data mining models and evaluation techniques

Data Mining Models & Data Mining Models & Evaluation TechniquesEvaluation Techniques

Created By – Shubham Pachori

Mentored By-Prof. K.P Agarwal

Motivation Metrics for Classifier’s Evaluation Methods for Classifier’s Evaluation Comparing the Performance of two

Classifiers Costs in Classification Ensemble Methods To Improve Accuracy

Overview

It is important to evaluate classifier’s generalization performance in order to: Determine whether to employ the classifier;

(For example: when learning the effectiveness of medical treatments from a limited-size data, it is important to estimate the accuracy of the classifiers.)

Optimize the classifier.(For example: when post-pruning decision trees we must evaluate the accuracy of the decision trees on each pruning step.)

Motivation

data

Targetdata Processed

data

Transformeddata Patterns

Knowledge

SelectionPreprocessing

& cleaning

Transformation& featureselection

Data Mining

InterpretationEvaluation

Model’s Evaluation in the KDD Process

Metrics for Classifier’s Evaluation

Predicted class

Actualclass

Pos Neg

Pos TP FN

Neg FP TN

P

N

Accuracy = (TP+TN)/(P+N) Error = (FP+FN)/(P+N) Precision = TP/(TP+FP) Recall/TP rate = TP/P FP Rate = FP/N

We can use: Training data; Independent test data; Hold-out method; k-fold cross-validation method; Leave-one-out method; Bootstrap method; Ensemble methods

How to Estimate the Metrics?

The accuracy/error estimates on the training data are not good indicators of performance on future data.

Q: Why? A: Because new data will probably not be exactly the same as the training data!

The accuracy/error estimates on the training data measure the degree of classifier’s overfitting.

Estimation with Training Data

Training set

Classifier

Training set

Estimation with independent test data is used when we have plenty of data and there is a natural way to forming training and test data.

For example: Quinlan in 1987 reported experiments in a medical domain for which the classifiers were trained on data from 1985 and tested on data from 1986.

Estimation with Independent Test Data

Training set

Classifier

Test set

The hold-out method splits the data into training data and test data (usually 2/3 for train, 1/3 for test). Then we build a classifier using the train data and test it using the test data.

The hold-out method is usually used when we have thousands of instances, including several hundred instances from each class.

Hold-out Method

Training set

Classifier

Test set

Data

Classification: Train, Validation, Test Split

Data

Predictions

Y N

Results Known

Training set

Validation set

++--+

Classifier BuilderEvaluate

+-+-

ClassifierFinal Test Set

+-+-

Final Evaluation

ModelBuilder

The test data can’t be used for parameter tuning!

Once evaluation is complete, all the data can be used to build the final classifier.

Generally, the larger the training data the better the classifier (but returns diminish).

The larger the test data the more accurate the error estimate.

Making the Most of the Data

The holdout method reserves a certain amount for testing and uses the remainder for training. Usually: one third for testing, the rest for training.

For “unbalanced” datasets, samples might not be representative. Few or none instances of some classes viz.

fraudulent transaction detection and Medical Diagnostic Tests

Stratified sample: advanced version of balancing the data. Make sure that each class is represented with

approximately equal proportions in both subsets.

Stratification

Holdout estimate can be made more reliable by repeating the process with different subsamples. In each iteration, a certain proportion is

randomly selected for training (possibly with stratification).

The error rates on the different iterations are averaged to yield an overall error rate.

This is called the repeated holdout method.

Repeated Holdout Method

Still not optimum: the different test sets overlap, but we would like all our instances from the data to be tested at least ones.

Can we prevent overlapping?

Repeated Holdout Method, 2

witten & eibe

k-fold cross-validation avoids overlapping test sets: First step: data is split into k subsets of equal

size; Second step: each subset in turn is used for

testing and the remainder for training. The subsets are stratified

before the cross-validation. The estimates are averaged to

yield an overall estimate.

k-Fold Cross-Validation

Classifier

Data

train train test

train test train

test train train

Standard method for evaluation: stratified 10-fold cross-validation.

Why 10? Extensive experiments have shown that this is the best choice to get an accurate estimate.

