Meta-cognitive skills to be developed in learning for the 21st century is the detection and correction of errors in solutions. These meta-cognitive skills can help to detect errors the learner has made her/himself as well as errors others have made. Our investigations in learning from errors have the ultimate goal to adapt the selection and presentation to the learner so that he/she can better learn from erroneous examples others have made. In our experiments we found that (1) erroneous examples with help provision can promote students skill of find errors, (2) the benefit from erroneous examples depends on the relation between the student's level and the example's difficulty, i.e. if the student is prepared for the problem, (3) for many students it is very difficult to correct errors.

Learners that have better metacognition acquire knowledge faster than others who do not. If we had better models of such learning, we would be able to build a better metacognitive educational system. In this paper, we propose a computational model that uses a probabilistic context free grammar induction algorithm yielding metacognitive learning by acquiring deep features to assist future learning. We discuss the challenges of integrating this model into a synthetic student, and possible future studies in using this model to better understand human learning. Preliminary results suggest that both stronger prior knowledge and a better learning strategy can speed up the learning process. Some model variations generate human-like error pattern.

Developing the capabilities of children to comprehend written texts is key to their development as young adults. Text comprehension skills develop enormously from the age of 7- 8 until the age of 11. Nowadays, several young children (˜5% – 10% of novice readers) turn out to be poor (text) comprehenders: they demonstrate text comprehension difficulties, related to inference-making skills, despite proficiency in lowlevel cognitive skills like word decoding. Though there are several pencil-and-paper reading interventions for improving inference-making skills on text, and addressed to poor comprehenders, the design and evaluation of Adaptive Learning Systems (ALSs) are lagging behind. The use of more intelligent ALSs to custom-tailor such interventions in the form of games for poor comprehenders has tremendous potential. Our system embodies that potential. This paper presents the design of our ALS by focusing on its intelligent adaptive engine and the related conceptual models, and by presenting the visual interfaces for story telling and gaming.

A new architectural framework for a metacognitive tutoring system is presented that is aimed to stimulate self-regulatory behavior in the learner.The new framework extends the cognitive architecture of TutorJ that has been already proposed by some of the authors. TutorJ relies mainly on dialogic interaction with the user, and makes use of a statistical dialogue planner implemented through a Partially Observable Markov Decision Process (POMDP). A suitable two-level structure has been designed for the statistical reasoner to cope with measuring and stimulating metacognitive skills in the user. Suitable actions have been designed to this purpose starting from the analysis of the main questionnaires proposed in the literature. Our reasoner has been designed to model the relation between each item in a questionnaire and the related metacognitive skill, so the proper action can be selected by the tutoring agent. The complete framework is detailed, the reasoner structure is discussed, and a simple application scenario is presented.

An experiment was conducted to test the efficacy of a new intelligent hypermedia system, MetaTutor, which is intended to prompt and scaffold the use of self-regulated learning (SRL) processes during learning about a human body system. Sixty-eight (N=68) undergraduate students learned about the human circulatory system under one of three conditions: prompt and feedback (PF), prompt-only (PO), and control (C) condition. The PF condition received timely prompts from animated pedagogical agents to engage in planning processes, monitoring processes, and learning strategies and also received immediate directive feedback from the agents concerning the deployment of the processes. The PO condition received the same timely prompts, but did not receive any feedback following the deployment of the processes. Finally, the control condition learned without any assistance from the agents during the learning session. All participants had two hours to learn using a 41-page hypermedia environment which included texts describing and static diagrams depicting various topics concerning the human circulatory system. Results indicate that the PF condition had significantly higher learning efficiency scores, when compared to the control condition. There were no significant differences between the PF and PO conditions. These results are discussed in the context of development of a fully-adaptive hypermedia learning system intended to scaffold self-regulated learning.

Successful learning with advanced learning technologies is based on the premise that learners adaptively regulate their cognitive and metacognitive behaviors during learning. However, there is abundant empirical evidence that suggests that learners typically do not adaptively modify their behavior, thus suggesting that they engage in what is called dysregulated behavior. Dysregulated learning is a new term that is used to describe a class of behaviors that learners use that lead to minimal learning. Examples of dysregulated learning include failures to: (1) encode contextual demands, (2) deploy effective learning strategies, (3) modify and update internal standards, (4) deal with the dynamic nature of the task, (5) metacognitive monitor the use of strategies and repeatedly make accurate metacognitive judgments, and (6) intelligently adapt behavior during learning so as to maximize learning and understanding of the instructional material. Understanding behaviors associated with dysregulated learning is critical since it has implications for determining what they are, when they occur, how often they occur, and how they can be corrected during learning.

