Variable Selection

This study is concerned with understanding of the formation of ore deposits (precious and base metals) and contributes to the exploration and discovery of new occurrences using artificial neural networks. From the different digital data sets available in BRGM's GIS ...

Recently, variable selection by penalized likelihood has attracted much research interest. In this paper, we propose adaptive Lasso quantile regression (BALQR) from a Bayesian perspective. The method extends the Bayesian Lasso quantile regression by allowing different penalization parameters for different regression coefficients. Inverse gamma prior distributions are placed on the penalty parameters. We treat the hyperparameters of the inverse gamma prior as unknowns and estimate them along with the other parameters. A Gibbs sampler is developed to simulate the parameters from the posterior distributions. Through simulation studies and analysis of a prostate cancer dataset, we compare the performance of the BALQR method proposed with six existing Bayesian and non-Bayesian methods. The simulation studies and the prostate cancer data analysis indicate that the BALQR method performs well in comparison to the other approaches.

Telemarketers of online job advertising firms face significant challenges understanding the advertising demands of small-sized enterprises. The effective use of data mining approach can offer e-recruitment companies an improved understanding of customers' patterns and greater insights of purchasing trends. However, prior studies on classifier built by data mining approach provided limited insights into the customer targeting problem of job advertising companies. In this paper we develop a single feature evaluator and propose an approach to select a desired feature subset by setting a threshold. The proposed feature evaluator demonstrates its stability and outstanding performance through empirical experiments in which real-world customer data of an e-recruitment firm are used. Practically, the findings together with the model may help telemarketers to better understand their customers. Theoretically, this paper extends existing research on feature selection for binary classification of imbalanced data.

A variable selection problem is analysed for use in Principal Component Analysis (PCA). In this case, the set of original variables is divided into disjoint groups. The problem resides in the selection of variables, but with the restriction that the set of variables that is selected should contain at least one variable from each group. The objective function under consideration is the sum of the first eigenvalues of the correlation matrix of the subset of selected variables. This problem, with no known prior references, has two further difficulties, in addition to that of the variable selection problem: the evaluation of the objective function and the restriction that the subset of selected variables should also contain elements from all of the groups. Two Branch & Bound methods are proposed to obtain exact solutions that incorporate two strategies: the first one is the use of ''fast'' guide functions as alternatives to the objective function; the second one is the preselection of variables that help to comply with the latter restriction. From the computational tests, it is seen that both strategies are very efficient and achieve significant reductions in calculation times.

Part I of this paper (Adjiman et al., 1997) described the theoretical foundations of a global optimization algorithm, the BB algorithm, which can be used to solve problems belonging to the broad class of twice-di erentiable NPLs. For any such problem, the ability to automatically generate progressively tighter convex lower bounding problems at each iteration guarantees the convergence of the branchand-bound BB algorithm to within of the global optimum solution. Several methods were presented for the construction of convex valid underestimators for general nonconvex functions. In this second part, the performance of the proposed algorithm and its alternative underestimators is studied through their application to a variety of problems. An implementation of the BB is described and a number of rules for branching variable selection and variable bound updates are shown to enhance convergence rates. A user-friendly parser facilitates problem input and provides exibility in the selection of an underestimating strategy. In addition, the package features both automatic di erentiation and interval arithmetic capabilities. Making use of all the available options, the BB algorithm successfully identi es the global optimum solution of small literature problems, of small and medium size chemical engineering problems in the areas of reactor network design, heat exchanger network design, reactor-separator network design, of generalized geometric programming problems for design and control, and of batch process design problems with uncertainty.

, restructuring banks and strengthening the resources of credit institutions. The objective of this Fund is to manage bank restructuring processes and help strengthen their resources. The initial funding provided for this Fund is 9.000 million euros. 2 Basilea III requires financial institutions to increase reserves to 7% of their of holding to be able to handle crisis situations.

LASSO (Least Absolute Shrinkage and Selection Operator) is a useful tool to achieve the shrinkage and variable selection simultaneously. Since LASSO uses the L 1 penalty, the optimization should rely on the quadratic program (QP) or general non-linear program which is known to be computational intensive. In this paper, we propose a gradient descent algorithm for LASSO. Even though the final result is slightly less accurate, the proposed algorithm is computationally simpler than QP or non-linear program, and so can be applied to large size problems. We provide the convergence rate of the algorithm, and illustrate it with simulated models as well as real data sets.

