Knowledge tracing (KT) defines the task of predicting whether students can correctly answer questions based on their historical response. Although much research has been devoted to exploiting the question information, plentiful advanced information among questions and skills hasn't been well extracted, making it challenging for previous work to perform adequately. In this paper, we demonstrate that large gains on KT can be realized by pre-training embeddings for each question on abundant side information, followed by training deep KT models on the obtained embeddings. To be specific, the side information includes question difficulty and three kinds of relations contained in a bipartite graph between questions and skills. To pre-train the question embeddings, we propose to use product-based neural networks to recover the side information. As a result, adopting the pre-trained embeddings in existing deep KT models significantly outperforms state-of-the-art baselines on three common KT datasets.
Abstract:In order to maintain the stability and security of the power system, the uncertainty and intermittency of wind power must be taken into account in economic dispatch (ED) problems. In this paper, a dynamic economic dispatch (DED) model based on chance constrained programming is presented and an improved particle swarm optimization (PSO) approach is proposed to solve the problem. Wind power is regarded as a random variable and is included in the chance constraint. New formulation of up and down spinning reserve constraints are presented under expectation meaning. The improved PSO algorithm combines a feasible region adjustment strategy with a hill climbing search operation based on the basic PSO. Simulations are performed under three distinct test systems with different generators. Results show that both the proposed DED model and the improved PSO approach are effective.
An accurate prediction of wind speed is crucial for the economic and resilient operation of power systems with a high penetration level of wind power. Meteorological information such as temperature, humidity, air pressure, and wind level has a significant influence on wind speed, which makes it difficult to predict wind speed accurately. This paper proposes a wind speed prediction method through an effective combination of principal component analysis (PCA) and long short-term memory (LSTM) network. Firstly, PCA is employed to reduce the dimensions of the original multidimensional meteorological data which affect the wind speed. Further, differential evolution (DE) algorithm is presented to optimize the learning rate, number of hidden layer nodes, and batch size of the LSTM network. Finally, the reduced feature data from PCA and the wind speed data are merged together as an input to the LSTM network for wind speed prediction. In order to show the merits of the proposed method, several prevailing prediction methods, such as Gaussian process regression (GPR), support vector regression (SVR), recurrent neural network (RNN), and other forecasting techniques, are introduced for comparative purposes. Numerical results show that the proposed method performs best in prediction accuracy.
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