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Formal Definition of Assessment Modeling (Assessment Modeling: Fundamental Pre-training Tasks for Interactive Educational Systems)

In each knowledge tracing task there is a sequence of interactions for each students: [I1,,IT][I_1, \cdots, I_T] and each of this interactions consist of several features: {ft1,,ftn}.\{f_t^1, \cdots, f_t^n\}.. In knowledge tracing we want to predict feature f at time t, which is formulated as: p(ftk{I1,,It1,It,It+1,,IT}÷Γ(ftk))p(f_t^k | \{ I_1, \cdots, I_{t-1}, I_t, I_{t+1}, \cdots, I_T \} \div \Gamma(f_t^k)) from which Γ(f)\Gamma(f) is a set of features that should be masked. In knowledge tracing typically the correctness of the response is predicted. The task that is different from knowledge tracing, is assessment predicting. In this case, we want to predict the assessment given the sequence of interactions: p(atk{I1,,It1,It,It+1,,IT}÷Γ(atk))p(a_t^k | \{ I_1, \cdots, I_{t-1}, I_t, I_{t+1}, \cdots, I_T \} \div \Gamma(a_t^k))

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Updated 2021-01-26

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Data Science