This study examined baseline characteristics associated with abstinence from tobacco 6 months after treatment for nicotine dependence. A total of 1224 cigarette smokers (619 females, 605 males) receiving clinical services for treatment of nicotine dependence between January 1, 1995 and June 30, 1997 were studied. The intervention involves a 45-min consultation with a nicotine dependence counselor. A treatment plan individualized to the patient's needs is then developed. The main outcome measure was the self-reported 7-day point prevalence abstinence from tobacco obtained by telephone interview 6-months after the consultation. A bootstrap resampling methodology for predictor variable selection was used to identify a set of multivariate predictors of 6-month tobacco abstinence. Five variables were multivariately associated with tobacco abstinence: male gender, no current psychiatric diagnosis, higher stage of change, longest duration of previous abstinence from tobacco of <1 or...

The problem of variable selection in neural network regression models with dependent data is considered. In this framework, a test procedure based on the introduction of a measure for the variable relevance to the model is discussed. The main di culty in using this procedure is related to the asymptotic distribution of the test statistic which is not one of the familiar tabulated distributions. Moreover, it depends on matrices which are very di cult to estimate because of their complex structure. To overcome these analytical issues and to get a consistent approximation for the sampling distribution of the statistic involved, a subsampling scheme is proposed. The procedure, which takes explicitly into account the dependence structure of the data, will be justiÿed from an asymptotic point of view and evaluated in ÿnite samples by a small Monte Carlo study.

In the presented research three measurement strategies of Fourier transform infrared (FT-IR) spectrometry (horizontal-and micro-attenuated total reflection (HATR and lATR, respectively) and a novel high throughput transmission (HTT)) in combination with extensive chemometric approach have been applied for analysis of beer. Fifty Belgian beer samples were analyzed: lager and white beers, dark and blonde ales, lambic and Trappist beers. Partial least square (PLS) regression was used for prediction of different physicochemical parameters of beer based on mid-IR data, modified with different spectral preprocessing and variable selection algorithms for higher prediction performance. It was found that HATR and lATR have the same prediction capability with a slight advantage of lATR and excellent correlations between spectra and reference values were demonstrated for original (R 2 0.95), apparent (R 2 0.89) and real (R 2 0.95) extracts, real and apparent degrees of fermentation (R 2 0.91 and 0.89), alcohol content (R 2 0.94) and energetic value (R 2 0.95). Good results (R 2 0.83) were obtained from the HTT experiments for prediction of real extract and allow measurement of large sample numbers in short time (1 sample/minute) with further potential increase in a sample throughput and has the possibility for automation. The obtained results indicate that mid-IR spectrometry in combination with advanced pre-processing and variable selection methods is a valuable analytical tool for high throughput measurement of beer quality attributes and thus has potential for use in product development and quality control.

The study examines the effectiveness of different neural networks in predicting bankruptcy filing. Two approaches for training neural networks, Back-Propagation and Optimal Estimation Theory, are considered. Within the back-propagation training method, four different models (Back-Propagation, Functional Link Back-Propagation With Sines, Pruned Back-Propagation, and Cumulative Predictive Back-Propagation) are tested. The neural networks are compared against traditional bankruptcy prediction techniques such as discriminant analysis, logit, and probit. The results show that the level of Type I and Type H errors varies greatly across techniques. The Optimal Estimation Theory neural network has the lowest level of Type 1 error and the highest level of Type H error while the traditional statistical techniques have the reverse relationship (i.e., high Type I error and low Type H error). The back-propagation neural networks have intermediate levels of Type I and Type H error. We demonstrate that the performance of the neural networks tested is sensitive to the choice of variables selected and that the networks cannot be relied upon to "sift through" variables and focus on the most important variables (network performance based on the combined set of Ohlson and Altman data was frequently worse than their performance with one of the subsets). It is also important to note that the results are quite sensitive to sampling error. The significant variations across replications for some of the models indicate the sensitivity of the models to variations in the data.

