Download Detecting Group Differences: Mining Contrast Sets

Detecting Group Differences:
Mining Contrast Sets
Author: Stephen D. Bay
Advisor: Dr. Hsu
Graduate: Yan-Cheng Lin
Outline
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Motivation
Objective
Research Review
Search for Contrast Sets
Filtering for Summarizing Contrast
Set
Evaluation
Conclusion
Motivation
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Learning group differences a central
problem in many domains
Contrasting groups especially
important in social science research
Objective
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Automatically detect differences
between contrasting groups from
observational multivariate data
Research Review
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time series research
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traditional statistical methods
rule learner and decision tree
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multiple observations
miss group differences
association rule mining
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multiple group and different search
criteria
Problem Definition
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itemset concept extends to contrast
set
Definition 1:
Let A1,A2,...,Ak be a set of k variables called
attributes.
Each Ai can take on values from the set
{Vi1,Vi2,...Vim}.
Contrast set a conjunction of attribute –
value pairs defined on groups G1,G2,...,Gn
with no Ai occurring more than once.
Define support of contrast set
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Definition 2:
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The support of a contrast set with respect to a group
G is the percentage of examples in G where the
contrast set is true.
minimum support difference δ user defined threshold
Search for Contrast Sets
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find contrast sets meet our criteria
though search
explore all possible contrast sets
return only sets meet our criteria
STUCCO (Search and Testing for
Understandable Consistent
Contrasts): breadth-first search
incorporates several efficiently
mining techniques
Framework
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use set-enumeration trees
use breadth-first search
counting phase organize nodes into candidate
groups
Finding Significant Contrast Sets
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testing the null hypothesis across all groups
support counts from contingency tables
Controlling Search Error
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data mining test many hypotheses
family of tests control Type I error
Bonferroni inequality:given any set of
events e1,e2,...,en, the probability of their
union is less than or equal to the sum of
the individual probabilities
Pruning
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prune when contrast sets fail to meet
effect size or statistical significance
criteria
prune when lead to uninteresting contrast
sets
Effect Size Pruning
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prune nodes when bound maximum support
difference groups below δ
Statistical Significance Pruning
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pruned when too few data or maximum value
X2 too small
Interest Based Pruning
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contrast sets are not interesting when have
identical support or relation between groups is
fixed
Specializations with Identical Support
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marital-status=husband
marital-status=husband ^ Sex = male
Fixed Relations
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Fixed Relations
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prune node as contrast set specializations do
not add new information
Relation to Itemset Mining
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minimum support difference criterion implies
constraints support levels in individual groups
eliminate large portions of the search space based
on:
subset infrequency pruning
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effect size pruning
superset frequency pruning
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interest based pruning
ab
abc
Filtering for Summarizing Contrast Set
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past approaches
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limit the rules shown by constraint the
variables or items
compare discovered rules, show only
unexpected results
new methods
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expectation based statistical approach
identify and select linear trend contrast
sets
Statistical Surprise
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show most general contrast sets
first, more complicated conjunctions
if surprising based on previously
shown sets
IPF(Iterative Proportional Fitting)
find maximum likelihood estimates
Detecting Linear Trends
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identical to finding change over time
detect significant contrast set by using the chisquare test
use regression techniques to find the portion of
the x2
Evaluation
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three research points:
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low support difference
 few high support attribute-value pairs, lower bounds
can’t take advantage
pruning rules
 δ -> 0 statistical significance pruning is more
important
filtering rules
Conclusion
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STUCCO algorithm combined
statistical hypothesis testing with
search for mining contrast sets
STUCOO has
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pruning rules efficient mining at low
support differences
guaranteed control over false positives
linear trend detection
compact summarization of result