Special Topics in
Educational Data Mining
HUDK5199
Spring term, 2013
February 18, 2013
Today’s Class
• Classification
• And then some discussion of features in Excel
between end of class and 5pm
– We will start today, and continue in future classes
as needed
Types of EDM method
(Baker & Siemens, under review)
• Prediction
– Classification
– Regression
– Latent Knowledge Estimation
• Structure Discovery
–
–
–
–
Clustering
Factor Analysis
Domain Structure Discovery
Network Analysis
• Relationship mining
–
–
–
–
Association rule mining
Correlation mining
Sequential pattern mining
Causal data mining
• Distillation of data for human judgment
• Discovery with models
3
We have already studied
• Prediction
– Classification
– Regression
– Latent Knowledge Estimation
• Structure Discovery
–
–
–
–
Clustering
Factor Analysis
Domain Structure Discovery
Network Analysis
• Relationship mining
–
–
–
–
Association rule mining
Correlation mining
Sequential pattern mining
Causal data mining
• Distillation of data for human judgment
• Discovery with models
4
Today’s Class
• Prediction
– Classification
– Regression
– Latent Knowledge Estimation
• Structure Discovery
–
–
–
–
Clustering
Factor Analysis
Domain Structure Discovery
Network Analysis
• Relationship mining
–
–
–
–
Association rule mining
Correlation mining
Sequential pattern mining
Causal data mining
• Distillation of data for human judgment
• Discovery with models
5
Prediction
• Pretty much what it says
• A student is using a tutor right now.
Is he gaming the system or not?
• A student has used the tutor for the last half hour.
How likely is it that she knows the skill in the next
step?
• A student has completed three years of high school.
What will be her score on the college entrance exam?
Classification
• There is something you want to predict (“the
label”)
• The thing you want to predict is categorical
– The answer is one of a set of categories, not a number
– CORRECT/WRONG (sometimes expressed as 0,1)
• This is what we used in Latent Knowledge Estimation
– HELP REQUEST/WORKED EXAMPLE
REQUEST/ATTEMPT TO SOLVE
– WILL DROP OUT/WON’T DROP OUT
– WILL SELECT PROBLEM A,B,C,D,E,F, or G
Where do those labels come from?
•
•
•
•
•
•
•
Field observations
Text replays
Post-test data
Tutor performance
Survey data
School records
Where else?
Classification
• Associated with each label are a set of
“features”, which maybe you can use to
predict the label
Skill
ENTERINGGIVEN
ENTERINGGIVEN
USEDIFFNUM
ENTERINGGIVEN
REMOVECOEFF
REMOVECOEFF
USEDIFFNUM
….
pknow
0.704
0.502
0.049
0.967
0.792
0.792
0.073
time
9
10
6
7
16
13
5
totalactions
1
2
1
3
1
2
2
right
WRONG
RIGHT
WRONG
RIGHT
WRONG
RIGHT
RIGHT
Classification
• The basic idea of a classifier is to determine
which features, in which combination, can
predict the label
Skill
ENTERINGGIVEN
ENTERINGGIVEN
USEDIFFNUM
ENTERINGGIVEN
REMOVECOEFF
REMOVECOEFF
USEDIFFNUM
….
pknow
0.704
0.502
0.049
0.967
0.792
0.792
0.073
time
9
10
6
7
16
13
5
totalactions
1
2
1
3
1
2
2
right
WRONG
RIGHT
WRONG
RIGHT
WRONG
RIGHT
RIGHT
Classification
• Of course, usually there are more than 4
features
• And more than 7 actions/data points
• These days, 800,000 student actions, and 26
features, would be a medium-sized data set
Classifiers
• There are literally hundreds of classification
algorithms that have been
proposed/published/tried out
• A good data mining package will have many
implementations
–
–
–
–
RapidMiner
SAS Enterprise Miner
Weka
KEEL
Domain-Specificity
• Specific algorithms work better for specific
domains and problems
• We often have hunches for why that is
• But it’s more in the realm of “lore” than really
“engineering”
Some algorithms you probably don’t
want to use
• Support Vector Machines
– Conducts dimensionality reduction on data space
and then fits hyperplane which splits classes
– Creates very sophisticated models
– Great for text mining
– Great for sensor data
– Usually pretty lousy for educational log data
Some algorithms you probably don’t
want to use
• Genetic Algorithms
– Uses mutation, combination, and natural selection
to search space of possible models
– Obtains a different answer every time (usually)
– Seems really awesome
– Usually doesn’t produce the best answer
Some algorithms you probably don’t
want to use
• Neural Networks
– Composes extremely complex relationships
through combining “perceptrons”
– Usually over-fits for educational log data
Note
• Support Vector Machines and Neural
Networks are great for some problems
• I just haven’t seen them be the best solution
for educational log data
Some algorithms you might find useful
•
•
•
•
•
Step Regression
Logistic Regression
J48/C4.5 Decision Trees
JRip Decision Rules
K* Instance-Based Classifier
• There are many others!
