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CSCE 582: Bayesian Networks

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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 ... – PowerPoint PPT presentation

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Title: CSCE 582: Bayesian Networks


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

2
Bayesian networks A teachers 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(SikXi)
  • -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(SikXi)
  • expected numbers of students in each proficiency
  • Si P(SikXi)
  • Average proficiency for the class
  • Si P(SikXi)
  • 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
  • maxP(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
EAP Expected a Posteriori
  • Assign numbers to states to get an expectation
    over posterior
  • High 1
  • Medium 0
  • Low -1

1P(Sik high Xi) 0 P(Sik med Xi)
-1P(Sik lowXi) 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
(No Transcript)
18
Comparing Groups
19
(No Transcript)
20
Reliability
  • Observed Score True Score Error
  • Signal to noise ration in signal processing
  • Applying the Spearmen Brown formula

21
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.
22
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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