Hutter (2007) recently introduced the loss rank principle (LoRP) as a generalpurpose principle for model selection. The LoRP enjoys many attractive properties and deserves further investigations. The LoRP has been well-studied for regression framework in Hutter and Tran (2010). In this paper, we study the LoRP for classification framework, and develop it further for model selection problems in unsupervised learning where the main interest is to describe the associations between input measurements, like cluster analysis or graphical modelling. Theoretical properties and simulation studies are presented.

Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularization algorithm, a consistent model selection criterion is proposed to select the best one among this preselected set. The approach leads to a fast and efficient procedure for variable selection, especially in high-dimensional settings. Model selection consistency of the suggested criterion is proven when the number of covariates d is fixed. Simulation studies suggest that the criterion still enjoys model selection consistency when d is much larger than the sample size. The simulations also show that our approach for variable selection works surprisingly well in comparison with existing competitors. The method is also applied to a real data set.

Preprint 1 The Lasso under Heteroscedasticity Jinzhu Jia 1, Karl Rohe 1 and Bin Yu 1, 2 Department of Statistics 1 and Department of EECS 2 University of California, Berkeley Abstract: The performance of the Lasso is well understood under the assumptions of the standard linear model with homoscedastic noise. However, in several applications, the standard model does not describe the important features of the data. This paper examines how the Lasso performs on a nonstandard model that is motivated by medical imaging applications. Like all heteroscedas-tic models, the noise terms in this Poisson-like model are not independent of the design matrix. More specifically, this paper studies the sign consistency of the Lasso under a sparse Poisson-like model. In addition to studying sufficient conditions for the sign consistency of the Lasso estimate, this paper also gives necessary conditions for sign consistency. Both sets of conditions are comparable to results for the homoscedastic model, showing that when a measure of the signal to noise ratio is large, the Lasso performs well on both Poisson-like data and homoscedastic data. Simulations reveal that the Lasso performs equally well in terms of model selection performance on both Poisson-like data and homoscedastic data (with properly scaled noise variance), across a range of parameterizations. Taken as a whole, these results suggest that the Lasso is robust to the Poisson-like heteroscedastic noise. Key words and phrases: Lasso, Poisson-like Model, Sign Consistency, Heteroscedas-ticity 1 Introduction The Lasso (Tibshirani, 1996) is widely used in high dimensional regression for variable selection. Its model selection performance has been well studied under a standard sparse and homoskedastic regression model. Several researchers have shown that under sparsity and regularity conditions, the Lasso can select the true model asymptotically even whenp n (Donoho et al., 2006; Meinshausen arXiv:1011.1026v1 To define the Lasso estimate, suppose the observed data are independent pairs { (x i,Y i)} R p R for i 1, 2,...,n following the linear regression model Y i x T i β i, (1) where x T i is a row vector representing the predictors for thei th observation,Y i is the correspondingi th response variable, i's are independent and mean zero noise terms, andβ R p . Let Y (Y 1,...,Y n)T and ( 1, 2,..., n)T R n . The Lasso estimate (Tibshirani, 1996) is then defined as the solution to a penalized least squares problem (with regularization parameterλ): ˆ β (λ) arg min β 1 2 n ‖Y X β‖ 2 2 λ‖β‖ 1, (2) where for some vectorx R k,‖ x ‖ r ( k i 1 x i r) 1/r .

The cardinal direction calculus (CDC) proposed by Goyal and Egenhofer is a very expressive qualitative calculus for directional information of extended objects. Early work has shown that consistency checking of complete networks of basic CDC constraints is tractable while reasoning with the CDC in general is NP-hard. This paper shows, however, if allowing some constraints unspecified, then consistency checking of possibly incomplete networks of basic CDC constraints is already intractable. This draws a sharp boundary between the tractable and intractable subclasses of the CDC. The result is achieved by a reduction from the well-known 3-SAT problem.