Evolutionary model trees for handling continuous classes in machine learning

Model trees are a particular case of decision trees employed to solve regression problems. They have the advantage of presenting an interpretable output, helping the end-user to get more confidence in the prediction and providing the basis for the end-user to have new insight about the data, confirming or rejecting hypotheses previously formed. Moreover, model trees present an acceptable level of predictive performance in comparison to most techniques used for solving regression problems. Since generating the optimal model tree is an NP-Complete problem, traditional model tree induction algorithms make use of a greedy top-down divide-and-conquer strategy, which may not converge to the global optimal solution. In this paper, we propose a novel algorithm based on the use of the evolutionary algorithms paradigm as an alternate heuristic to generate model trees in order to improve the convergence to globally near-optimal solutions. We call our new approach evolutionary model tree induction (E-Motion). We test its predictive performance using public UCI data sets, and we compare the results to traditional greedy regression/model trees induction algorithms, as well as to other evolutionary approaches. Results show that our method presents a good trade-off between predictive performance and model comprehensibility, which may be crucial in many machine learning applications. (C) 2010 Elsevier Inc. All rights reserved.

PK/DB: database for pharmacokinetic properties and predictive in silico ADME models

The study of pharmacokinetic properties (PK) is of great importance in drug discovery and development. In the present work, PK/DB (a new freely available database for PK) was designed with the aim of creating robust databases for pharmacokinetic studies and in silico absorption, distribution, metabolism and excretion (ADME) prediction. Comprehensive, web-based and easy to access, PK/DB manages 1203 compounds which represent 2973 pharmacokinetic measurements, including five models for in silico ADME prediction (human intestinal absorption, human oral bioavailability, plasma protein binding, bloodbrain barrier and water solubility).

Intrinsically Multivariate Predictive Genes

Canalizing genes possess such broad regulatory power, and their action sweeps across a such a wide swath of processes that the full set of affected genes are not highly correlated under normal conditions. When not active, the controlling gene will not be predictable to any significant degree by its subject genes, either alone or in groups, since their behavior will be highly varied relative to the inactive controlling gene. When the controlling gene is active, its behavior is not well predicted by any one of its targets, but can be very well predicted by groups of genes under its control. To investigate this question, we introduce in this paper the concept of intrinsically multivariate predictive (IMP) genes, and present a mathematical study of IMP in the context of binary genes with respect to the coefficient of determination (CoD), which measures the predictive power of a set of genes with respect to a target gene. A set of predictor genes is said to be IMP for a target gene if all properly contained subsets of the predictor set are bad predictors of the target but the full predictor set predicts the target with great accuracy. We show that logic of prediction, predictive power, covariance between predictors, and the entropy of the joint probability distribution of the predictors jointly affect the appearance of IMP genes. In particular, we show that high-predictive power, small covariance among predictors, a large entropy of the joint probability distribution of predictors, and certain logics, such as XOR in the 2-predictor case, are factors that favor the appearance of IMP. The IMP concept is applied to characterize the behavior of the gene DUSP1, which exhibits control over a central, process-integrating signaling pathway, thereby providing preliminary evidence that IMP can be used as a criterion for discovery of canalizing genes.

Deviance residuals in generalised log-gamma regression models with censored observations

In this article, we compare three residuals based on the deviance component in generalised log-gamma regression models with censored observations. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. For all cases studied, the empirical distributions of the proposed residuals are in general symmetric around zero, but only a martingale-type residual presented negligible kurtosis for the majority of the cases studied. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for the martingale-type residual in generalised log-gamma regression models with censored data. A lifetime data set is analysed under log-gamma regression models and a model checking based on the martingale-type residual is performed.

Improved likelihood inference for the shape parameter in Weibull regression

We obtain adjustments to the profile likelihood function in Weibull regression models with and without censoring. Specifically, we consider two different modified profile likelihoods: (i) the one proposed by Cox and Reid [Cox, D.R. and Reid, N., 1987, Parameter orthogonality and approximate conditional inference. Journal of the Royal Statistical Society B, 49, 1-39.], and (ii) an approximation to the one proposed by Barndorff-Nielsen [Barndorff-Nielsen, O.E., 1983, On a formula for the distribution of the maximum likelihood estimator. Biometrika, 70, 343-365.], the approximation having been obtained using the results by Fraser and Reid [Fraser, D.A.S. and Reid, N., 1995, Ancillaries and third-order significance. Utilitas Mathematica, 47, 33-53.] and by Fraser et al. [Fraser, D.A.S., Reid, N. and Wu, J., 1999, A simple formula for tail probabilities for frequentist and Bayesian inference. Biometrika, 86, 655-661.]. We focus on point estimation and likelihood ratio tests on the shape parameter in the class of Weibull regression models. We derive some distributional properties of the different maximum likelihood estimators and likelihood ratio tests. The numerical evidence presented in the paper favors the approximation to Barndorff-Nielsen`s adjustment.

