FAST: Feature-Aware Student Knowledge Tracing

Various kinds of e-learning systems, such as Massively Open Online Courses and intelligent tutoring systems, are now producing amounts of feature-rich data from students solving items at different levels of proficiency over time. To analyze such data, researchers often use Knowledge Tracing [4], a 20-year old method that has become the de-facto standard for inferring student’s knowledge from performance data. Knowledge Tracing uses Hidden Markov Models (HMM) to estimate the latent cognitive state (student’s knowledge) from the student’s performance answering items. Since the original Knowledge Tracing formulation does not allow to model general features, a considerable amount of research has focused on ad-hoc modifications to the Knowledge Tracing algorithm to enable modeling a specific feature of interest. This has led to a plethora of different Knowledge Tracing reformulations for very specific purposes. For example, Pardos et al. [5] proposed a new model to measure the effect of students’ individual characteristics, Beck et al. [2] modified Knowledge Tracing to assess the effect of help in a tutor system, and Xu and Mostow [7] proposed a new model that allows measuring the effect of subskills. These ad hoc models are successful for their own specific purpose, but they do not generalize to arbitrary features. Other student modeling methods which allow more flexible features have been proposed. For example, Performance Factor Analysis [6] uses logistic regression to model arbitrary features, but unfortunately it does not make inferences of whether the student has learned a skill. We present FAST (Feature-Aware Student knowledge Tracing), a novel method that allows general features into Knowledge Tracing. FAST combines Performance Factor Analysis (logistic regression) with Knowledge Tracing, by leveraging on previous work on unsupervised learning with features [3]. Therefore, FAST is able to infer student’s knowledge, like Knowledge Tracing does, while also allowing for arbitrary features, like Performance Factor Analysis does. FAST allows general features into Knowledge Tracing by replacing the generative emission probabilities (often called guess and slip probabilities) with logistic regression [3], so that these probabilities can change with time to infer student’s knowledge. FAST allows arbitrary features to train the logistic regression model and the HMM jointly. Training the parameters simultaneously enables FAST to learn from the features. This differs from using regression to analyze the slip and guess probabilities [1]. To validate our approach, we use data collected from real students interacting with a tutor. We present experimental results comparing FAST with Knowledge Tracing and Performance Factor Analysis. We conduct experiments with our model using features like item difficulty, prior successes and failures of a student for the skill (or multiple skills) associated with the item, according to the formulation of Performance Factor Analysis

Many-body localization dynamics from gauge invariance

We show how lattice gauge theories can display many-body localization dynamics in the absence of disorder. Our starting point is the observation that, for some generic translationally invariant states, Gauss law effectively induces a dynamics which can be described as a disorder average over gauge super-selection sectors. We carry out extensive exact simulations on the real-time dynamics of a lattice Schwinger model, describing the coupling between U(1) gauge fields and staggered fermions. Our results show how memory effects and slow entanglement growth are present in a broad regime of parameters - in particular, for sufficiently large interactions. These findings are immediately relevant to cold atoms and trapped ions experiments realizing dynamical gauge fields, and suggest a new and universal link between confinement and entanglement dynamics in the many-body localized phase of lattice models.Comment: 5Pages + appendices; V2: updated discussion in page 2, more numerical results, added reference

Cities, Language Academies and the State of Minority Languages : Observations from the Quechua Academy in Cuzco, Peru

【言語文化専攻編