# Identifying At-Risk Students for Early Intervention--A Probabilistic Machine Learning Approach
## 2 Literature Review
### Predictive Analytics for at-Risk Student Identification  
In higher education, identifying at-risk students for timely intervention is a significant problem [5; 6; 8]. Studies on at-risk student identification provide evidence on the usefulness of utilizing various machine learning algorithms to identify low-performing or at-risk students as a course progresses. A time-series clustering approach to identifying at-risk online students was proposed by [8], who investigated if time-series clustering can outperform traditional methods in terms of accuracy, using dynamic data that consisted of Moodle logs, and static data representing students' demographics and academic performances observed over 16 weeks. The analysis used six predictive algorithms: logistic regression (forward, backward, and stepwise), decision trees, rule induction, and boosting. The study concludes that the time-series clustering approach, in accuracy and feasibility, outperforms aggregated models built on machine learning and time-series algorithms alone. The decision tree was the best-performing algorithm, achieving an accuracy of 84%, and it had the ability to accurately capture at-risk students from week 10. [PERSON] [6] investigated the effects of time-variant (dynamic) data and time-invariant (static) data on the accurate prediction of at-risk students in an online course. [PERSON] [6] suggests combining multiple algorithms to achieve more accurate results. This was presented in three decision schemes: Scheme 1 requires at least one algorithm to classify a student as being at-risk for the student to be considered at-risk; and Schemes 2 and 3 needed at least two and three algorithms, respectively. The three algorithms used to support the three schemes for 10 weeks were the instance-based learning classifier, decision trees, and naive Bayes. The study concludes that excluding time-invariant data has no significant influence on the overall results of classifying at-risk students. In another study, low-cost learning analytics practices were used to identify at-risk students in a quantitative methods in business course taken by undergraduate students [5]. The study used student demographic data, summative assessments, and clicker responses as formative assessments. Using data generated from the learning management system, the researchers used Google Sheets and Google Forms to collect and analyze clicker data. The study used linear and logistic regression to identify at-risk students in five stages over 12 weeks, with three weeks intervals per stage. The study found that linear regression could be more acceptable, due to its more refined recall performance (the ability of predictive models to identify at-risk students) with prediction intervals. It is less frequently used than logistic regression in previous studies. Reading data from Student's eBook was used to develop an early identification system for students at-risk of academic failure in the context of eBook-based teaching and learning [17]. This study used data from 90 undergraduate students in an elementary informatics course over 16 weeks. The researchers created prediction models using 13 algorithms. The algorithms were evaluated using [PERSON]'s kappa to determine the degree to which the model performed better than chance, and accuracy. The study found that the algorithms achieved their best performances from week 15, and the predictive models classified at-risk students with an accuracy of over 79% from week three. The researchers noted that predictive models with transformed data yielded poor performances. Various machine learning techniques have been applied to identify at-risk students [5; 6; 8; 17], the most common ones being decision trees, the random forest, neural networks, the support vector machine, and naive Bayes. The machine learning techniques are implemented and compared using accuracy, F-score, recall, and precision [1; 7; 10].