Species distribution modelling is central to both fundamental and applied research in biogeography. Despite widespread use of models, there are still important conceptual ambiguities as well as biotic and algorithmic uncertainties that need to be investigated in order to increase confidence in model results. We identify and discuss five areas of enquiry that are of high importance for species distribution modelling: (1) clarification of the niche concept; (2) improved designs for sampling data for building models; (3) improved parameterization;

Extensive optimisation of a mathematical model's fit to a relatively small set of empirical data, may lead to over-optimistic validation results. If the assessment of the final, optimised model is based on the same validation method and the same input data that were used as basis for the extensive model optimisation, accumulated spurious correlations may appear as real predictive ability in the final model validation. An example of this is the use of extensive variable selection in multiple regression, based on a cross-model validation scheme.

. The relationship between absorption in the near-infrared NIR spectral region and the target analytical parameter is frequently of the non-linear type. The origin of the non-linearity can be widely varied and difficult to identify. In some cases, the relationship between absorption and the analytical parameter of interest is intrinsically non-linear owing to the very chemical nature of the sample or analyte concerned. In this work, various multivariate calibration procedures were tested with a view to overcoming intrinsic non-linearity in NIR reflectance. An approach to solving the problem is suggested. Calibration was done, after transformation of spectra, by using linear and non-linear techniques. The linear calibration techniques Ž . Ž . Ž . used are partial least squares PLS regression with and without variable selection , linear PLS with X projection LP-PLS Ž . and stepwise polynomial principal component SWP-PC regression. Non-linear calibration methods included polynomial PLS Ž . Ž . PPLS and artificial neural networks ANNs . Results were compared on the basis of NIR spectra for ampicillin trihydrate samples, where the simultaneous presence of crystallization water and surface moisture gives rise to intrinsic non-linearity that affects the determination of the total water content in the sample. The best results were obtained by using the non-linear calibration techniques. q

The problem of predicting a future value of a time series is considered in this paper. If the series follows a stationary Markov process, this can be done by nonparametric estimation of the autoregression function. Two forecasting algorithms are introduced. They only differ in the nonparametric kernel-type estimator used: the Nadaraya-Watson estimator and the local linear estimator. There are three major issues in the implementation of these algorithms: selection of the autoregressor variables; smoothing parameter selection and computing prediction intervals. These have been tackled using recent techniques borrowed from the nonparametric regression estimation literature under dependence. The performance of these nonparametric algorithms has been studied by applying them to a collection of 43 well-known time series. Their results have been compared to those obtained using classical Box-Jenkins methods. Finally, the practical behaviour of the methods is also illustrated by a detailed analysis of two data sets.

Physically based models are commonly used as an integral step in landslide hazard assessment. Geomorphic principles can be applied to a broad area, resulting in first order assessment of landslide susceptibility. New techniques are now available that may result in the increased accuracy of such models. We investigate the possibility to enhance landslide susceptibility modeling by integrating two physically-based landslide models, the Factor of Safety (FS) and the Shallow Stability model (SHALSTAB), with traditional empirical-statistical methods that utilize terrain attribute information derived from a digital elevation model and land use characteristics related to forest harvesting. The model performance is measured by the area under the receiver operating characteristic curve (AUROC) and sensitivity at 90% and 80% specificity both estimated by bootstrap resampling. Our study examines 278 landslide initiation points in the Klanawa Watershed located on Vancouver Island, British Columbia, Canada. We use a generalized additive model (GAM)and a logistic regression model (GLM) combining physical landslide models, terrain attributes and land use data, and GAMs and GLMs using only subsets of these variables.In this study, all empirical and combined physical-empirical models outperformthe physically-based models, with GAMs often performing significantly better than GLMs. The strongest predictive performance is achieved by the GAMsusing terrain attributes in combination with land use data. Variables representing physically-based models do not significantly improve the empirical models, but they may allow for a better physical interpretation of empirical models. Also, based on bootstrap variable-selection frequencies,land use data, FS, slope and plan/profile curvature are relatively the most important predictor variables.

