CSCE 582: Bayesian Networks

Paper Presentation conducted by

Nick StifflerBen 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

In this Paper it spans three sequence types

Arithmetic Geometric Recursive

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

Geometric Sequence Model

Proficiency Levels available to each node

•Low .

•Medium

•High .

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

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

The Four Statistics (at least the ones we look at)

Margin

Cut

Mode

EAP

Margin The Marginal Distribution of Proficiency P(Sik|Xi)

expected numbers of students in each proficiency

Σi P(Sik|Xi)

Average proficiency for the class Σi P(Sik|Xi) class size

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

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

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)

EAP (cont.)

What it means The EAP would return the average ability

level for each class Standard Deviation variability of

proficiency

Scores coming out of the BN

Individual Level Plots

Comparing Groups

Comparing Groups

Reliability

Observed Score = True Score + Error Signal to noise ration in signal

processing Applying the Spearmen – Brown

formula

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 timescreating 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.

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