model. We verify the performance of these two algorithms by applying them to real diabetes data and find that the LARS algorithm cannot be easily applied in a multiple linear model. We also illustrate the excellent performance of MRS by applying this algorithm on a simulated dataset.

Evaluation of the effect of chance correlations on variable selection using Partial Least Squares-Discriminant Analysis

A novel ensemble L1 regularization based variable selection framework with an application in near infrared spectroscopy

This paper considers the problem of variable selection when some of the variables have a functional nature and can be mixed with other type of variables (scalar, multivariate, directional, etc). Our proposal begins with a simple null model and sequentially selects a new variable to be incorporated into the model. For the sake of simplicity, this paper only uses additive models. However, the proposed algorithm may assess the type of contribution (linear, non linear, …) of each variable. The algorithm have showed quite promising results when applied to real data sets.

The eigenmodes of the time reversal operator are studied for a single rigid cylinder with elliptical cross-section leading to an asymmetric inter-element response matrix in reflection measurement mode. The elliptical cylinder is of considerable interest in scattering problems and it encompasses within the limit both the circular cross-section case and the strip. Variable cylinder properties will include cross-sectional area, eccentricity and angle of inclination of the semi-major axis with respect to the axis of symmetry of a probing transducer array. Approximations of the exact solutions determining the far-field response using a modal expansion with scattering coefficients computed via Mathieu functions will be discussed. Analysis of simulated results will indicate that for scatterers near the Rayleigh limit it is possible to characterize the aspect ratio of the target using subarray methods.

Image fusion serves as the basis for automatic target recognition; it maps images of teh same scene received from different sensors into a common reference system. A novel fusion method is described that employs image local response and the hybrid evolutionary algorithm (HEA). Given geometric transformation A(V) under parameter vector V (e.g. affine image transformation) of the images subjected to fusion, image local response is defined as image transform components of the parameter vector V are applied to the image, and the corresponding variations of the least squared differences of the gray levels of the two images (i.e. before and after parameter variation) form the image response matrix. The transform R(V) extracts only the dynamic contents of the image, i.e. the salient features that are most sensitive to geometric transformation A(V). Since R(V) maps the image onto itself, the result of the mapping is largely invariant to the type of the sensor that was used to obtain the image. Once the response matrices are built for all images subjected to fusion, HEA is used to map the images into the common reference system.