Knowledge tracing aims to trace students’ evolving knowledge states by predicting their future performance on concept-related exercises. Recently, some graph-based models have been developed to incorporate the relationships between exercises to improve knowledge tracing, but only a single type of relationship information is generally explored. In this article, we present a novel Dual Graph Ensemble learning method for Knowledge Tracing (DGEKT), which establishes a dual graph structure of students’ learning interactions to capture the heterogeneous exercise–concept associations and interaction transitions by hypergraph modeling and directed graph modeling, respectively. To combine the dual graph models, we introduce the technique of online knowledge distillation. This choice arises from the observation that, while the knowledge tracing model is designed to predict students’ responses to the exercises related to different concepts, it is optimized merely with respect to the prediction accuracy on a single exercise at each step. With online knowledge distillation, the dual graph models are adaptively combined to form a stronger ensemble teacher model, which provides its predictions on all exercises as extra supervision for better modeling ability. In the experiments, we compare DGEKT against eight knowledge tracing baselines on three benchmark datasets, and the results demonstrate that DGEKT achieves state-of-the-art performance.

Image aesthetics assessment has emerged as a hot topic in recent years due to its potential in numerous high-level vision applications. In this paper, distinguished from existing studies relying on a single label, we propose quantifying image aesthetics by a distribution over multiple quality levels. The distribution-based representation characterizes the disagreement among users' aesthetic preferences regarding the same image, and is also compatible with the traditional task of aesthetic label prediction. Our framework is developed based on fully convolutional networks and enables inputs of varying sizes. In this way, we circumvent the fixed-size constraint of prevalent convolutional neural networks, and avoid the risk of impairing the intrinsic aesthetic appeal of images. Moreover, given the fact that aesthetic perceiving is coupled with semantic understanding, we present a novel semantic-aware hybrid NEtwork (SANE), which harvests the information from object categorization and scene recognition to enhance image aesthetics assessment. Experiments on two benchmark datasets have well verified the effectiveness of our approach in both scenarios of aesthetic distribution prediction and aesthetic label prediction, and highlighted the benefits of input preserving as well as semantic understanding for images.

Recently, the valuation of variable annuity products has become a hot topic in actuarial science. In this paper, we use the Fourier cosine series expansion (COS) method to value the guaranteed minimum death benefit (GMDB) products. We first express the value of GMDB by the discounted density function approach, then we use the COS method to approximate the valuation Equations. When the distribution of the time-until-death random variable is approximated by a combination of exponential distributions and the price of the fund is modeled by an exponential Lévy process, explicit equations for the cosine coefficients are given. Some numerical experiments are also made to illustrate the efficiency of our method.

In this paper, we assume that the reserve level of an insurance company can only be observed at discrete time points, then a new risk model is proposed by introducing a periodic capital injection strategy and a barrier dividend strategy into the classical risk model. We derive the equations and the boundary conditions satisfied by the Gerber-Shiu function, the expected discounted capital injection function and the expected discounted dividend function by assuming that the observation interval and claim amount are exponentially distributed, respectively. Numerical examples are also given to further analyze the influence of relevant parameters on the actuarial function of the risk model.

Unsupervised domain adaptation (UDA) aims to adapt models learned from a well-annotated source domain to a target domain, where only unlabeled samples are available. To this end, adversarial training is widely used in conventional UDA methods to reduce the discrepancy between source and target domains. Recently, prompt tuning has emerged as an efficient way to adapt large pre-trained vision-language models like CLIP to a variety of downstream tasks. In this paper, we present a novel method named Adversarial DuAl Prompt Tuning (ADAPT) for UDA, which employs text prompts and visual prompts to guide CLIP simultaneously. Rather than simply performing a joint optimization of text prompts and visual prompts, we integrate text prompt tuning and visual prompt tuning into a collaborative framework where they engage in an adversarial game: text prompt tuning focuses on distinguishing between source and target images, whereas visual prompt tuning seeks to align source and target domains. Unlike most existing adversarial training-based UDA approaches, ADAPT does not require explicit domain discriminators for domain alignment. Instead, the objective is effectively achieved at both global and category levels through modeling the joint probability distribution of images on domains and categories. Extensive experiments on four benchmark datasets demonstrate the effectiveness of our ADAPT method for UDA. We have released our code at https://github.com/Liuziyi1999/ADAPT.