Data Mining Practical Machine Learning Tools and Techniques

Data Mining
Practical Machine Learning Tools and Techniques
Slides for Chapter 7 of Data Mining by I. H. Witten and E. Frank

2
Data Mining: Practical Machine Learning Tools and Techniques (Chapter 7)
Engineering the input and output
●
Attribute selection
♦ Schemeindependent, schemespecific
●
Attribute discretization
♦ Unsupervised, supervised, error vs entropybased, converse of discretization
●
Data transformations
♦ Principal component analysis, random projections, text, time series
●
Dirty data
♦ Data cleansing, robust regression, anomaly detection
●
Metalearning
♦ Bagging (with costs), randomization, boosting, additive (logistic) regression,
option trees, logistic model trees, stacking, ECOCs
●
Using unlabeled data
♦ Clustering for classification, cotraining, EM and cotraining

3
Just apply a learner? NO!
●
Scheme/parameter selection
treat selection process as part of the learning
process
●
Modifying the input:
♦ Data engineering to make learning possible or
easier
●
Modifying the output
♦ Combining models to improve performance

4
Attribute selection
●
Adding a random (i.e. irrelevant) attribute can
significantly degrade C4.5’s performance
♦ Problem: attribute selection based on smaller and
smaller amounts of data
●
IBL very susceptible to irrelevant attributes
♦ Number of training instances required increases
exponentially with number of irrelevant attributes
●
Naïve Bayes doesn’t have this problem
●
Relevant attributes can also be harmful

5
Schemeindependent attribute selection
●
Filter approach: assess based on general characteristics of the data
●
One method: find smallest subset of attributes that separates data
●
Another method: use different learning scheme
♦ e.g. use attributes selected by C4.5 and 1R, or coefficients of linear
model, possibly applied recursively (recursive feature elimination)
●
IBLbased attribute weighting techniques:
♦ can’t find redundant attributes (but fix has been suggested)
●
Correlationbased Feature Selection (CFS):
♦ correlation between attributes measured by symmetric uncertainty:
♦ goodness of subset of attributes measured by (breaking ties in favor of
smaller subsets):
UA ,B=2 HAHB−HA,B
HAHB
∈[0,1]
∑j UAj ,C/∑i ∑j UAi ,Aj

6
Attribute subsets for weather data

7
Searching attribute space
● Number of attribute subsets is
exponential in number of attributes
● Common greedy approaches:
● forward selection
● backward elimination
● More sophisticated strategies:
● Bidirectional search
● Bestfirst search: can find optimum solution
● Beam search: approximation to bestfirst search
● Genetic algorithms

8
Schemespecific selection
● Wrapper approach to attribute selection
● Implement “wrapper” around learning scheme
● Evaluation criterion: crossvalidation performance
● Time consuming
● greedy approach, k attributes ⇒ k2
× time
● prior ranking of attributes ⇒ linear in k
● Can use significance test to stop crossvalidation for
subset early if it is unlikely to “win” (race search)
● can be used with forward, backward selection, prior ranking, or special
purpose schemata search
● Learning decision tables: schemespecific attribute
selection essential
● Efficient for decision tables and Naïve Bayes

9
Attribute discretization
●
Avoids normality assumption in Naïve Bayes and
clustering
●
1R: uses simple discretization scheme
●
C4.5 performs local discretization
●
Global discretization can be advantageous because
it’s based on more data
●
Apply learner to
♦ k valued discretized attribute or to
♦ k – 1 binary attributes that code the cut points

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Discretization: unsupervised
● Determine intervals without knowing class labels
● When clustering, the only possible way!
● Two strategies:
● Equalinterval binning
● Equalfrequency binning
(also called histogram equalization)
● Normally inferior to supervised schemes in
classification tasks
● But equalfrequency binning works well with naïve Bayes if
number of intervals is set to square root of size of dataset
(proportional kinterval discretization)

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Discretization: supervised
● Entropybased method
● Build a decision tree with prepruning on the
attribute being discretized
● Use entropy as splitting criterion
● Use minimum description length principle as stopping
criterion
● Works well: the state of the art
● To apply min description length principle:
● The “theory” is
● the splitting point (log2[N – 1] bits)
● plus class distribution in each subset
● Compare description lengths before/after adding split

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Example: temperature attribute
Pl ay
Tem
per at ur e
Yes No Yes Yes Yes No No Yes Yes Yes No Yes Yes No
64 65 68 69 70 71 72 72 75 75 80 81 83 85