Logistic Regression
Logistic Regression
• Already discussed in class
• Fits logistic function to data to find out the
frequency/odds of a specific value of the
dependent variable
• Given a specific set of values of predictor
variables
Logistic Regression
m = a0 + a1v1 + a2v2 + a3v3 + a4v4…
Logistic Regression
p(m)
1.2
1
0.8
0.6
0.4
0.2
0
-4
-3
-2
-1
0
1
2
3
4
Parameters fit
• Through Expectation Maximization
Relatively conservative
• Thanks to simple functional form, is a
relatively conservative algorithm
– Less tendency to over-fit
Good for
• Cases where changes in value of predictor
variables have predictable effects on
probability of predictor variable class
Good when multi-level interactions
are not particularly common
• Can be given interaction effects through
automated feature distillation
– We’ll look at this later
• But is not particularly optimal for this
Note
• RapidMiner and Weka do not actually choose
features for you
• You have to select features by hand
• Or in java code that calls RapidMiner or Weka
• Easy to implement step-wise regression by hand,
painful to implement other feature selection
algorithms
Step Regression
Step Regression
• Fits a linear regression function
– (discussed in detail in a later class)
– with an arbitrary cut-off
• Selects parameters
• Assigns a weight to each parameter
• Computes a numerical value
• Then all values below 0.5 are treated as 0, and
all values >= 0.5 are treated as 1
Example
• Y= 0.5a + 0.7b – 0.2c + 0.4d + 0.3
• Cut-off 0.5
a
b
c
d
1
1
1
1
0
0
0
0
-1
-1
1
3
Parameters fit
• Through Iterative Gradient Descent
• This is a simple enough model that this
approach actually works…
Most conservative
• This is the most conservative classifier except
for the fabled “0R”
– More on that in a minute
Good for
• Cases where relationships between predictor
and predicted variables are relatively linear
Good when multi-level interactions
are not particularly common
• Can be given interaction effects through
automated feature distillation
– We’ll look at this later
• But is not particularly optimal for this
Feature Selection
• Greedy – simplest model
• M5’ – in between
• None – most complex model
Greedy
• Also called Forward Selection
– Even simpler than Stepwise Regression
1. Start with empty model
2. Which remaining feature best predicts the data
when added to current model
3. If improvement to model is over threshold (in
terms of SSR or statistical significance)
4. Then Add feature to model, and go to step 2
5. Else Quit
M5’
• Will be discussed in detail in regression lecture
0R
0R
• Always say 0
Decision Trees
Decision Tree
PKNOW
<0.5
>=0.5
TIME
Skill
COMPUTESLOPE
TOTALACTIONS
<6s.
>=6s.
RIGHT
WRONG
pknow
0.544
time
9
<4
RIGHT
>=4
WRONG
totalactions
1
right
?
Decision Tree Algorithms
• There are several
• I usually use J48, which is an open-source reimplementation of C4.5 (Quinlan, 1993)
J48/C4.5
• Can handle both numerical and categorical predictor
variables
– Tries to find optimal split in numerical variable
• Repeatedly looks for variable which best splits the data
in terms of predictive power for each variable (using
information gain)
• Later prunes out branches that turn out to have low
predictive power
• Note that different branches can have different
features!
