With the advance of online education systems, accessibility to learning materials has increased. In these systems, students can practice independently and learn from different learning materials over long periods of time. As a result, it is essential to trace students' knowledge states over long learning sequences while maintaining a personalized model of each individual student's progress. However, the existing deep learning-based knowledge tracing models are either not personalized or not tailored for handling long sequences. Handling long sequences are especially essential in the online education environments, in where models are preferred to be updated with the newly collected user data in a timely manner as students could acquire knowledge on each learning activity. In this paper, we propose a knowledge tracing model, Continuous Personalized Knowledge Tracing (CPKT), that can mimic the real-world long-term continuous learning scenario by incorporating a novel online model training paradigm that is suitable for the knowledge tracing problem. To achieve personalized knowledge tracing, we propose two model components: 1) personalized memory slots to maintain learner's knowledge in a lifelong manner, and 2) personalized user embeddings that help to accurately predict the individual responses, correctly detect the personalized knowledge acquisition and forgetting patterns, and better interpret and analyze the learner's progress. Additionally, we propose transition-aware stochastic shared embedding according to the learning transition matrix to regularize the online model training. Extensive experiments on four real-world datasets showcase the effectiveness and superiority of CPKT, especially for students with longer sequences.

We propose a new approach, the calibrated nonparametric scan statistic (CNSS), for more accurate detection of anomalous patterns in large-scale, real-world graphs. Scan statistics identify connected subgraphs that are interesting or unexpected through maximization of a likelihood ratio statistic; in particular, nonparametric scan statistics (NPSSs) identify subgraphs with a higher than expected proportion of individually significant nodes. However, we show that recently proposed NPSS methods are miscalibrated, failing to account for the maximization of the statistic over the multiplicity of subgraphs. This results in both reduced detection power for subtle signals, and low precision of the detected subgraph even for stronger signals. Thus we develop a new statistical approach to recalibrate NPSSs, correctly adjusting for multiple hypothesis testing and taking the underlying graph structure into account. While the recalibration, based on randomization testing, is computationally expensive, we propose both an efficient (approximate) algorithm and new, closed-form lower bounds (on the expected maximum proportion of significant nodes for subgraphs of a given size, under the null hypothesis of no anomalous patterns). These advances, along with the integration of recent core-tree decomposition methods, enable CNSS to scale to large real-world graphs, with substantial improvement in the accuracy of detected subgraphs. Extensive experiments on both semi-synthetic and real-world datasets are demonstrated to validate the effectiveness of our proposed methods, in comparison with state-of-the-art counterparts.

Accurate modeling of student knowledge is essential for large-scale online learning systems that are increasingly used for student training. Knowledge tracing aims to model student knowledge state given the student’s sequence of learning activities. Modern Knowledge tracing (KT) is usually formulated as a supervised sequence learning problem to predict students’ future practice performance according to their past observed practice scores by summarizing student knowledge state as a set of evolving hidden variables. Because of this formulation, many current KT solutions are not fit f or modeling student learning from non-assessed learning activities with no explicit feedback or score observation (e.g., watching video lectures that are not graded). Additionally, these models cannot explicitly represent the dynamics of knowledge transfer among different learning activities, particularly between the assessed (e.g., quizzes) and non-assessed (e.g., video lectures) learning activities. In this paper, we propose Transition-Aware Multi-activity Knowledge Tracing (TAMKOT), which models knowledge transfer between learning materials, in addition to student knowledge, when students transition between and within assessed and non-assessed learning materials. TAMKOT is formulated as a deep recurrent multi-activity learning model that explicitly learns knowledge transfer by activating and learning a set of knowledge transfer matrices, one for each transition type between student activities. Accordingly, our model allows for representing each material type in a different yet transferrable latent space while maintaining student knowledge in a shared space. We evaluate our model on three real-world publicly available datasets and demonstrate TAMKOT’s capability in predicting student performance and modeling knowledge transfer.

Knowledge Tracing (KT), which aims to model student knowledge level and predict their performance, is one of the most important applications of user modeling. Modern KT approaches model and maintain an up-to-date state of student knowledge over a set of course concepts according to students’ historical performance in attempting the problems. However, KT approaches were designed to model knowledge by observing relatively small problem-solving steps in Intelligent Tutoring Systems. While these approaches were applied successfully to model student knowledge by observing student solutions for simple problems, such as multiple-choice questions, they do not perform well for modeling complex problem solving in students. Most importantly, current models assume that all problem attempts are equally valuable in quantifying current student knowledge. However, for complex problems that involve many concepts at the same time, this assumption is deficient. It results in inaccurate knowledge states and unnecessary fluctuations in estimated student knowledge, especially if students guess the correct answer to a problem that they have not mastered all of its concepts or slip in answering the problem that they have already mastered all of its concepts. In this paper, we argue that not all attempts are equivalently important in discovering students’ knowledge state, and some attempts can be summarized together to better represent student performance. We propose a novel student knowledge tracing approach, Granular RAnk based TEnsor factorization (GRATE), that dynamically selects student attempts that can be aggregated while predicting students’ performance in problems and discovering the concepts presented in them. Our experiments on three real-world datasets demonstrate the improved performance of GRATE, compared to the state-of-the-art baselines, in the task of student performance prediction. Our further analysis shows that attempt aggregation eliminates the unnecessary fluctuations from students’ discovered knowledge states and helps in discovering complex latent concepts in the problems.

We propose a generalized optimization framework for detecting anomalous patterns (subgraphs that are interesting or unexpected) in interdependent networks, such as multi-layer networks, temporal networks, networks of networks, and many others. We frame the problem as a non-convex optimization that has a general nonlinear score function and a set of block-structured and non-convex constraints. We develop an effective, efficient, and parallelizable projection-based algorithm, namely Graph Block-structured Gradient Projection (GBGP), to solve the problem. It is proved that our algorithm 1) runs in nearly-linear time on the network size, and 2) enjoys a theoretical approximation guarantee. Moreover, we demonstrate how our framework can be applied to two very practical applications, and we conduct comprehensive experiments to show the effectiveness and efficiency of our proposed algorithm.

Subjective Logic (SL), as one of the state-of-the-art belief models, has been proposed to model an opinion that explicitly deals with its uncertainty. SL offers a variety of operators to update opinions consisting of belief, disbelief, and uncertainty. However, SL operators lack scalability to derive opinions from a large-scale network data due to the sequential procedures of combining two opinions, instead of collective procedures dealing with multiple opinions concurrently. In addition, SL's performance in predicting unknown opinions has been validated only when the uncertainty mass is sufficiently low. To enhance scalability and prediction accuracy of unknown opinions in SL, we take a hybrid approach by combining SL with Probabilistic Soft Logic (PSL). PSL provides collective reasoning with high scalability based on relationships between opinions but does not deal with uncertainty. By taking the merits of both SL and PSL, we propose a probabilistic logic algorithm, called Collective Subjective Logic (CSL) that provides high scalability and high prediction accuracy while dealing with uncertain opinions. Our proposed CSL is generic to deal with uncertain opinions with both high scalability and high prediction accuracy of unknown opinions over a large-scale network dataset. Through the extensive simulation experiments, we validated the outperformance of CSL compared against SL and PSL in terms of prediction accuracy of unknown opinions and algorithmic complexity using Epinions and two road traffic datasets.