13
Formula for MDLP
● N instances
● Original set: k classes, entropy E
● First subset: k1 classes, entropy E1
● Second subset: k2 classes, entropy E2
● Results in no discretization intervals for
temperature attribute
gain
log2N−1
N

log23k
−2−kEk1E1k2E2
N

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Supervised discretization: other methods
●
Can replace topdown procedure by bottomup
method
●
Can replace MDLP by chisquared test
●
Can use dynamic programming to find optimum
kway split for given additive criterion
♦ Requires time quadratic in the number of instances
♦ But can be done in linear time if error rate is used
instead of entropy

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Errorbased vs. entropybased
● Question:
could the best discretization ever have two
adjacent intervals with the same class?
● Wrong answer: No. For if so,
● Collapse the two
● Free up an interval
● Use it somewhere else
● (This is what errorbased discretization will do)
● Right answer: Surprisingly, yes.
● (and entropybased discretization can do it)

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Errorbased vs. entropybased
A 2class,
2attribute
problem
Entropybased discretization can detect change of class distribution

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The converse of discretization
● Make nominal values into “numeric” ones
1. Indicator attributes (used by IB1)
• Makes no use of potential ordering information
2. Code an ordered nominal attribute into binary
ones (used by M5’)
• Can be used for any ordered attribute
• Better than coding ordering into an integer (which
implies a metric)
● In general: code subset of attribute values as
binary

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Data transformations
●
Simple transformations can often make a large difference
in performance
●
Example transformations (not necessarily for
performance improvement):
♦ Difference of two date attributes
♦ Ratio of two numeric (ratioscale) attributes
♦ Concatenating the values of nominal attributes
♦ Encoding cluster membership
♦ Adding noise to data
♦ Removing data randomly or selectively
♦ Obfuscating the data

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Principal component analysis
●
Method for identifying the important “directions”
in the data
●
Can rotate data into (reduced) coordinate system
that is given by those directions
●
Algorithm:
1.Find direction (axis) of greatest variance
2.Find direction of greatest variance that is perpendicular
to previous direction and repeat
● Implementation: find eigenvectors of covariance
matrix by diagonalization
● Eigenvectors (sorted by eigenvalues) are the directions

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Example: 10dimensional data
●
Can transform data into space given by components
●
Data is normally standardized for PCA
●
Could also apply this recursively in tree learner

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Random projections
●
PCA is nice but expensive: cubic in number of
attributes
●
Alternative: use random directions
(projections) instead of principle components
●
Surprising: random projections preserve
distance relationships quite well (on average)
♦ Can use them to apply kDtrees to high
dimensional data
♦ Can improve stability by using ensemble of
models based on different projections

22
Text to attribute vectors
●
Many data mining applications involve textual data (eg. string
attributes in ARFF)
●
Standard transformation: convert string into bag of words by
tokenization
♦ Attribute values are binary, word frequencies (fij
),
log(1+fij
), or TF × IDF:
●
Only retain alphabetic sequences?
●
What should be used as delimiters?
●
Should words be converted to lowercase?
●
Should stopwords be ignored?
●
Should hapax legomena be included? Or even just the k most
frequent words?
fij log#documents
#documentsthatincludeword i

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Time series
●
In time series data, each instance represents a different
time step
●
Some simple transformations:
♦ Shift values from the past/future
♦ Compute difference (delta) between instances (ie.
“derivative”)
●
In some datasets, samples are not regular but time is
given by timestamp attribute
♦ Need to normalize by step size when transforming
●
Transformations need to be adapted if attributes
represent different time steps

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Automatic data cleansing
●
To improve a decision tree:
♦ Remove misclassified instances, then relearn!
●
Better (of course!):
♦ Human expert checks misclassified instances
●
Attribute noise vs class noise
♦ Attribute noise should be left in training set
(don’t train on clean set and test on dirty one)
♦ Systematic class noise (e.g. one class substituted for
another): leave in training set
♦ Unsystematic class noise: eliminate from training
set, if possible

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Robust regression
● “Robust” statistical method ⇒one that
addresses problem of outliers
● To make regression more robust:
● Minimize absolute error, not squared error
● Remove outliers (e.g. 10% of points farthest from
the regression plane)
● Minimize median instead of mean of squares
(copes with outliers in x and y direction)
● Finds narrowest strip covering half the observations

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Example: least median of squares
Number of international phone calls from
Belgium, 1950–1973

