Using Subset Log-Likelihoods to Trim Outliers in Gaussian Mixture Models

Mixtures of Gaussian distributions are a popular choice in model-based clustering. Outliers can affect parameters estimation and, as such, must be accounted for. Predicting the proportion of outliers correctly is paramount as it minimizes misclassification error. It is proved that, for a finite Gaussian mixture model, the log-likelihoods of the subset models are distributed according to a mixture of beta distributions. An algorithm is then proposed that predicts the proportion of outliers by measuring the adherence of a set of subset log-likelihoods to a beta mixture reference distribution. This algorithm removes the least likely points, which are deemed outliers, until model assumptions are met

Long-Term Impact of Lifelong Fitness: Examining Longitudinal Exercise Behavior in College Students

Over time, the United States population has gradually shifted to an increasingly inactive lifestyle, and there has been a decline in health behavior. Only 50% of the population meet the recommended guidelines for weekly physical activity. With this glaring increase of inactive lifestyles, programs designed to increase health behavior change have become crucial. One solution to this problem has been a required Lifelong Fitness class at George Fox University where new college students learn knowledge and skills to implement for healthier lifestyles during this transformative time. A multiple regression model predicting long-term exercise by pre-minutes of exercise, post-minutes of exercise, and current exercise self-efficacy was fit to data. The model accounted for 18% of variance shared in all the predictors. When all variables were entered in the model, pre-minutes of exercise and current exercise self-efficacy were significant. There were no significant changes in mean levels of exercise longitudinally, suggesting the course helped students maintain levels of activity, but not increase them

Predicting software project effort: A grey relational analysis based method

This is the post-print version of the final paper published in Expert Systems with Applications. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2011 Elsevier B.V.The inherent uncertainty of the software development process presents particular challenges for software effort prediction. We need to systematically address missing data values, outlier detection, feature subset selection and the continuous evolution of predictions as the project unfolds, and all of this in the context of data-starvation and noisy data. However, in this paper, we particularly focus on outlier detection, feature subset selection, and effort prediction at an early stage of a project. We propose a novel approach of using grey relational analysis (GRA) from grey system theory (GST), which is a recently developed system engineering theory based on the uncertainty of small samples. In this work we address some of the theoretical challenges in applying GRA to outlier detection, feature subset selection, and effort prediction, and then evaluate our approach on five publicly available industrial data sets using both stepwise regression and Analogy as benchmarks. The results are very encouraging in the sense of being comparable or better than other machine learning techniques and thus indicate that the method has considerable potential.National Natural Science Foundation of Chin

Implementation of Winsorizing and random oversampling on data containing outliers and unbalanced data with the random forest classification method

Many researchers conduct research using the classification method, to find out the best method for predicting the class of an observation. Some of these studies explain that random forest is the best method. However, the classification of data containing outliers and unbalanced data is a complicated problem. Many researchers are also conducting research to deal with these problems. In this study, we propose a winsorizing to deal with outliers by replacing the outlier values with the upper and lower limit values obtained from the interquartile range method and random oversampling to balance the data. It is also known that cases of the Human Development Index (HDI) in regencies/cities in eastern Indonesia vary widely, so cases of HDI in these areas can be used as case studies of data containing outliers and unbalanced data. The purpose of this study was to compare the performance of the random forest before and after the data were applied to the winsorizing and random oversampling to predict HDI in districts/cities in eastern Indonesia. Classification method random forest after handling data containing outliers and unbalanced data has better performance in terms of accuracy and kappa values, which are 96.43% and 93.41%, respectively. The variables of expenditure per capita and the mean years of schooling are the most important