Hypothesis testing is a model selection problem for which the solution proposed by the two main statistical streams of thought, frequentists and Bayesians, substantially differ. One may think that this fact might be due to the prior chosen in the Bayesian analysis and that a convenient prior selection may reconcile both approaches. However, the Bayesian robustness viewpoint has shown that, in general, this is not so and hence a profound disagreement between both approaches exists. In this paper we briefly revise the basic aspects of hypothesis testing for both the frequentist and Bayesian procedures and discuss the variable selection problem in normal linear regression for which the discrepancies are more apparent. Illustrations on simulated and real data are given.

In this paper we introduce two procedures for variable selection in cluster analysis and classification rules. One is mainly oriented to detect the "noisy" non-informative variables, while the other deals also with multicolinearity. A forward-backward algorithm is also proposed to make feasible these procedures in large data sets. A small simulation is performed and some real data examples are analyzed.

A problem of supervised learning from the multivariate time series (MTS) data where the target variable is potentially a highly complex function of MTS features is considered. This paper focuses on finding a compressed representation of MTS while preserving its predictive potential. Each time se- quence is decomposed into Chebyshev polynomials, and the decomposition coefficients are used as predictors in a statisti- cal learning model. The feature selection method capable of handling true multivariate effects is then applied to identify relevant Chebyshev features. MTS compression is achieved by keeping only those predictors that are pertinent to the re- sponse. The paper considers a problem of multivariate time series compression. We start with a dataset where each sample con- sists of several time series and a single response value. Indi- vidual series from the same sample correspond to the differ- ent variables with different physical characteristics generated by a process. Our g...

. The goal of the presented study is two-fold. First, we want to emphasize the power of Near Infrared Reflectance NIR spectroscopy for discrimination between mayonnaise samples containing different vegetable oils. Secondly, we want to use our data to compare the performances of different classification procedures. The NIR spectra with 351 variables correspond to equally spaced wavelengths in the 1100-2500 nm area. Feature extraction both by automatic wavelength-selection and by Ž . projection onto principal components PCs is discussed. The discriminant methods considered are linear discriminant analy-Ž . Ž . Ä 4 sis LDA , quadratic discriminant analysis QDA and regression with categorical 0,1 -responses. A dataset containing 162 spectra of mayonnaise samples based on six different vegetable oils is analyzed. By LDA with authentic cross-validation Ž . PC-models re-estimated for each cross-validation segment , only one sample was misclassified. Classification by allocating Ž Ž . a sample according to the largest fitted value of a linear regression Discriminant-Partial least squares DPLS or Discrimi-Ž .. nant-Principal components regression DPCR is demonstrated sub-optimal compared to LDA of the corresponding PLS-or Ž PCR-scores. QDA significantly outperforms LDA for projections of the data onto subspaces of moderate size scores of 7-9 . Ž. PCs . Two automatic variable-selection procedures choose 16 and 26 wavelengths variables , respectively from the spectra. Based on the selected wavelengths, LDA gives considerably better classification than the regression approach. By reporting the performances of several feature extraction techniques in tandem with three of the most common classification methods, Ž . Ž we hope that the reader will notice two relevant aspects: 1 By using the DPLS and DPCR classification by 'dummy' re-. Ž . gressions one is exposed to a significant risk of obtaining sub-optimal classification results; 2 The automatic wavelength selections may give valuable information about what is actually causing a successful discrimination. Such knowledge can, for instance, be used to select the most suited filters for online applications of NIR. Besides, from demonstrating different classification strategies, our study clearly shows that classification methods with NIR spectra can be used to discriminate between mayonnaise samples of different oil types and fatty acid composition. q 1999 Elsevier Science B.V. All rights reserved.

Dimension reduction and variable selection are two types of effective methods that deal with high-dimensional data. In particular, variable selection techniques are of wide-spread use and essentially consist of individual selection methods and interval selection methods. Given the fact that the vibrational spectra have continuous features of spectral bands, interval selection instead of individual spectral wavelength point selection allows for more stable models and easier interpretation. Numerous methods have been suggested for interval selection recently. Therefore, this paper is devoted to a selective review on interval selection methods with partial least squares (PLS) as the calibration model. We described the algorithms in the five classes: classic methods, penalty-based, sampling-based, correlation-based, and projection-based methods. Finally, we compared and discussed the performances of a subset of these methods on three real-world spectroscopic datasets.