Stratification reduces the estimate’s variance. Even better: repeated stratified cross-validation:

E.g. ten-fold cross-validation is repeated ten times and results are averaged (reduces the variance).

More on Cross-Validation

Leave-One-Out is a particular form of cross-validation: Set number of folds to number of training

instances; I.e., for n training instances, build classifier

n times. Makes best use of the data. Involves no random sub-sampling. Very computationally expensive.

Leave-One-Out Cross-Validation

A disadvantage of Leave-One-Out-CV is that stratification is not possible: It guarantees a non-stratified sample because

there is only one instance in the test set! Extreme example - random dataset split

equally into two classes: Best inducer predicts majority class; 50% accuracy on fresh data; Leave-One-Out-CV estimate is 100% error!

Leave-One-Out Cross-Validation and Stratification

Cross validation uses sampling without replacement: The same instance, once selected, can not be

selected again for a particular training/test set The bootstrap uses sampling with replacement

to form the training set: Sample a dataset of n instances n times with

replacement to form a new dataset of n instances; Use this data as the training set; Use the instances from the original dataset that don’t

occur in the new training set for testing.

Bootstrap Method

The bootstrap method is also called the 0.632 bootstrap: A particular instance has a probability of 1–1/n of

not being picked; Thus its probability of ending up in the test data is:

This means the training data will contain approximately 63.2% of the instances and the test data will contain approximately 36.8% of the instances.

Bootstrap Method

368.011 1

e

n

n

The error estimate on the test data will be very pessimistic because the classifier is trained on just ~63% of the instances.

Therefore, combine it with the training error:

The training error gets less weight than the error on the test data.

Repeat process several times with different replacement samples; average the results.

Estimating Error with the Bootstrap Method

instances traininginstancestest 368.0632.0 eeerr

• Assume that we have two classifiers, M1 and M2, and we would like to know which one is better for a classification problem.

• We test the classifiers on n test data sets D1, D2, …, Dn, and we receive error rate estimates e11, e12, …, e1n for classifier M1 and error rate estimates e21, e22, …, e2n for classifier M2.

• Using rate estimates we can compute the mean error rate e1

for classifier M1 and the mean error rate e2 for classifier M2. • These mean error rates are just estimates of error on the

true population of future data cases. What if the difference between the two error rates is just attributed to chance?

Comparing Two Classifier Models

• We note that error rate estimates e11, e12, …, e1n for classifier M1 and error rate estimates e21, e22, …, e2n for classifier M2 are paired. Thus, we consider the differences d1, d2, …, dn where dj= | e1j- e2j|.

• The differences d1, d2, …, dn are instantiations of n random variables D1, D2, …, Dn with mean µD and standard deviation σD.

• We need to establish confidence intervals for µD in order to decide whether the difference in the generalization performance of the classifiers M1 and M2 is statistically significant or not.


• Since the standard deviation σD is unknown, we approximate it using the sample standard deviation sd:

• Since we approximate the true standard deviation σD, we introduce T statistics:

2212

11 )]()[(1 eeee

ns i

n

iid

nsDT

d

D

/


• The T statistics is governed by t-distribution with n - 1 degrees of freedom. Area = 1 -

t/2 t1- /2


• If d and sd are the mean and standard deviation of the normally distributed differences of n random pairs of errors, a (1 – α)100% confidence interval for µD = µ1 - µ2 is :

where tα/2 is the t-value with v = n -1 degrees of freedom, leaving an area of α/2 to the right.

• Thus, if the interval contains 0.0 we can conclude on significance level α that the difference is 0.0.

,2/2/ nstd

nstd d

Dd


In practice, different types of classification errors often incur different costs

Examples: ¨ Terrorist profiling

“Not a terrorist” correct 99.99% of the time Loan decisions Fault diagnosis Promotional mailing

Counting the Costs

Cost MatricesPos Neg

Pos TP Cost FN CostNeg FP Cost TN Cost

Usually, TP Cost and TN Cost are set equal to 0!

Hypothesized classTrue class

Cost-Sensitive Classification If the classifier outputs probability for each class, it can be

adjusted to minimize the expected costs of the predictions. Expected cost is computed as dot product of vector of

class probabilities and appropriate column in cost matrix.

