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CSCE 582: Bayesian Networks

CSCE 582: Bayesian Networks. Paper Presentation conducted by Nick Stiffler Ben Fine. Bayesian networks: A teacher’s view. Russel G Almond Valerie J Shute Jody S. Underwood Juan-Diego Zapata-Rivera. ACED. A Computer-Based-Assessment-for-Learning system covering the topic of sequences

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CSCE 582: Bayesian Networks

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  1. CSCE 582: Bayesian Networks Paper Presentation conducted by Nick Stiffler Ben Fine

  2. Bayesian networks: A teacher’s view Russel G Almond Valerie J Shute Jody S. Underwood Juan-Diego Zapata-Rivera

  3. ACED • A Computer-Based-Assessment-for-Learning system covering the topic of sequences • In this Paper it spans three sequence types • Arithmetic • Geometric • Recursive

  4. ACED • A Prototype that explores • Madigan and Almond Algorithms for selection of the next task in an assessment • The use of targeted diagnostic feedback • Tech solutions to make the assessment accessible to students with visual impairments

  5. Geometric Sequence Model • Proficiency Levels available to each node • Low . • Medium • High .

  6. Bayesian Network (SS) • Individual task outcome variables -are entered as findings in task specific nodes where the results are propagated through the proficiency model • Posterior Proficiency Model -gives the belief about the proficiency state for a particular student Note: Any functional of the posterior distribution can be used as a sore

  7. Terminology • Si0, Si1,…,Sik – proficiency variables for student i Si0 – special overall PV (Solve Geo. Problems) • Xi – Body of evidence • P(Sik|Xi) -conditional distribution of Sk given the observed outcomes

  8. The Four Statistics (at least the ones we look at) • Margin • Cut • Mode • EAP

  9. Margin • The Marginal Distribution of Proficiency P(Sik|Xi) • expected numbers of students in each proficiency ΣiP(Sik|Xi) • Average proficiency for the class ΣiP(Sik|Xi) class size

  10. Cut • Identifier for a special state Ex. students ≥ medium are proficient P(Sik ≥ medium|Xi) • Average cut score is the expected proportion of “proficient” students in the class

  11. Mode • The value of m the produces max{P(Sik = m|Xi)} • Improvements • If student is within a threshold should be identified as being on the boundary • When the Marginal Distribution is evenly spread out the system should identify students who have the greatest uncertainty • To get modal scores count the number of students assigned to each category

  12. EAPExpected a Posteriori • Assign numbers to states to get an expectation over posterior • High : 1 • Medium : 0 • Low : -1 1*P(Sik = high|Xi) + 0 * P(Sik = med|Xi) -1*P(Sik = low|Xi) Reduces to: P(Sik = high|Xi) - P(Sik = low|Xi)

  13. EAP (cont.) • What it means • The EAP would return the average ability level for each class • Standard Deviation variability of proficiency

  14. Scores coming out of the BN

  15. Individual Level Plots

  16. Comparing Groups

  17. Comparing Groups

  18. Reliability • Observed Score = True Score + Error • Signal to noise ration in signal processing • Applying the Spearmen – Brown formula

  19. Spearmen – Brown formula      is the predicted reliability N is the number of "tests" combined is the reliability of the current "test" predicts the reliability of a new test by replicating the current test N times creating a test with N parallel forms of the current exam. Thus N = 2 implies doubling the exam length by adding items with the same properties as those in the current exam.

  20. Why BN Works Well • Offers significant improvement over number right scoring • Bayes network estimates stabilize sub scores by borrowing strength from the overall reliability • Differs from other methods b/c it starts with an expert constructed model of how the proficiencies interact • Other methods use observed correlations b/t the scores on subtest

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