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Detecting anomalies
●
Visualization can help to detect anomalies
●
Automatic approach:
committee of different learning schemes
♦ E.g.
● decision tree
● nearestneighbor learner
● linear discriminant function
♦ Conservative approach: delete instances
incorrectly classified by all of them
♦ Problem: might sacrifice instances of small
classes

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Combining multiple models
●
Basic idea:
build different “experts”, let them vote
●
Advantage:
♦ often improves predictive performance
●
Disadvantage:
♦ usually produces output that is very hard to
analyze
♦ but: there are approaches that aim to produce
a single comprehensible structure

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Bagging
● Combining predictions by voting/averaging
● Simplest way
● Each model receives equal weight
● “Idealized” version:
● Sample several training sets of size n
(instead of just having one training set of size n)
● Build a classifier for each training set
● Combine the classifiers’ predictions
● Learning scheme is unstable ⇒
almost always improves performance
● Small change in training data can make big
change in model (e.g. decision trees)

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Biasvariance decomposition
●
Used to analyze how much selection of any
specific training set affects performance
●
Assume infinitely many classifiers,
built from different training sets of size n
●
For any learning scheme,
♦ Bias = expected error of the combined
classifier on new data
♦ Variance= expected error due to the
particular training set used
● Total expected error ≈ bias + variance

31
More on bagging
●
Bagging works because it reduces variance by
voting/averaging
♦ Note: in some pathological hypothetical situations the
overall error might increase
♦ Usually, the more classifiers the better
●
Problem: we only have one dataset!
●
Solution: generate new ones of size n by sampling
from it with replacement
●
Can help a lot if data is noisy
●
Can also be applied to numeric prediction
♦ Aside: biasvariance decomposition originally only
known for numeric prediction

32
Bagging classifiers
Let n be the number of instances in the training data
For each of t iterations:
Sample n instances from training set
(with replacement)
Apply learning algorithm to the sample
Store resulting model
For each of the t models:
Predict class of instance using model
Return class that is predicted most often
Model generation
Classification

33
Bagging with costs
●
Bagging unpruned decision trees known to produce
good probability estimates
♦ Where, instead of voting, the individual classifiers'
probability estimates are averaged
♦ Note: this can also improve the success rate
●
Can use this with minimumexpected cost approach
for learning problems with costs
●
Problem: not interpretable
♦ MetaCost relabels training data using bagging with
costs and then builds single tree

34
Randomization
●
Can randomize learning algorithm instead of input
●
Some algorithms already have a random component:
eg. initial weights in neural net
●
Most algorithms can be randomized, eg. greedy
algorithms:
♦ Pick from the N best options at random instead of
always picking the best options
♦ Eg.: attribute selection in decision trees
●
More generally applicable than bagging: e.g. random
subsets in nearestneighbor scheme
●
Can be combined with bagging

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Boosting
●
Also uses voting/averaging
●
Weights models according to performance
●
Iterative: new models are influenced by
performance of previously built ones
♦ Encourage new model to become an “expert”
for instances misclassified by earlier models
♦ Intuitive justification: models should be
experts that complement each other
●
Several variants

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AdaBoost.M1
Assign equal weight to each training instance
For t iterations:
Apply learning algorithm to weighted dataset,
store resulting model
Compute model’s error e on weighted dataset
If e = 0 or e ≥ 0.5:
Terminate model generation
For each instance in dataset:
If classified correctly by model:
Multiply instance’s weight by e/(1-e)
Normalize weight of all instances
Model generation
Classification
Assign weight = 0 to all classes
For each of the t (or less) models:
For the class this model predicts
add –log e/(1-e) to this class’s weight
Return class with highest weight

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More on boosting I
● Boosting needs weights … but
● Can adapt learning algorithm ... or
● Can apply boosting without weights
● resample with probability determined by weights
● disadvantage: not all instances are used
● advantage: if error > 0.5, can resample again
● Stems from computational learning theory
● Theoretical result:
● training error decreases exponentially
● Also:
● works if base classifiers are not too complex, and
● their error doesn’t become too large too quickly

38
More on boosting II
● Continue boosting after training error = 0?
● Puzzling fact:
generalization error continues to decrease!
● Seems to contradict Occam’s Razor
● Explanation:
consider margin (confidence), not error
● Difference between estimated probability for true
class and nearest other class (between –1 and 1)
● Boosting works with weak learners
only condition: error doesn’t exceed 0.5
● In practice, boosting sometimes overfits (in
contrast to bagging)