Pos Neg

Pos TP Cost FN CostNeg FP Cost TN Cost


Assume that the classifier returns for an instance ppos = 0.6 and pneg = 0.4. Then, the expected cost if the instance is classified as positive is 0.6 * 0 + 0.4 * 10 = 4. The expected cost if the instance is classified as negative is 0.6 * 5 + 0.4 * 0 = 3. To minimize the costs the instance is classified as negative.

Cost Sensitive Classification

Pos Neg

Pos 0 5Neg 10 0


Cost Sensitive Learning Simple methods for cost sensitive learning:

Resampling of instances according to costs; Weighting of instances according to costs.

In Weka Cost Sensitive Classification and Learning can be applied for any classifier using the meta scheme: CostSensitiveClassifier.

Pos Neg

Pos 0 5Neg 10 0


ROC Curves and Analysis

TruePredictedpos neg

pos 60 40neg 20 80


pos 70 30neg 50 50


pos 40 60neg 30 70

Classifier 1TPr = 0.4FPr = 0.3



ROC SpaceIdeal classifier

chance

always negative

always positive

True Negative Rate

Fals

e N

egat

ive

Rat

e

Dominance in the ROC Space

Classifier A dominates classifier B if and only if TPrA > TPrB and FPrA < FPrB.

35

Ensemble Methods

Data

……

model 1

model 2

model k

Ensemble model

Applications: classification, clustering, collaborative filtering, anomaly

detection……

Combine multiple models into one!

36

Motivations

Ensemble model improves accuracy and robustness over single model methods

Applications: distributed computing privacy-preserving applications large-scale data with reusable models multiple sources of data

Efficiency: a complex problem can be decomposed into multiple sub-problems that are easier to understand and solve (divide-and-conquer approach)

37

Why Ensemble Works? (1)

Intuition combining diverse, independent opinions in human

decision-making as a protective mechanism (e.g. stock portfolio)

Uncorrelated error reduction Suppose we have 5 completely independent classifiers

for majority voting If accuracy is 70% for each

10 (.7^3)(.3^2)+5(.7^4)(.3)+(.7^5) 83.7% majority vote accuracy

101 such classifiers 99.9% majority vote accuracy

38

Why Ensemble Works? (2)

Model 1Model 2

Model 3Model 4

Model 5Model 6

Some unknown distribution

Ensemble gives the global picture!

39

Why Ensemble Works? (3)• Overcome limitations of single hypothesis– The target function may not be implementable with individual

classifiers, but may be approximated by model averaging

Decision Tree Model Averaging

40

Ensemble of Classifiers—Learn to Combine

labeled data

unlabeled data

……

final prediction

slearn the combination from labeled data

Training test

classifier 1

classifier 2

classifier k

Ensemble model

Algorithms: boosting, stacked generalization, rule ensemble, Bayesian

model averaging……

41

Ensemble of Classifiers—Consensus

labeled data

unlabeled data

……

final predictio

ns

training test

classifier 1

classifier 2

classifier k

combine the

predictions by

majority voting

Algorithms: bagging, random forest, random decision tree, model averaging of

probabilities……

42

Pros and Cons

Combine by learning

Combine by consensus

Pros Get useful feedbacks from labeled dataCan potentially improve accuracy

Do not need labeled dataCan improve the generalization performance

Cons Need to keep the labeled data to train the ensembleMay overfit the labeled dataCannot work when no labels are available

No feedbacks from the labeled dataRequire the assumption that consensus is better

Bagging

• Also known as bootstrap aggregation• Sampling uniformly with replacement • Build classifier on each bootstrap sample• 0.632 bootstrap• Each bootstrap sample Di contains approx.