In this presentation a methodology is suggested for site assessment and site selection based in a data analysis framework. This framework consists in tree steeps using different data analysis methods from cluster analysis, classification trees and regression analysis. The different variables selected in all the models used for the three steeps are compared and the spatial analysis data importance in site assessment is evaluated. For variable importance several measures can be used. In this text we use the discriminant power for the selection of profiling variables and a precision index for classification trees. Dominance analysis is used for the multiple regression models in the forecasting procedure. The advantage of this technique over other techniques as the standardized coefficients is that it overcomes some limitations of stepwise regression. The different measures of variable importance result in a clear pattern for the relevance of spatial analysis variables, being only dominated by the "trade area". So, spatial analysis resulting variables are of special importance in site assessment studies and the delimitation method used for their calculation is relevant in their usefulness.

Ž . The application of a genetic algorithm GA to the selection of principal components PCs is proposed as an efficient method to determine the optimal multivariate regression model. This stochastic method was compared with other determinis-Ž . tic methods such as: exhaustive search here taken as a validation procedure , forward and backward-stepwise variable selec-Ž . tion and correlation principal components regression CPCR . It is shown that for the range of data sets used, the GA gives the same result as the those obtained by an exhaustive search and by CPCR whereas the stepwise procedures do not. These Ž . results also show that in order to build optimal predictive models using principal components regression PCR one needs to select the best subset of PCs rather than simply use those with the highest eigenvalues. q

We propose a data mining approach to predict human wine taste preferences that is based on easily available analytical tests at the certification step. A large dataset (when compared to other studies in this domain) is considered, with white and red vinho verde samples (from Portugal). Three regression techniques were applied, under a computationally efficient procedure that performs simultaneous variable and model selection. The support vector machine achieved promising results, outperforming the multiple regression and neural network methods. Such model is useful to support the oenologist wine tasting evaluations and improve wine production.

This work deals with the use of multiple correspondence analysis (MCA) and a weighted Euclidean distance (the tolerance distance) as an exploratory tool in developing predictive logistic models. The method was applied to a living-donor kidney transplant data set with 109 cases and 13 predictors. This approach, followed by backward and forward selection procedures, yielded two models, one with four and another with two predictors. These models were compared to two other models, ordinarily built by backward and forward stepwise selection, which yielded, respectively, five and two predictors. After internal validation, the models performance statistics showed similar results. Likelihood ratio tests suggested that backward approach achieved a better fit than the forward modelling in both methods and the Vuong's non-nested test between backward-built models suggested that these were undistinguishable. We conclude that the tolerance distance, in combination with MCA, could be a feasible method for variable selection in logistic modelling, when there are several categorical predictors. c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 9 5 ( 2 0 0 9 ) 116-128 117 1.

Wind energy is having an increasing influence on the energy supply in many countries, but in contrast to conventional power plants, it is a fluctuating energy source. For its integration into the electricity supply structure, it is necessary to predict the wind power hours or days ahead. There are models based on physical, statistical and artificial intelligence approaches for the prediction of wind power. This paper introduces a new short-term prediction method based on the application of evolutionary optimization algorithms for the automated specification of two well-known time series prediction models, i.e., neural networks and the nearest neighbour search. Two optimization algorithms are applied and compared, namely particle swarm optimization and differential evolution. To predict the power output of a certain wind farm, this method uses predicted weather data and historic power data of that wind farm, as well as historic power data of other wind farms far from the location of the wind farm considered. Using these optimization algorithms, we get a reduction of the prediction error compared to the model based on neural networks with standard manually selected variables. An additional reduction in error can be obtained by using the mean model output of the neural network model and of the nearest neighbour search based prediction approach.

