We explore a new research direction in Bayesian variational inference with discrete latent variable priors where we exploit Kronecker matrix algebra for efficient and exact computations of the evidence lower bound (ELBO). The proposed DIRECT approach has several advantages over its predecessors; (i) it can exactly compute ELBO gradients (i.e.

We explore a new research direction in Bayesian variational inference with discrete latent variable priors where we exploit Kronecker matrix algebra for efficient and exact computations of the evidence lower bound (ELBO). The proposed DIRECT approach has several advantages over its predecessors; (i) it can exactly compute ELBO gradients (i.e.

It can also be seen as a local approximation of the nonconvex-nonconcave minimax games--e.g., the generative adversarial network (GAN)

Here we aim to design a deep network which by construction is the gradient of a certain function. The first property is a necessary condition for a network to be a gradient, and there is no apparent way to directly enforce it. One may consider additional regularization or constraints on the solution. D.1 Proof of Theorem 1 By inequality (14), for any k 0 we have || F (x The selected hyperparameters, used in the experiments, are detailed in Table 2.

Automatic question generation is a critical task that involves evaluating question quality by considering factors such as engagement, pedagogical value, and the ability to stimulate critical thinking. These aspects require human-like understanding and judgment, which automated systems currently lack. However, human evaluations are costly and impractical for large-scale samples of generated questions. Therefore, we propose a novel system, MIRROR (Multi-LLM Iterative Review and Response for Optimized Rating), which leverages large language models (LLMs) to automate the evaluation process for questions generated by automated question generation systems. We experimented with several state-of-the-art LLMs, such as GPT-4, Gemini, and Llama2-70b. We observed that the scores of human evaluation metrics, namely relevance, appropriateness, novelty, complexity, and grammaticality, improved when using the feedback-based approach called MIRROR, tending to be closer to the human baseline scores. Furthermore, we observed that Pearson's correlation coefficient between GPT-4 and human experts improved when using our proposed feedback-based approach, MIRROR, compared to direct prompting for evaluation. Error analysis shows that our proposed approach, MIRROR, significantly helps to improve relevance and appropriateness.

The interest in predicting online learning performance using ML algorithms has been steadily increasing. We first conducted a scientometric analysis to provide a systematic review of research in this area. The findings show that most existing studies apply the ML methods without considering learning behavior patterns, which may compromise the prediction accuracy and precision of the ML methods. This study proposes an integration framework that blends learning behavior analysis with ML algorithms to enhance the prediction accuracy of students' online learning performance. Specifically, the framework identifies distinct learning patterns among students by employing clustering analysis and implements various ML algorithms to predict performance within each pattern. For demonstration, the integration framework is applied to a real dataset from edX and distinguishes two learning patterns, as in, low autonomy students and motivated students. The results show that the framework yields nearly perfect prediction performance for autonomous students and satisfactory performance for motivated students. Additionally, this study compares the prediction performance of the integration framework to that of directly applying ML methods without learning behavior analysis using comprehensive evaluation metrics. The results consistently demonstrate the superiority of the integration framework over the direct approach, particularly when integrated with the best-performing XGBoosting method. Moreover, the framework significantly improves prediction accuracy for the motivated students and for the worst-performing random forest method. This study also evaluates the importance of various learning behaviors within each pattern using LightGBM with SHAP values. The implications of the integration framework and the results for online education practice and future research are discussed.

Neural networks were used to classify infrasound data. Two different approaches were compared. One based on the direct classification of time series data, using a custom implementation of the InceptionTime network. For the other approach, we generated 2D images of the wavelet transformation of the signals, which were subsequently classified using a ResNet implementation. Choosing appropriate hyperparameter settings, both achieve a classification accuracy of above 90 %, with the direct approach reaching 95.2 %.