In higher educational institutes, many students have to struggle hard to complete different courses since there is no dedicated support offered to students who need special attention in the registered courses. Machine learning techniques can be utilized for students' grades prediction in different courses. Such techniques would help students to improve their performance based on predicted grades and would enable instructors to identify such individuals who might need assistance in the courses. In this paper, we use Collaborative Filtering (CF), Matrix Factorization (MF), and Restricted Boltzmann Machines (RBM) techniques to systematically analyze a real-world data collected from Information Technology University (ITU), Lahore, Pakistan. We evaluate the academic performance of ITU students who got admission in the bachelor's degree program in ITU's Electrical Engineering department. The RBM technique is found to be better than the other techniques used in predicting the students' performance in the particular course.
Hidden Markov model has been used widely to model student learning. @cite_23 investigated solutions of hidden Markov model and concluded that the utilization of a maximum likelihood test should be the preferred method for finding parameter values for the hidden Markov Model. @cite_1 in a separate study developed and analyzed a new fitting procedure for Bayesian Knowledge Tracing and concluded that empirical probabilities had the comparable predictive accuracy to that of expectation maximization.
@cite_1 @cite_23
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Hidden Markov models (HMMs) have during the last decade become a widespread tool for modeling sequences of dependent random variables. Inference for such models is usually based on the maximum-likelihood estimator (MLE), and consistency of the MLE for general HMMs was recently proved by Leroux. In this paper we show that under mild conditions the MLE is also asymptotically normal and prove that the observed information matrix is a consistent estimator of the Fisher information. This paper describes an extension to the hidden Markov model for part-of-speech tagging using second-order approximations for both contextual and lexical probabilities. This model increases the accuracy of the tagger to state of the art levels. These approximations make use of more contextual information than standard statistical systems. New methods of smoothing the estimated probabilities are also introduced to address the sparse data problem. Bayesian knowledge tracing has been used widely to model student learning. However, the name “Bayesian knowledge tracing” has been applied to two related, but distinct, models: The first is the Bayesian knowledge tracing Markov chain which predicts the student-averaged probability of a correct application of a skill. We present an analytical solution to this model and show that it is a function of three parameters and has the functional form of an exponential. The second form is the Bayesian knowledge tracing hidden Markov model which can use the individual student's performance at each opportunity to apply a skill to update the conditional probability that the student has learned that skill. We use a fixed point analysis to study solutions of this model and find a range of parameters where it has the desired behavior. *Revised version, Feb 2017 The problem of estimating the number of hidden states in a hidden Markov model is considered. Emphasis is placed on cross-validated likelihood criteria. Using cross-validation to assess the number of hidden states allows to circumvent the well-documented technical difficulties of the order identification problem in mixture models. Moreover, in a predictive perspective, it does not require that the sampling distribution belongs to one of the models in competition. However, computing cross-validated likelihood for hidden Markov models for which only one training sample is available, involves difficulties since the data are not independent. Two approaches are proposed to compute cross-validated likelihood for a hidden Markov model. The first one consists of using a deterministic half-sampling procedure, and the second one consists of an adaptation of the EM algorithm for hidden Markov models, to take into account randomly missing values induced by cross-validation. Numerical experiments on both simulated and real data sets compare different versions of cross-validated likelihood criterion and penalised likelihood criteria, including BIC and a penalised marginal likelihood criterion. Those numerical experiments highlight a promising behaviour of the deterministic half-sampling criterion.