Variable selection is fundamenta l to high-dimensiona l statistical modeling, including nonparametri c regression. Many approaches in use are stepwise selection procedures , which can be computationally expensive and ignore stochastic errors in the variable selection process. In this article, penalized likelihood approache s are proposed to handle these kinds of problems. The proposed methods select variables and estimate coef cients simultaneously. Hence they enable us to construct con dence intervals for estimated parameters. The proposed approaches are distinguished from others in that the penalty functions are symmetric, nonconcav e on 401ˆ5, and have singularities at the origin to produce sparse solutions. Furthermore, the penalty functions should be bounded by a constant to reduce bias and satisfy certain conditions to yield continuous solutions. A new algorithm is proposed for optimizing penalized likelihood functions. The proposed ideas are widely applicable. They are readily applied to a variety of parametric models such as generalized linear models and robust regression models. They can also be applied easily to nonparametri c modeling by using wavelets and splines. Rates of convergenc e of the proposed penalized likelihood estimators are established. Furthermore, with proper choice of regularization parameters, we show that the proposed estimators perform as well as the oracle procedure in variable selection; namely, they work as well as if the correct submodel were known. Our simulation shows that the newly proposed methods compare favorably with other variable selection techniques. Furthermore, the standard error formulas are tested to be accurate enough for practical applications.

We provide an overview of latent variable methods used in pharmaceutics and integrated with advanced characterization techniques such as vibrational spectroscopy. The basics of the most common latent variable methods, principal component analysis (PCA), principal component regression (PCR) and partial least-squares (PLS) regression, are presented. Multiple linear regression (MLR) and methods for improved interpretation, variable selection, classification and validation are also briefly discussed. Extensive use of the methods is demonstrated by compilation of the recent literature.

Selection of proper phenotypic trait among various traits related with interesting performance plays an important role in genetic evaluation. In this study, principal components analysis (PCA) was adapted to generate a new index as a measure of racing performance of 12,279 horses. This method allows us to reduce the number of variables considered in the evaluation of the horses' racing performance, which may facilitate modeling genetic programs. The resulted racing time, earning prize and rank were selected for generating new indices as the representation of racing performance of the horses. Three indices used in this study were: 1) PCA1 generated from the modified values of racing time, earning prize and rank, 2) PCA2 generated from the modified racing time and rank, and 3) the adjusted racing time. The first principal components (PCs), elements in the eigenvector corresponding to the largest eigenvalue of PCA, of PCA1 and PCA2 explained the variance of the selected variables about 75.6% and 75.4% respectively. Linear combinations of the first PCs and adjusted variables were used as new performance indices. Those animal models were composed of significant explanatory variables selected by Akaike information criterion (AIC). Heritability and repeatability were 0.324 (± 0.026) and 0.334 (±0.034) for adjusted racing time, 0.319 (± 0.014) and 0.326 (± 0.018) for PCA1, and 0.324 (±0.010) and 0.332 (± 0.012) for PCA2 respectively. Estimated heritabilities and repeatabilities for three indices showed similar values for domestic racing records. However, models using PCA showed better fitting for data than model using racing time as a performance index. The proposed methodology is efficient to evaluate the total variance in this group of correlated traits, allowing reduction in the number of variables for genetic evaluation and construction of better fitting model.

Mixture designs and corresponding analysis techniques are of considerable importance in food science and industry. Mixture data are generally challenging to model, since the mixture restrictions leads to both exact and near collinearity. Scheffé found an excellent way to eliminate the exact collinearity, by using a certain reparameterization of the ordinary least squares (OLS) regression model. Near collinearities can be eliminated by, for instance, variable selection. Partial least squares (PLS) regression does not assume linearly independent variables and handles both exact and near collinearity by projecting onto a lower dimensional subspace. Lately also variable selection has been combined with PLS regression in order to get more parsimonious models. In the present study, models found by OLS and PLS regression, both combined with variable selection, are compared with regard to interpretation, response optimisation and prediction, for regular mixtures, mixture -process and crossed mixture data. Examples from sausages and hearth bread production are considered. D

Least Angle Regression is a promising technique for variable selection applications, offering a nice alternative to stepwise regression. It provides an explanation for the similar behavior of LASSO (ℓ 1 -penalized regression) and forward stagewise regression, and provides a fast implementation of both. The idea has caught on rapidly, and sparked a great deal of research interest. In this paper, we give an overview of Least Angle Regression and the current state of related research.