Can be adjusted…
• To split based on more or less evidence
• To prune based on more or less predictive
power
Relatively conservative
• Thanks to pruning step, is a relatively
conservative algorithm
– Less tendency to over-fit
Good when data has natural splits
16
14
12
10
8
6
4
2
20
0
1
18
16
14
12
10
8
6
4
2
0
1
2
3
4
5
6
7
8
9
10
11
2
3
4
5
6
7
8
9
10
11
Good when multi-level interactions
are common
Good when same construct can be
arrived at in multiple ways
• A student is likely to drop out of college when
he
– Starts assignments early but lacks prerequisites
• OR when he
– Starts assignments the day they’re due
Decision Rules
Many Algorithms
• Differences are in terms of what metric is used
and how rules are generated
• Most popular subcategory (including JRip and
PART) repeatedly creates decision trees and
distills best rules
Generating Rules from Decision Tree
1. Create Decision Tree
2. If there is at least one path that is worth keeping, go
to 3 else go to 6
3. Take the “Best” single path from root to leaf and
make that path a rule
4. Remove all data points classified by that rule from
data set
5. Go to step 1
6. Take all remaining data points
7. Find the most common value for those data points
8. Make an “otherwise” rule using that
Relatively conservative
• Leads to simpler models than most decision
trees
– Less tendency to over-fit
Very interpretable model
• Unlike most other approaches
Example
(Baker & Clarke-Midura, under review)
1. IF the student spent at least 66 seconds reading the parasite information
page,
THEN the student will obtain the correct final conclusion (confidence =
81.5%)
2. IF the student spent at least 12 seconds reading the parasite information
page AND the student read the parasite information page at least twice
AND the student spent no more than 51 seconds reading the pesticides
information page,
THEN the student will obtain the correct final conclusion (confidence =
75.0%)
3. IF the student spent at least 44 seconds reading the parasite information
page AND the student spent under 56 seconds reading the pollution
information page,
THEN the student will obtain the correct final conclusion (confidence =
68.8%)
4. OTHERWISE the student will not obtain the correct final conclusion
(confidence = 89.0%)
Good when multi-level interactions
are common
Good when same construct can be
arrived at in multiple ways
• A student is likely to drop out of college when
he
– Starts assignments early but lacks prerequisites
• OR when he
– Starts assignments the day they’re due
K*
Instance-Based Classifier
• Takes a data point to predict
• Finds the K closest points to that data point,
by Euclidean distance
– K often equals 3
• Gives data point whichever class is most
common among those 3 points
Good when data is very divergent
• Lots of different processes can lead to the
same result
• Impossible to find general rules
• But data points that are similar tend to be
from the same class
Big Drawback
• To use the model, you need to have the whole
data set
Big Advantage
• Sometimes works when nothing else works
• Has been useful for my group in affect
detection
Comments? Questions?
Generating Confidences
• Each of these approaches gives not just a final
answer, but a confidence (or pseudoconfidence)
• Many applications of confidences – we’ll
discuss in detail in next lecture
Generating Confidences
• Step Regression – raw value of regression
• Logistic Regression – p(m)
• Jrip/J48 – ratio of correct classifications to
incorrect classifications in each leaf
– I will show you an example of this in a minute
Hands-On Activity
• Running algorithm in RapidMiner 4.6
• Using some made-up data, just to see how
things work
Open RapidMiner
• And open classifier.xml
• Let’s go through this script
Use RapidMiner
• Run JRip without cross-validation
• Run JRip with action-level cross-validation
• Run Jrip with batch-level cross-validation
– Set to implement student-level cross-validation
– We’ll discuss this more in the next lecture
Confidences
• How to interpret model confidence from
RapidMiner output
Let’s look at the data
• Are there any features we shouldn’t be using?
Remove those features
• Run the model again
Run other algorithms
• J48
Run other algorithms
• J48
• K*
Run other algorithms
• J48
• K*
• Step Regression
Run other algorithms
• J48
• K*
• Step Regression
– Why didn’t Step Regression work?
– How can we fix it?
Comments? Questions?
Comments or Questions
• About Assignment 3?
Next Class
• Wednesday, February 20
• Behavior Detection
• Assignment Due: 3. Behavior Detection
Excel
• Plan is to go as far as we can by 5pm
• We will continue after next class session
• Vote on which topics you most want to hear
about
Topics
•
•
•
•
•
•
•
•
•
•
•
•
Using average, count, sum, stdev (asgn. 4 data set)
Relative and absolute referencing (made up data)
Copy and paste values only (made up data)
Using sort, filter (asgn. 4 data set)
Making pivot table (asgn. 4 data set)
Using vlookup (Jan. 28 class data set)
Using countif (asgn. 4 data set)
Making scatterplot (Jan. 28 class data set)
Making histogram (asgn. 4 data set)
Equation Solver (Jan. 28 class data set)
Z-test (made up data)
2-sample t-test (made up data)
• Other topics?
The End