Measuring time series predictability using support vector regression

Most studies involving statistical time series analysis rely on assumptions of linearity, which by its simplicity facilitates parameter interpretation and estimation. However, the linearity assumption may be too restrictive for many practical applications. The implementation of nonlinear models in time series analysis involves the estimation of a large set of parameters, frequently leading to overfitting problems. In this article, a predictability coefficient is estimated using a combination of nonlinear autoregressive models and the use of support vector regression in this model is explored. We illustrate the usefulness and interpretability of results by using electroencephalographic records of an epileptic patient.

On beta regression residuals

We propose two new residuals for the class of beta regression models, and numerically evaluate their behaviour relative to the residuals proposed by Ferrari and Cribari-Neto. Monte Carlo simulation results and empirical applications using real and simulated data are provided. The results favour one of the residuals we propose.

Improved score tests in symmetric linear regression models

The class of symmetric linear regression models has the normal linear regression model as a special case and includes several models that assume that the errors follow a symmetric distribution with longer-than-normal tails. An important member of this class is the t linear regression model, which is commonly used as an alternative to the usual normal regression model when the data contain extreme or outlying observations. In this article, we develop second-order asymptotic theory for score tests in this class of models. We obtain Bartlett-corrected score statistics for testing hypotheses on the regression and the dispersion parameters. The corrected statistics have chi-squared distributions with errors of order O(n(-3/2)), n being the sample size. The corrections represent an improvement over the corresponding original Rao`s score statistics, which are chi-squared distributed up to errors of order O(n(-1)). Simulation results show that the corrected score tests perform much better than their uncorrected counterparts in samples of small or moderate size.

Size and power properties of some tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the non-null distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the Birnbaum-Saunders regression model. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the shape parameter. Monte Carlo simulation is presented in order to compare the finite-sample performance of these tests. We also present two empirical applications. (C) 2010 Elsevier B.V. All rights reserved.

Signed likelihood ratio tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders regression model is becoming increasingly popular in lifetime analyses and reliability studies. In this model, the signed likelihood ratio statistic provides the basis for testing inference and construction of confidence limits for a single parameter of interest. We focus on the small sample case, where the standard normal distribution gives a poor approximation to the true distribution of the statistic. We derive three adjusted signed likelihood ratio statistics that lead to very accurate inference even for very small samples. Two empirical applications are presented. (C) 2010 Elsevier B.V. All rights reserved.

Comparing diagnostic tests with missing data

When missing data occur in studies designed to compare the accuracy of diagnostic tests, a common, though naive, practice is to base the comparison of sensitivity, specificity, as well as of positive and negative predictive values on some subset of the data that fits into methods implemented in standard statistical packages. Such methods are usually valid only under the strong missing completely at random (MCAR) assumption and may generate biased and less precise estimates. We review some models that use the dependence structure of the completely observed cases to incorporate the information of the partially categorized observations into the analysis and show how they may be fitted via a two-stage hybrid process involving maximum likelihood in the first stage and weighted least squares in the second. We indicate how computational subroutines written in R may be used to fit the proposed models and illustrate the different analysis strategies with observational data collected to compare the accuracy of three distinct non-invasive diagnostic methods for endometriosis. The results indicate that even when the MCAR assumption is plausible, the naive partial analyses should be avoided.

Improved likelihood inference in beta regression

We consider the issue of performing accurate small-sample likelihood-based inference in beta regression models, which are useful for modelling continuous proportions that are affected by independent variables. We derive small-sample adjustments to the likelihood ratio statistic in this class of models. The adjusted statistics can be easily implemented from standard statistical software. We present Monte Carlo simulations showing that inference based on the adjusted statistics we propose is much more reliable than that based on the usual likelihood ratio statistic. A real data example is presented.

Three Bartlett-type corrections for score statistics in symmetric nonlinear regression models

We present simple matrix formulae for corrected score statistics in symmetric nonlinear regression models. The corrected score statistics follow more closely a chi (2) distribution than the classical score statistic. Our simulation results indicate that the corrected score tests display smaller size distortions than the original score test. We also compare the sizes and the powers of the corrected score tests with bootstrap-based score tests.

Bayesian estimation of regression parameters in elliptical measurement error models

The main object of this paper is to discuss the Bayes estimation of the regression coefficients in the elliptically distributed simple regression model with measurement errors. The posterior distribution for the line parameters is obtained in a closed form, considering the following: the ratio of the error variances is known, informative prior distribution for the error variance, and non-informative prior distributions for the regression coefficients and for the incidental parameters. We proved that the posterior distribution of the regression coefficients has at most two real modes. Situations with a single mode are more likely than those with two modes, especially in large samples. The precision of the modal estimators is studied by deriving the Hessian matrix, which although complicated can be computed numerically. The posterior mean is estimated by using the Gibbs sampling algorithm and approximations by normal distributions. The results are applied to a real data set and connections with results in the literature are reported. (C) 2011 Elsevier B.V. All rights reserved.

Prediction in Multilevel Logistic Regression

The purpose of this article is to present a new method to predict the response variable of an observation in a new cluster for a multilevel logistic regression. The central idea is based on the empirical best estimator for the random effect. Two estimation methods for multilevel model are compared: penalized quasi-likelihood and Gauss-Hermite quadrature. The performance measures for the prediction of the probability for a new cluster observation of the multilevel logistic model in comparison with the usual logistic model are examined through simulations and an application.