A new approach for variable influence on projection (VIP) is described, which takes full advantage of the orthogonal projections to latent structures (OPLS) model formalism for enhanced model interpretability. This means that it will include not only the predictive components in OPLS but also the orthogonal components. Four variants of variable influence on projection (VIP) adapted to OPLS have been developed, tested and compared using three different data sets, one synthetic with known properties and two real-world cases.

The archives of species range polygons developed under comprehensive assessments of the conservation status of species, such as the IUCN's Global Assessments, are a significant resource in the analysis of biodiversity for conservation planning. Species range polygons obtained from these studies are known to exhibit omissions (because of knowledge gaps) and imprecision in their boundaries. In this work, we present a method to refine those species range polygons in order to create more realistic representations of species geographic ranges. Using range polygons of four species of mammals in South America and environmental variables at a 1 km resolution, combined with a set of GIS algorithms, a procedure was developed to map the confidence that sub-polygon elements belong to a logical species range. The confidence map is then used as a weight for a Mahalanobis typicality empirical modelling procedure to generate a map of species-weighted typicalities that is then thresholded to generate the refined species range map. Methods for variable selection and quality assessment of the refined range are also included in the procedure. Analysis using independent validation data shows the power of this methodology to redefine species ranges in a more biophysically reasonable way. The quality of the final-range map depends on the habitat suitability threshold used to define the species range. The report of quality assessment produced is useful for identifying not only the threshold that produces the highest match to the original expert range but also for flagging those ranges with higher discrepancies, facilitating the identification of ranges that need further revision.

We present a new Stata program, vselect, that helps users perform variable selection after performing a linear regression. Options for stepwise meth- ods such as forward selection and backward elimination are provided. The user may specify Mallows’s Cp, Akaike’s information criterion, Akaike’s corrected informa- tion criterion, Bayesian information criterion, or R2 adjusted as the information criterion for the selection. When

We present a new Stata program, vselect, that helps users perform variable selection after performing a linear regression. Options for stepwise meth- ods such as forward selection and backward elimination are provided. The user may specify Mallows’s Cp, Akaike’s information criterion, Akaike’s corrected informa- tion criterion, Bayesian information criterion, or R2 adjusted as the information criterion for the selection. When the user specifies the best subset option, the leaps-and-bounds algorithm (Furnival and Wilson, Technometrics 16: 499–511) is used to determine the best subsets of each predictor size. All the previously men- tioned information criteria are reported for each of these subsets. We also provide options for doing variable selection only on certain predictors (as in [R] nestreg) and support for weighted linear regression. All options are demonstrated on real datasets with varying numbers of predictors.

In this paper, we describe an extension approach to the backtracking with look-ahead forward checking method that adopts weighted partial satisfaction of soft constraints that has been implemented to the development of an automated teaching assignment timetabling system. Determining the optimal solution for a teaching assignment problem is a challenging task. The objective is to construct a timetable for professors from already scheduled courses that satisfy both hard constraints (problem requirements such as no teacher should be assigned two courses at the same time) and soft constraints (teacher preferences) based on fairness principle in distributing courses among professors. The approach is done mainly to modify the variable selection method and the value assignment technique taking into account preferences and based on fairness principle. The optimized look-ahead backtracking method applied to the solution is presented and discussed along with computational results.

Penalized regression methods for simultaneous variable selection and coefficient estimation, especially those based on the lasso of , have received a great deal of attention in recent years, mostly through frequentist models. Properties such as consistency have been studied, and are achieved by different lasso variations. Here we look at a fully Bayesian formulation of the problem, which is flexible enough to encompass most versions of the lasso that have been previously considered. The advantages of the hierarchical Bayesian formulations are many. In addition to the usual ease-of-interpretation of hierarchical models, the Bayesian formulation produces valid standard errors (which can be problematic for the frequentist lasso), and is based on a geometrically ergodic Markov chain. We compare the performance of the Bayesian lassos to their frequentist counterparts using simulations, data sets that previous lasso papers have used, and a difficult modeling problem for predicting the collapse of governments around the world. In terms of prediction mean squared error, the Bayesian lasso performance is similar to and, in some cases, better than, the frequentist lasso.

