Download Evaluating Models

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Evaluating Induced Models
with
Daniel L. Silver
Copyright (c), 2004
All Rights Reserved
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Agenda
 Interpretation
and Evaluation Phase
 Model accuracy (fitness) and
confidence
 Testing the difference between two
models
 Testing the difference between two
DM methods (e.g. IDT versus ANN)
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The KDD Process
Interpretation
and Evaluation
Data Mining
Knowledge
Selection and
Preprocessing
Data
Consolidation
p(x)=0.02
Patterns &
Models
Data
Warehouse
Prepared Data
Consolidated
Data
Data Sources
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Inductive Modeling = Data Mining
Basic Framework for Inductive Learning
Testing
Examples
Environment
Training
Examples
(x, f(x))
Inductive
Learning System
Induced
Model of
Classifier
~ f(x)?
h(x) =
Focus is on developing models that
can accurately classify new examples.
Output Classification
(x, h(x))
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Model Accuracy and Confidence
Preferably a separate verification set is used
to judge fitness or accuracy
 Statistical confidence in the accuracy of a
model can be expressed as an interval

Mean
Error
or
Error
Rate
h1
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The Normal Curve and
Confidence Intervals
 Consider
a class of 30 persons
 True mean (average) mark of 75%
 How can we estimate this from the
marks of only 10 sample persons?
 Let’s do an example using Excel
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Model Accuracy and Confidence
Approach #1:
Large Sample
When the amount of available data is large ...
Available Examples
70%
Divide randomly
Training
Set
Used to develop one model
Test
Set
30%
Verify
Set
Generalization
= test/verify fit
Compute
Test error
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Model Accuracy and Confidence
Generalization statistic (fit, error or accuracy)
is provided by the learning system
 Confidence interval must be computed:

• Continuous target variable - Compute mean error
over n examples and confidence interval using
Excel (evaluate_models.xls)
• Nominal (binary) target variable - Given an error
rate of P from a sample of n examples, then the
95%conf. interval = 1.96 sqrt(P(1-P)/n) = 1.96 stdev
o
P = number incorrect / n
• Strictly speaking this is for n >= 30
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Testing the Difference Between
Two Models
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 Which
of the following two hypotheses
is the better? … h1 or h2 ?
Fitness
or
Error
Rate
h1
h2
h3
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Testing the Difference Between
Two Models
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 Assumption:
If some measurable
characteristic of the models is
statistically different then we will
consider the models different
 We will focus on the characteristics:
mean error, and error rate (proportion
incorrect) which can be computed from
the test results
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Testing the Difference Between
Two Models
 Continuous
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target variable
• Use a Difference of Means Test
 Nominal
(binary) target variable
• Use a Difference of Proportions Test
 For
95% confidence in a difference then
p-value statistic must be <= 0.05
(see Excel spreadsheet example)
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Testing the Difference Between
Two DM Methods
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 Cross-Validation
must be performed
 Requires generating several models
with different train, test and verify sets
 With WEKA use the accuracy or error
rate on the test sets
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Network Training
Approach #2: Cross-validation
Provides a sense of confidence in model ...
Available Examples
10%
90%
Training
Set
Used to develop 10 different models
Repeat 10
times
Test
Set
Ver.
Set
Generalization
determined by mean
test fit and stddev
Accumulate
test errors
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Testing the Difference Between
Two DM Methods
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A
Difference of Means T-test can be
used to determine a p-value statistic
 For 95% confidence in a difference then
p-value statistic must be <= 0.05
(see Excel spreadsheet example)
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Example: Using Census Data
 Problem: To identify males given census
data
 Performance
measure:
• Accuracy = Goodness of fit
 Model
generation: IDT and ANN
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Example: Using Census Data
 Record results: Goodness of fit stats on test set
for 10 different models
• Mean fitness: ANN= 26.6, IDT = 31.8
 Test difference between models: Use a
difference of means T-test (see evaluate_models.xls)
• p-value = 0.00124
• Since p-value < 0.05, the two models are
significantly different
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THE END
[email protected]
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