63.2% of the original training data• Remaining (36.8%) are used as test set

Original Data 1 2 3 4 5 6 7 8 9 10Bagging (Round 1) 7 8 10 8 2 5 10 10 5 9Bagging (Round 2) 1 4 9 1 2 3 2 7 3 2Bagging (Round 3) 1 8 5 10 5 5 9 6 3 7

Bagging

Accuracy of bagging:

Works well for small data sets Example:

))(*368.0)(*632.0()( __1

settrainisettest

k

ii MAccMAccMAcc

X 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

y 1 1 1 -1 -1 -1 -1 1 1 1

Bagging• Decision Stump

• Single level decision binary tree

• Entropy – x<=0.35 or x<=0.75

• Accuracy at most 70%

Bagging

Accuracy of ensemble classifier: 100%

Bagging- Final Points

• Works well if the base classifiers are unstable• Increased accuracy because it reduces the

variance of the individual classifier• Does not focus on any particular instance of

the training data• Therefore, less susceptible to model over-

fitting when applied to noisy data• What if we want to focus on a particular

instances of training data?

Boosting Principles Boost a set of weak learners to a strong learner An iterative procedure to adaptively change

distribution of training data by focusing more on previously misclassified records Initially, all N records are assigned equal weights Unlike bagging, weights may change at the end of a

boosting round

Boosting Records that are wrongly classified will have their

weights increased Records that are classified correctly will have their

weights decreasedOriginal Data 1 2 3 4 5 6 7 8 9 10Boosting (Round 1) 7 3 2 8 7 9 4 10 6 3Boosting (Round 2) 5 4 9 4 2 5 1 7 4 2Boosting (Round 3) 4 4 8 10 4 5 4 6 3 4

• Example 4 is hard to classify

• Its weight is increased, therefore it is more likely to be chosen again in

subsequent rounds

Boosting

• Equal weights are assigned to each training tuple (1/d for round 1)

• After a classifier Mi is learned, the weights are adjusted to allow the subsequent classifier Mi+1 to “pay more attention” to tuples that were misclassified by Mi.

• Final boosted classifier M* combines the votes of each individual classifier

• Weight of each classifier’s vote is a function of its accuracy

• Adaboost – popular boosting algorithm

Adaboost

Input: Training set D containing d tuples k rounds A classification learning scheme

Output: A composite model

Adaboost Data set D containing d class-labeled tuples

(X1,y1), (X2,y2), (X3,y3),….(Xd,yd) Initially assign equal weight 1/d to each tuple To generate k base classifiers, we need k rounds

or iterations Round i, tuples from D are sampled with

replacement , to form Di (size d) Each tuple’s chance of being selected depends on

its weight

Adaboost

Base classifier Mi, is derived from training tuples of Di

Error of Mi is tested using Di Weights of training tuples are adjusted depending

on how they were classified Correctly classified: Decrease weight Incorrectly classified: Increase weight

Weight of a tuple indicates how hard it is to classify it (directly proportional)

Adaboost Some classifiers may be better at classifying some

“hard” tuples than others We finally have a series of classifiers that

complement each other! Error rate of model Mi:

where err(Xj) is the misclassification error for Xj(=1) If classifier error exceeds 0.5, we abandon it Try again with a new Di and a new Mi derived from it

d

jjji XerrwMerror )(*)(

Adaboost error (Mi) affects how the weights of training tuples

are updated If a tuple is correctly classified in round i, its weight

is multiplied by

Adjust weights of all correctly classified tuples Now weights of all tuples (including the

misclassified tuples) are normalized Normalization factor =

Weight of a classifier Mi’s weight is

)(1)(

i

i

MerrorMerror

weightsnewofsumweightsoldofsum

______

)(1)(log

i

i

MerrorMerror

Adaboost

The lower a classifier error rate, the more accurate it is, and therefore, the higher its weight for voting should be

Weight of a classifier Mi’s vote is

For each class c, sum the weights of each classifier that assigned class c to X (unseen tuple)

The class with the highest sum is the WINNER!

)(1)(log

i

i

MerrorMerror

Use test sets and the hold-out method for “large” data;

Use the cross-validation method for “middle-sized” data;

Use the leave-one-out and bootstrap methods for small data;

Don’t use test data for parameter tuning - use separate validation data.

Metric Evaluation Summary:

In this seminar report we have considered: Metrics for Classifier’s Evaluation Methods for Classifier’s Evaluation Comparing Data Mining Schemes Costs in Data Mining Ensemble Methods

Summary

Thank You

data mining models and evaluation techniques

Documents