Parallel Prediction Method of Knowledge Proficiency Based on Bloom’s Cognitive Theory

Knowledge proficiency refers to the extent to which students master knowledge and reflects their cognitive status. To accurately assess knowledge proficiency, various pedagogical theories have emerged. Bloom’s cognitive theory, proposed in 1956 as one of the classic theories, follows the cognitive progression from foundational to advanced levels, categorizing cognition into multiple tiers including “knowing”, “understanding”, and “application”, thereby constructing a hierarchical cognitive structure. This theory is predominantly employed to frame the design of teaching objectives and guide the implementation of teaching activities. Additionally, due to the large number of students in real-world online education systems, the time required to calculate knowledge proficiency is significantly high and unacceptable. To ensure the applicability of this method in large-scale systems, there is a substantial demand for the design of a parallel prediction model to assess knowledge proficiency. The research in this paper is grounded in Bloom’s Cognitive theory, and a Bloom Cognitive Diagnosis Parallel Model (BloomCDM) for calculating knowledge proficiency is designed based on this theory. The model is founded on the concept of matrix decomposition. In the theoretical modeling phase, hierarchical and inter-hierarchical assumptions are initially established, leading to the abstraction of the mathematical model. Subsequently, subject features are mapped onto the three-tier cognitive space of “knowing”, “understanding”, and “applying” to derive the posterior distribution of the target parameters. Upon determining the objective function of the model, both student and topic characteristic parameters are computed to ascertain students’ knowledge proficiency. During the modeling process, in order to formalize the mathematical expressions of “understanding” and “application”, the notions of “knowledge group” and “higher-order knowledge group” are introduced, along with a parallel method for identifying the structure of higher-order knowledge groups. Finally, the experiments in this paper validate that the model can accurately diagnose students’ knowledge proficiency, affirming the scientific and meaningful integration of Bloom’s cognitive hierarchy in knowledge proficiency assessment

Model the Complex Dependence Structures of Financial Variables by Using Canonical Vine

Financial variables such as asset returns in the massive market contain various hierarchical and horizontal relationships forming complicated dependence structures. Modeling and mining of these structures is challenging due to their own high structural complexities as well as the stylized facts of the market data. This paper introduces a new canonical vine dependence model to identify the asymmetric and non-linear dependence structures of asset returns without any prior independence assumptions. To simplify the model while maintaining its merit, a partial correlation based method is proposed to optimize the canonical vine. Compared with the original canonical vine, the new model can still maintain the most important dependence but many unimportant nodes are removed to simplify the canonical vine structure. Our model is applied to construct and analyze dependence structures of European stocks as case studies. Its performance is evaluated by measuring portfolio of Value at Risk, a widely used risk management measure. In comparison to a very recent canonical vine model and the `full' model, our experimental results demonstrate that our model has a much better quality of Value at Risk, providing insightful knowledge for investors to control and reduce the aggregation risk of the portfolio