39
Additive regression I
●
Turns out that boosting is a greedy algorithm for
fitting additive models
●
More specifically, implements forward stagewise
additive modeling
●
Same kind of algorithm for numeric prediction:
1.Build standard regression model (eg. tree)
2.Gather residuals, learn model predicting
residuals (eg. tree), and repeat
● To predict, simply sum up individual predictions
from all models

40
Additive regression II
●
Minimizes squared error of ensemble if base learner
minimizes squared error
●
Doesn't make sense to use it with standard multiple
linear regression, why?
●
Can use it with simple linear regression to build
multiple linear regression model
●
Use crossvalidation to decide when to stop
●
Another trick: shrink predictions of the base models by
multiplying with pos. constant < 1
♦ Caveat: need to start with model 0 that predicts the
mean

41
Additive logistic regression
●
Can use the logit transformation to get algorithm for
classification
♦ More precisely, class probability estimation
♦ Probability estimation problem is transformed into
regression problem
♦ Regression scheme is used as base learner (eg.
regression tree learner)
●
Can use forward stagewise algorithm: at each stage, add
model that maximizes probability of data
● If fj
is the jth regression model, the ensemble predicts
probability for the first class
p1|
a= 1
1exp−∑ f j
a

42
LogitBoost
●
Maximizes probability if base learner minimizes squared error
●
Difference to AdaBoost: optimizes probability/likelihood instead of
exponential loss
●
Can be adapted to multiclass problems
● Shrinking and crossvalidationbased selection apply
For j = 1 to t iterations:
For each instance a[i]:
Set the target value for the regression to
z[i] = (y[i] – p(1|a[i])) / [p(1|a[i]) × (1-p(1|a[i])]
Set the weight of instance a[i] to p(1|a[i]) × (1-p(1|a[i])
Fit a regression model f[j] to the data with class
values z[i] and weights w[i]
Model generation
Classification
Predict 1st
class if p(1 | a) > 0.5, otherwise predict 2nd
class

43
Option trees
●
Ensembles are not interpretable
●
Can we generate a single model?
♦ One possibility: “cloning” the ensemble by using lots
of artificial data that is labeled by ensemble
♦ Another possibility: generating a single structure that
represents ensemble in compact fashion
●
Option tree: decision tree with option nodes
♦ Idea: follow all possible branches at option node
♦ Predictions from different branches are merged using
voting or by averaging probability estimates

44
Example
●
Can be learned by modifying tree learner:
♦ Create option node if there are several equally promising
splits (within userspecified interval)
♦ When pruning, error at option node is average error of
options

45
Alternating decision trees
●
Can also grow option tree by incrementally adding
nodes to it
●
Structure called alternating decision tree, with splitter
nodes and prediction nodes
♦ Prediction nodes are leaves if no splitter nodes have
been added to them yet
♦ Standard alternating tree applies to 2class problems
♦ To obtain prediction, filter instance down all
applicable branches and sum predictions
● Predict one class or the other depending on whether
the sum is positive or negative

46
Example

47
Growing alternating trees
●
Tree is grown using a boosting algorithm
♦ Eg. LogitBoost described earlier
♦ Assume that base learner produces single conjunctive rule in
each boosting iteration (note: rule for regression)
♦ Each rule could simply be added into the tree, including the
numeric prediction obtained from the rule
♦ Problem: tree would grow very large very quickly
♦ Solution: base learner should only consider candidate rules
that extend existing branches
● Extension adds splitter node and two prediction nodes
(assuming binary splits)
♦ Standard algorithm chooses best extension among all possible
extensions applicable to tree
♦ More efficient heuristics can be employed instead

48
Logistic model trees
●
Option trees may still be difficult to interpret
●
Can also use boosting to build decision trees with linear
models at the leaves (ie. trees without options)
●
Algorithm for building logistic model trees:
♦ Run LogitBoost with simple linear regression as base learner
(choosing the best attribute in each iteration)
♦ Interrupt boosting when crossvalidated performance of
additive model no longer increases
♦ Split data (eg. as in C4.5) and resume boosting in subsets of
data
♦ Prune tree using crossvalidationbased pruning strategy (from
CART tree learner)

