Calculating Probabilistic Distance to Solution in a Complex Problem Solving Domain

ABSTRACT In complex problem solving domains, correct solutions are often comprised of a combination of individual components. Students usually go through several attempts, each attempt reflecting an individual solution state that can be observed during practice. Classic metrics to measure student performance over time rely on counting the number of submissions or focusing on time taken to complete the problem correctly. These metrics are not robust to the correction of errors that may increase problem solving time, and do not reflect topical misunderstandings on the part of the student. In this paper we propose a metric to measure the probabilistic distance between an observed student solution and a correct solution. Students working in an online programming environment completed four practice problems. Their submissions were then evaluated against a model of the algorithmic components necessary for a correct solution. A Markov Model was used to generate a problem state graph. Our proposed Probabilistic Distance to Solution (PDS) metric was applied to the graph to determine the distance, in program states, from an observed program model to the model of a correct solution. Results indicate that the PDS is useful in determining if an edit or student path is (a) typical of students who have mastered content, and (b) productive in progressing toward a solution. We offer implementation details of PDS and implications for future work based upon current observations

Batch Informed Trees (BIT*): Informed Asymptotically Optimal Anytime Search

Path planning in robotics often requires finding high-quality solutions to continuously valued and/or high-dimensional problems. These problems are challenging and most planning algorithms instead solve simplified approximations. Popular approximations include graphs and random samples, as respectively used by informed graph-based searches and anytime sampling-based planners. Informed graph-based searches, such as A*, traditionally use heuristics to search a priori graphs in order of potential solution quality. This makes their search efficient but leaves their performance dependent on the chosen approximation. If its resolution is too low then they may not find a (suitable) solution but if it is too high then they may take a prohibitively long time to do so. Anytime sampling-based planners, such as RRT*, traditionally use random sampling to approximate the problem domain incrementally. This allows them to increase resolution until a suitable solution is found but makes their search dependent on the order of approximation. Arbitrary sequences of random samples approximate the problem domain in every direction simultaneously and but may be prohibitively inefficient at containing a solution. This paper unifies and extends these two approaches to develop Batch Informed Trees (BIT*), an informed, anytime sampling-based planner. BIT* solves continuous path planning problems efficiently by using sampling and heuristics to alternately approximate and search the problem domain. Its search is ordered by potential solution quality, as in A*, and its approximation improves indefinitely with additional computational time, as in RRT*. It is shown analytically to be almost-surely asymptotically optimal and experimentally to outperform existing sampling-based planners, especially on high-dimensional planning problems.Comment: International Journal of Robotics Research (IJRR). 32 Pages. 16 Figure

Compressive Mining: Fast and Optimal Data Mining in the Compressed Domain

Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance estimation when the data are represented using different sets of coefficients is still a largely unexplored area. This work studies the optimization problems related to obtaining the \emph{tightest} lower/upper bound on Euclidean distances when each data object is potentially compressed using a different set of orthonormal coefficients. Our technique leads to tighter distance estimates, which translates into more accurate search, learning and mining operations \textit{directly} in the compressed domain. We formulate the problem of estimating lower/upper distance bounds as an optimization problem. We establish the properties of optimal solutions, and leverage the theoretical analysis to develop a fast algorithm to obtain an \emph{exact} solution to the problem. The suggested solution provides the tightest estimation of the $L_2$-norm or the correlation. We show that typical data-analysis operations, such as k-NN search or k-Means clustering, can operate more accurately using the proposed compression and distance reconstruction technique. We compare it with many other prevalent compression and reconstruction techniques, including random projections and PCA-based techniques. We highlight a surprising result, namely that when the data are highly sparse in some basis, our technique may even outperform PCA-based compression. The contributions of this work are generic as our methodology is applicable to any sequential or high-dimensional data as well as to any orthogonal data transformation used for the underlying data compression scheme.Comment: 25 pages, 20 figures, accepted in VLD

Activity recognition from videos with parallel hypergraph matching on GPUs

In this paper, we propose a method for activity recognition from videos based on sparse local features and hypergraph matching. We benefit from special properties of the temporal domain in the data to derive a sequential and fast graph matching algorithm for GPUs. Traditionally, graphs and hypergraphs are frequently used to recognize complex and often non-rigid patterns in computer vision, either through graph matching or point-set matching with graphs. Most formulations resort to the minimization of a difficult discrete energy function mixing geometric or structural terms with data attached terms involving appearance features. Traditional methods solve this minimization problem approximately, for instance with spectral techniques. In this work, instead of solving the problem approximatively, the exact solution for the optimal assignment is calculated in parallel on GPUs. The graphical structure is simplified and regularized, which allows to derive an efficient recursive minimization algorithm. The algorithm distributes subproblems over the calculation units of a GPU, which solves them in parallel, allowing the system to run faster than real-time on medium-end GPUs

CBR and MBR techniques: review for an application in the emergencies domain

The purpose of this document is to provide an in-depth analysis of current reasoning engine practice and the integration strategies of Case Based Reasoning and Model Based Reasoning that will be used in the design and development of the RIMSAT system. RIMSAT (Remote Intelligent Management Support and Training) is a European Commission funded project designed to: a.. Provide an innovative, 'intelligent', knowledge based solution aimed at improving the quality of critical decisions b.. Enhance the competencies and responsiveness of individuals and organisations involved in highly complex, safety critical incidents - irrespective of their location. In other words, RIMSAT aims to design and implement a decision support system that using Case Base Reasoning as well as Model Base Reasoning technology is applied in the management of emergency situations. This document is part of a deliverable for RIMSAT project, and although it has been done in close contact with the requirements of the project, it provides an overview wide enough for providing a state of the art in integration strategies between CBR and MBR technologies.Postprint (published version