Special Issue “Statistical Data Modeling and Machine Learning with Applications II”

Currently, we are witnessing rapid progress and synergy between mathematics and computer science [...

Assessment of Students’ Achievements and Competencies in Mathematics Using CART and CART Ensembles and Bagging with Combined Model Improvement by MARS

The aim of this study is to evaluate students’ achievements in mathematics using three machine learning regression methods: classification and regression trees (CART), CART ensembles and bagging (CART-EB) and multivariate adaptive regression splines (MARS). A novel ensemble methodology is proposed based on the combination of CART and CART-EB models in a new ensemble to regress the actual data using MARS. Results of a final exam test, control and home assignments, and other learning activities to assess students’ knowledge and competencies in applied mathematics are examined. The exam test combines problems on elements of mathematical analysis, statistics and a small practical project. The project is the new competence-oriented element, which requires students to formulate problems themselves, to choose different solutions and to use or not use specialized software. Initially, empirical data are statistically modeled using six CART and six CART-EB competing models. The models achieve a goodness-of-fit up to 96% to actual data. The impact of the examined factors on the students’ success at the final exam is determined. Using the best of these models and proposed novel ensemble procedure, final MARS models are built that outperform the other models for predicting the achievements of students in applied mathematics

Multi-Step Ahead Ex-Ante Forecasting of Air Pollutants Using Machine Learning

In this study, a novel general multi-step ahead strategy is developed for forecasting time series of air pollutants. The values of the predictors at future moments are gathered from official weather forecast sites as independent ex-ante data. They are updated with new forecasted values every day. Each new sample is used to build- a separate single model that simultaneously predicts future pollution levels. The sought forecasts were estimated by averaging the actual predictions of the single models. The strategy was applied to three pollutants—PM10, SO2, and NO2—in the city of Pernik, Bulgaria. Random forest (RF) and arcing (Arc-x4) machine learning algorithms were applied to the modeling. Although there are many highly changing day-to-day predictors, the proposed averaging strategy shows a promising alternative to single models. In most cases, the root mean squared errors (RMSE) of the averaging models (aRF and aAR) for the last 10 horizons are lower than those of the single models. In particular, for PM10, the aRF’s RMSE is 13.1 vs. 13.8 micrograms per cubic meter for the single model; for the NO2 model, the aRF exhibits 21.5 vs. 23.8; for SO2, the aAR has 17.3 vs. 17.4; for NO2, the aAR’s RMSE is 22.7 vs. 27.5, respectively. Fractional bias is within the same limits of (−0.65, 0.7) for all constructed models