49
Stacking
●
To combine predictions of base learners, don’t vote,
use meta learner
♦ Base learners: level0 models
♦ Meta learner: level1 model
♦ Predictions of base learners are input to meta learner
●
Base learners are usually different schemes
●
Can’t use predictions on training data to generate
data for level1 model!
♦ Instead use crossvalidationlike scheme
●
Hard to analyze theoretically: “black magic”

50
More on stacking
●
If base learners can output probabilities,
use those as input to meta learner instead
●
Which algorithm to use for meta learner?
♦ In principle, any learning scheme
♦ Prefer “relatively global, smooth” model
● Base learners do most of the work
● Reduces risk of overfitting
●
Stacking can be applied to numeric
prediction too

51
Errorcorrecting output codes
● Multiclass problem ⇒binary problems
● Simple scheme:
Oneperclass coding
● Idea: use errorcorrecting
codes instead
● base classifiers predict
1011111, true class = ??
● Use code words that have
large Hamming distance
between any pair
● Can correct up to (d – 1)/2 singlebit errors
0001
d
0010
c
0100
b
1000
a
class vector
class
0101010
d
0011001
c
0000111
b
1111111
a
class vector
class

52
More on ECOCs
● Two criteria :
● Row separation:
minimum distance between rows
● Column separation:
minimum distance between columns
● (and columns’ complements)
● Why? Because if columns are identical, base classifiers will likely
make the same errors
● Errorcorrection is weakened if errors are correlated
● 3 classes ⇒only 23
possible columns
● (and 4 out of the 8 are complements)
● Cannot achieve row and column separation
● Only works for problems with > 3 classes

53
Exhaustive ECOCs
● Exhaustive code for k classes:
● Columns comprise every
possible kstring …
● … except for complements
and allzero/one strings
● Each code word contains
2k–1
– 1 bits
● Class 1: code word is all ones
● Class 2: 2k–2
zeroes followed by 2k–2
–1 ones
● Class i : alternating runs of 2k–i
0s and 1s
● last run is one short
0101010
d
0011001
c
0000111
b
1111111
a
class vector
class
Exhaustive code, k = 4

54
More on ECOCs
● More classes ⇒exhaustive codes infeasible
● Number of columns increases exponentially
● Random code words have good errorcorrecting
properties on average!
● There are sophisticated methods for generating
ECOCs with just a few columns
● ECOCs don’t work with NN classifier
● But: works if different attribute subsets are used to predict
each output bit

55
Using unlabeled data
●
Semisupervised learning: attempts to use
unlabeled data as well as labeled data
♦ The aim is to improve classification performance
●
Why try to do this? Unlabeled data is often
plentiful and labeling data can be expensive
♦ Web mining: classifying web pages
♦ Text mining: identifying names in text
♦ Video mining: classifying people in the news
●
Leveraging the large pool of unlabeled
examples would be very attractive

56
Clustering for classification
●
Idea: use naïve Bayes on labeled examples and
then apply EM
♦ First, build naïve Bayes model on labeled data
♦ Second, label unlabeled data based on class probabilities
(“expectation” step)
♦ Third, train new naïve Bayes model based on all the data
(“maximization” step)
♦ Fourth, repeat 2nd
and 3rd
step until convergence
●
Essentially the same as EM for clustering with
fixed cluster membership probabilities for
labeled data and #clusters = #classes

57
Comments
●
Has been applied successfully to document
classification
♦ Certain phrases are indicative of classes
♦ Some of these phrases occur only in the unlabeled
data, some in both sets
♦ EM can generalize the model by taking advantage of
cooccurrence of these phrases
●
Refinement 1: reduce weight of unlabeled data
●
Refinement 2: allow multiple clusters per class

58
Cotraining
●
Method for learning from multiple views (multiple sets of
attributes), eg:
♦ First set of attributes describes content of web page
♦ Second set of attributes describes links that link to the web page
●
Step 1: build model from each view
●
Step 2: use models to assign labels to unlabeled data
●
Step 3: select those unlabeled examples that were most
confidently predicted (ideally, preserving ratio of classes)
●
Step 4: add those examples to the training set
●
Step 5: go to Step 1 until data exhausted
●
Assumption: views are independent

59
EM and cotraining
●
Like EM for semisupervised learning, but
view is switched in each iteration of EM
♦ Uses all the unlabeled data (probabilistically
labeled) for training
●
Has also been used successfully with
support vector machines
♦ Using logistic models fit to output of SVMs
●
Cotraining also seems to work when views
are chosen randomly!
♦ Why? Possibly because cotrained classifier is
more robust

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