Roberta A. de A. Fagundes

Robust regression with application to symbolic interval data

This paper presents a robust regression model that deals with cases that have interval-valued outliers in the input data set. Each interval of the input data is represented by its range and midpoint and the fitting to interval-valued data is not sensible in the presence of midpoint and/or range outliers on the interval response. The predictions of the lower and upper bounds of new intervals are performed and simulation studies are carried out to validate these predictions. Two applications with real-life interval data sets are considered. The prediction quality is assessed by a mean magnitude of relative error calculated from a test data set.

Interval kernel regression

Kernel regression is more attractive when it is not possible to determine explicit parametric form of the model and moreover, it does not depend on probabilistic distribution. This paper introduces kernel regression in which the input data set is described by interval-value variables. Two model families are considered. The first family estimates the bounds of the intervals regarding either a smooth function for center variables of the intervals (first model) or two smooth functions for range and center variables, respectively (second model). The second family performs the estimates of the intervals based on regression mixtures. These mixtures assume either a smooth function for center variables and a linear function based on least squares for range variables (third model) or a smooth function for range variables and a linear function for center variables (fourth model). The predictions of the lower and upper bounds of new intervals are computed and two different simulation studies are carried out to validate these predictions. Five real-life interval data sets are also considered. The prediction quality is assessed by a mean magnitude of relative error calculated from a test data set.

Quantile regression of interval-valued data

Linear regression is a standard statistical method widely used for prediction. It focuses on modeling the mean the target variable without accounting for all the distributional properties of this variable. In contrast, the quantile regression model facilitates the analysis of the full distributional properties, it allows to model different quantities of the target variable. This paper proposes a quantile regression model for interval data. In this model, each interval variable of the input data is represented by its range and center and a smooth function between two vectors composed by interval variables are defined. In order to test the usefulness of the proposed model, a simulation study is undertaken and an application using a scientific production interval data set of institutions from Brazil is performed. The quality of the interval prediction obtained by the proposed model is assessed by mean magnitude of relative error calculated from test data.

Nearest-neighborhood linear regression in an application with software effort estimation

This paper discusses nearest-neighborhood linear regression methods in a statistical view of learning and present an application of these models to software project effort estimation. The usefulness of the models is highlighted through experiments with a well-known NASA software project data set. A comparative study with global regression methods such as bagging predictors, support vector regression, radial basis functions neural networks is also introduced.

A Robust Prediction Method for Interval Symbolic Data

This paper introduces a robust prediction method for symbolic interval data based on the simple linear regression methodology. Each example of the data set is described by feature vector, for which each feature is an interval. Two classic robust regression models are fitted, respectively for range and mid-points of the interval values assumed by the variables in the data set. The prediction of the lower and upper bounds of the new intervals is performed from these fits. To validate this model, experiments with a synthetic interval data set and an application with a cardiology interval-valued data set are considered. The fit and prediction qualities are assessed by a pooled root mean square error measure calculated from learning and test data sets, respectively.

Zero-inflated prediction model in software-fault data

Software fault data with many zeroes in addition to large non-zero values are common in the software estimation area. A two-component prediction approach that provides a robust way to predict this type of data is introduced in this study. This approach allows to combine parametric and non-parametric models to improve the prediction accuracy. This way provides a more flexible structure to understand data. To show the usefulness of the proposed approach, experiments using eight projects from the NASA repository are considered. In addition, this method is compared with methods from the machine learning and statistical literature. The performance of the methods is measured by the prediction accuracy that is assessed based on the mean magnitude of relative errors.

An interval nonparametric regression method

This paper proposes a nonparametric multiple regression method for interval data. Regression smoothing investigates the association between an explanatory variable and a response variable. Here, each interval variable of the input data is represented by its range and center and a smooth function between a pair of vector of interval variables is defined. In order to test the suitability of the proposed model, a simulation study is undertaken and an application using thirteen project data of the NASA repository to estimate interval software size is also considered. These real data represent variability and/or uncertainty innate to the project data. The prediction quality is assessed by a mean magnitude of relative errors calculated from test data.

Two pattern classifiers for interval data based on binary regression models

This paper introduces two classifiers for interval symbolic data based on logit and probit regression models, respectively. Each example of the learning set is described by a feature vector, for which each feature value is an interval and a binary response that defines the class of this example. For each classifier two versions are considered. First fits a classic binary regression model conjointly on the lower and upper bounds of the interval values assumed by the variables in the learning set. Second fits a classic binary regression model separately on the lower and upper bounds of the intervals. The prediction of the class for new examples is accomplished from the computation of the posterior probabilities of the classes. To show the usefulness of this method, examples with synthetic symbolic data sets with overlapping classes are considered.

A Symbolic Pattern Classifier for Interval Data Based on Binary Probit Analysis

This paper introduces a classifier for interval symbolic data based on the probit regression model. Each example of the learning set is described by a feature vector, for which each feature value is an interval. Two versions of this classifier are considered. First fits the classic probit regression model conjointly on the lower and upper bounds of the interval values assumed by the variables in the learning set. Second fits the classic probit model separately on the lower and upper bounds of the intervals. The prediction of the class for new examples is accomplished from the computation of the posterior probabilities of the classes. To show the usefulness of this method, examples with synthetic symbolic data sets with overlapping classes are considered. The assessment of the proposed classification method is based on the estimation of the average behaviour of the error rate in the framework of the Monte Carlo method.

Performance Evaluation of CORBA Concurrency Control Service Using Stochastic Petri Nets

The interest in performance evaluation of middleware systems is increasing. Measurement techniques are still predominant among those used to carry out performance evaluation. However, performance models are currently being defined due to their flexibility, precision and facilities to carry out capacity planning activities. This paper presents stochastic Petri net models for performance evaluation of the CORBA Concurrency Control Service (CCS), which mediates concurrent access to objects. In order to validate the proposed models, CCS performance results obtained using those models are then compared against ones obtained through actual measurements.