Similar to variable selection in the linear regression model, selecting significant components in the popular additive regression model is of great interest. However, such components are unknown smooth functions of independent variables, which are unobservable. As such, some approximation is needed. In this paper, we suggest a combination of penalized regression spline approximation and group variable selection, called the lasso-type spline method (LSM), to handle this component selection problem with a diverging number of strongly correlated variables in each group. It is shown that the proposed method can select significant components and estimate nonparametric additive function components simultaneously with an optimal convergence rate simultaneously. To make the LSM stable in computation and able to adapt its estimators to the level of smoothness of the component functions, weighted power spline bases and projected weighted power spline bases are proposed. Their performance is examined by simulation studies across two set-ups with independent predictors and correlated predictors, respectively, and appears superior to the performance of competing methods.

Eight different variable selection techniques for model-based and non-model-based clustering are evaluated across a wide range of cluster structures. It is shown that several methods have difficulties when non-informative variables (i.e., random noise) are included in the model. Furthermore, the distribution of the random noise greatly impacts the performance of nearly all of the variable selection procedures. Overall, a variable

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many 9 Extensions 96 10 Conclusions 98 Acknowledgements 101

The relationship between climatic change and human evolution can be framed in terms of three major hypotheses. A modern version of the long-held savanna hypothesis posits that the expansion of grassland ecosystems in Africa was driven by global climatic change and led to the divergence of hominins from the apes and to the origin of the Homo clade. A related idea suggests that hominins originated in the late Miocene, and Homo in the late Pliocene, as constituents of broader pulses of faunal turnover synchronized by episodes of global climatic change. A more recent concept, the variability selection hypothesis, emphasizes the importance of fluctuating climates and environments, rather than any single trend, in shaping human adaptation and evolution. Here we evaluate these ideas for the Plio-Pleistocene in light of new analyses of fossil mammals from the Turkana Basin of Kenya and Ethiopia. Our results show that between 4 and 1 Ma (million years ago), there were profound faunal changes in the Turkana Basin. The most important of these changes include significant shifts in the abundance of the common families of mammals, episodes of high faunal turnover, and an increase in the number and abundance of species that show adaptations to grassland ecosystems. Episodes of relatively high faunal turnover occurred in the intervals 3.4 -3.2, 2.8 -2.6, 2.4 -2.2, and 2.0 -1.8 Ma. Paranthropus and Homo appear in the Turkana Basin during successive intervals of high turnover at 2.8 -2.6 and at 2.4 -2.2 Ma, while the appearance of Homo erectus is coupled to a major episode of turnover and grassland expansion after 2 Ma. Thus, there was not a single turnover pulse of relevance to late Pliocene hominins, but multiple events that successively led to the appearance of Paranthropus, early Homo, and H. erectus. Our results also show evidence of large-scale, 100 ky-periodicity shifts in the fauna beginning at 2.5 Ma, during the time that Homo and lithic artifacts first appear in the Turkana Basin, lending support to the variability selection hypothesis [Science 273 (1996) 922;

A web-based application has been designed from a genetic-epidemiology point of view to analyze association studies. Main capabilities include: descriptive analysis, test for Hardy-Weinberg equilibrium and linkage disequilibrium. Analysis of association is based on linear or logistic regression according to the response variable (quantitative or binary disease status respectively). Analysis of single SNPs: multiple inheritance models (co-dominant, dominant, recessive, additive and super-dominant), and analysis of interactions (gene-gene or gene-environment). Analysis of multiple SNPs: haplotype frequency estimation, analysis of association of haplotypes with the response, including analysis of interactions. Availability: Main page: http://bioinfo.iconcologia.net/SNPstats. Source code for local installation is available under GNU license. Contact: [email protected] Supplementary information: Figures with a sample run are available on Bioinformatics online. A detailed online tutorial is available within the application.

It is frequently the case with Big Data that you have a gazillion exogenous predictor time series that you need to analyze so you can build a dynamic regression time series model. 1 The %ARIMA_SELECT macro can help you to determine which exogenous predictors 2 are strongly correlated with your response variable and which are not. The %ARIMA_SELECT macro is designed to rank-order individual exogenous time series according to a user-specified performance measure, and can be a valuable tool for reducing the dimensionality of your data. It can also perform variable selection using forward selection or " all subsets " selection for model building.