CrossValidation_v2

```Manu Chandran
Outline
 Background and motivation
 Over view of techniques
 Cross validation
 Bootstrap method
 Setting up the problem
 Comparing AIC,BIC,Crossvalidation,Bootstrap
 For small data set
 For large data set
- iris data set
- ellipse data set
 Finding number of relevant parameters – cancer data set
(from class text)
 Conclusion
Background and Motivation
 Model Selection
 Parameters to change
 Overview of error measures and when is it used
 AIC
-> Low data count, strives for less complexity
 BIC
-> High data count, less complexity
 Cross validation
 Boot strap methods
Motivation for Cross validation
 Small number of data set
 Enables re use of data.
 Basic idea of cross validation
 K fold cross-validation .
 K = 5 in this example
Simple enough! What more ?
 Points to consider
 Why is it important ?

Finding the Test Error?
 Selection of K-fold


What K is good enough for given data set ?
How is it important – bias, variance
 Selection of features in “low data-high feature” problem


Important do’s and don’ts in feature selection when using
cross validation
Finds application in bio informatics, where more than often
number of parameters too high than data.
Overview of error terms
 Recap from last class
 In sample error : Errin
 Expected Error : Err
 Training error : err
 True Error
: ErrT
 AIC and BIC attempts to find Errin
 Crossvalidation attempts to find average error Err
Selection of K
 K = N , N fold CV or Leave One Out
 Unbiased
 High varaince
 K = 5, 5 fold CV
 Lower variance
 High Bias
 Subset p means
 best set of linear predictors
Selection of features using CV
 Often finds application in bio informatics
 One way of selecting predictors
 Screen predictors which show high correlation with
class labels
 Build multivariate classifier
 Use CV to find tuning parameter

Estimate prediction error of final model
The problem in this method
 The CV is done after feature selection.
This means the test samples had an effect on
selecting predictors
 Right way to do cross validation
 Divide samples into K cross validation folds at random
 Say for K = 5



Find predictors based on the 4 training data
Using these predictors, tune the classifier with these 4 sets
Test on the left out 5th set
Correlation of predictors with
outcome
Boot strapping
 Explanation of boot strapping
 Probability of having ith sample in boot strap sample
 Given by Poisson distribution with  = 1 for large N
 So Expectation of Error = 0.5*0.368 = 0.184
 Far below 0.5
 To avoid this leave one out boot strap is suggested
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