CS545: Linear
Modeling
Chuck Anderson
R Tips for Linear
Modeling
Backing up Files in
Unix
Collinearity
CS545: Linear Modeling
Chuck Anderson
Department of Computer Science
Colorado State University
Fall, 2009
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R Tips for Linear Modeling: Handling Collinearity and Backing up Files in Unix - Prof. Cha, Study notes of Computer Science
R tips for linear modeling, focusing on handling collinearity and backing up files in unix. It covers standardizing inputs, calculating means and standard deviations, and creating a function for standardizing data. The document also discusses what makells should return and collecting and combining multiple results.
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Modeling
Chuck Anderson
R Tips for Linear Modeling
Backing up Files in Unix
Collinearity
CS545: Linear Modeling
Chuck Anderson
Department of Computer Science
Colorado State University
Fall, 2009
Modeling
Chuck Anderson
R Tips for Linear Modeling
Backing up Files in Unix
Collinearity
Outline
R Tips for Linear Modeling
Backing up Files in Unix
Collinearity
Modeling
Chuck Anderson
R Tips for Linear Modeling
Backing up Files in Unix
Collinearity
Standardizing Inputs
Standardize attribute values (each has mean zero, unit
variance):
Calculate mean of each attribute for training data.
means <โ colMeans(Xtrain)
Modeling
Chuck Anderson
R Tips for Linear Modeling
Backing up Files in Unix
Collinearity
Standardizing Inputs
Standardize attribute values (each has mean zero, unit
variance):
Calculate mean of each attribute for training data.
means <โ colMeans(Xtrain)
Calculate standard deviation of each attribute for
training data.
stdevs <โ sd(Xtrain)
Modeling
Chuck Anderson
R Tips for Linear Modeling
Backing up Files in Unix
Collinearity
Standardizing Inputs
Standardize attribute values (each has mean zero, unit
variance):
Calculate mean of each attribute for training data.
means <โ colMeans(Xtrain)
Calculate standard deviation of each attribute for
training data.
stdevs <โ sd(Xtrain)
Subtract means and divide by stdevs, column by column
Xstrain <โ (Xtrain โ matrix(means,nrow(Xtrain),ncol(Xtrain),byrow=TRUE)) / matrix(stdevs ,nrow(Xtrain),ncol(Xtrain ), byrow=TRUE)
To standardize testing data, use means and stdevs
calculated from training data.
Xstest <โ (Xtest โ matrix(means,nrow(Xtest),ncol(Xtest),byrow=TRUE)) / matrix(stdevs ,nrow(Xtest),ncol(Xtest ), byrow=TRUE)
Modeling
Chuck Anderson
R Tips for Linear Modeling
Backing up Files in Unix
Collinearity
Must keep track of means and stdevs from training
data. Can do as variables returned from standardize
function:
standardize <โ function(X,means=apply(X,2,mean),stdevs=apply(X,2,sd), returnParms=FALSE) {
X is nSamples by nInputComponents
stdevs [ stdevs==0] <โ 1 N <โ nrow(X) p <โ ncol(X) X <โ (X โ matrix(rep(means,N),N,p,byrow=TRUE))/ matrix(rep( stdevs ,N),N,p,byrow=TRUE) if (returnParms) list (data=X,means=means,stdevs=stdevs) else X }
used like
tp <โ standardize(Xtrain,returnParms=TRUE) Xstrain <โ tp$data Xstest <โ standardize(Xtest, tp$means, tp$stdevs)
Modeling
Chuck Anderson
R Tips for Linear Modeling
Backing up Files in Unix
Collinearity
What should makeLLS return?
Certainly want the weights returned. After all, that is
the model. What else?
Modeling
Chuck Anderson
R Tips for Linear Modeling
Backing up Files in Unix
Collinearity
What should makeLLS return?
Certainly want the weights returned. After all, that is
the model. What else?
The means and stdevs should also be associated with
this model. Different models will have different weights
and different standardization parameters.
Modeling
Chuck Anderson
R Tips for Linear Modeling
Backing up Files in Unix
Collinearity
What should makeLLS return?
Certainly want the weights returned. After all, that is
the model. What else?
The means and stdevs should also be associated with
this model. Different models will have different weights
and different standardization parameters.
How would makeLLS return all of this?
return( list ( weights=w, standardize=standardize ) )
Modeling
Chuck Anderson
R Tips for Linear Modeling
Backing up Files in Unix
Collinearity
What should makeLLS return?
Certainly want the weights returned. After all, that is
the model. What else?
The means and stdevs should also be associated with
this model. Different models will have different weights
and different standardization parameters.
How would makeLLS return all of this?
return( list ( weights=w, standardize=standardize ) )
Use like
model <โ makeLLS(Xtrain,Ttrain,lambda) predictions <โ useLLS(model,Xtest)
Modeling
Chuck Anderson
R Tips for Linear Modeling
Backing up Files in Unix
Collinearity
What should makeLLS return?
Certainly want the weights returned. After all, that is
the model. What else?
The means and stdevs should also be associated with
this model. Different models will have different weights
and different standardization parameters.
How would makeLLS return all of this?
return( list ( weights=w, standardize=standardize ) )
Use like
model <โ makeLLS(Xtrain,Ttrain,lambda) predictions <โ useLLS(model,Xtest)
Inside useLLS how would you use model?
Say useLLS has arguments named model and X:
Xs <โ model$standardize(X) predictions <โ Xs %*% model$weights
Modeling
Chuck Anderson
R Tips for Linear Modeling
Backing up Files in Unix
Collinearity
Collecting and Combiningg Multiple Results
We often want to repeat a calculation a number of
times using different parameter values, like values of ฮป
and of training set fraction. So, you might use a for
loop like
for ( trainf in c (0.2, 0.4, 0.6, 0.8, 0.9)) { for ( repi in 1:200) { for (lambda in seq (0,10, by=0.5)) {
do calculation here using trainf and lambda to obtain
trainRMSE and testRMSE
} } }
Modeling
Chuck Anderson
R Tips for Linear Modeling
Backing up Files in Unix
Collinearity
Collecting and Combiningg Multiple Results
We often want to repeat a calculation a number of
times using different parameter values, like values of ฮป
and of training set fraction. So, you might use a for
loop like
for ( trainf in c (0.2, 0.4, 0.6, 0.8, 0.9)) { for ( repi in 1:200) { for (lambda in seq (0,10, by=0.5)) {
do calculation here using trainf and lambda to obtain
trainRMSE and testRMSE
} } }
Can try to do sums of RMSEโs so you can calculate
average later. But, letโs use that cheap memory, and
just collect each result in a new row in a matrix.
do calculation here using trainf and lambda to obtain
trainRMSE and testRMSE
results <โ rbind(results, c( trainf ,lambda, trainRMSE, testRMSE))
Donโt forget to initialize results
results <โ c()
before you start the for loops.
Modeling
Chuck Anderson
R Tips for Linear Modeling
Backing up Files in Unix
Collinearity
Now, the matrix has many rows (200) for each pair of
(trainf, lambda) values. How can we calculate the
means of those 200 values? Check out ?unique.
results [,1] [,2] [,3] [,4] [1,] 0.2 0.1 3.2 3. [2,] 0.2 0.5 5.3 3. [3,] 0.2 0.1 5.5 3. unique(results [,1:2]) [,1] [,2] [1,] 0.2 0. [2,] 0.2 0.