1. Gene Set Enrichment Analysis
Xiaole Shirley Liu
STAT115/STAT215

2. Gene Set Enrichment Analysis
In some microarray experiments comparing two conditions, there might be no single gene significantly diff expressed, but a group of genes slightly diff expressed
Check a set of genes with similar annotation (e.g. GO) and see their expression values
Kolmogorov-Smirnov test
GSEA at Broad Institute

3. Gene Set Enrichment Analysis
Mootha et al, PNAS 2003
Kolmogorov-Smirnov test
Cumulative fraction function: What fraction of genes are below this fold change? FC
T*-test

4. Gene Set Enrichment Analysis
Alternative to KS: one sample z-test
Population with all the genes follow normal ~ N(,2)
Avg of the genes (X) with a specific annotation:
STAT115 03/18/2008

5. Gene Set Enrichment Analysis
Set of genes with specific annotation involved in coordinated down-regulation
Need to define the set before looking at the data
Can only see the significance by looking at the whole set

6. Expanded Gene Sets
Subramanian, et al PNAS 2005

7. Examples of GSEA
Break

8. Microarray Classification
Xiaole Shirley Liu
STAT115/STAT215

9. Microarray Classification?

10. Classification Equivalent to machine learning methods
Task: assign object to class based on measurements on object
E.g. is sample normal or cancer based on expression profile?
Unsupervised learning
Ignore known class labels
Sometimes can’t separate even the known classes
Supervised learning:
Extract useful features based on known class labels to best separate classes
Can over fit the data, so need to separate training and test set

11. Clustering Classification
Which known samples does the unknown sample cluster with?
No guarantee that the known sample will cluster
Try batch removal or different clustering methods
Change linkage, select subset genes (semi-supervised)

12. K Nearest Neighbor Used in missing value estimation
For observation X with unknown label, find the K observations in the training data closest (e.g. correlation) to X
Predict the label of X based on majority vote by KNN
K can be determined by predictability of known samples, semi-supervised again!

13. KNN Example
Can extend KNN by assigning weights to the neighbors by inverse distance from the test-sample
Offer little insights into mechanism

14. MDS Break Multidimensional scaling
Based on distance between data in high dimensional space (e.g. correlations)
Give 2-3D representation approximating the pairwise distance relationship as much as possible
Non-linear projection
Can directly predict
new sample based on dist
Break

15. Principal Component Analysis
Linear transformation that projects the data on to new coordinate system (linear combinations of the original variables) to capture as much of the variation in data as possible
The first principal component accounts for the greatest possible variance in dataset
The second principal component accounts for the next highest variance and is uncorrelated with (orthogonal to) the first principal component.

16. Finding the Projections
Looking for a linear combination to transform the original data matrix X to:
Y= T X=1 X1+ 2 X2+..+ p Xp
Where  =(1 , 2 ,.., p)T is a column vector of weights with
1²+ 2²+..+ p² =1
Maximize the variance of the projection of the observations on the Y variables

17. Finding the Projections
Good
Better
The direction of  is given by the eigenvector 1 correponding to the largest eigenvalue of matrix C
The second vector that is orthogonal (uncorrelated) to the first is the one that has the second highest variance which comes to be the eignevector corresponding to the second eigenvalue

18. Principal Component Analysis
Achieved by singular value decomposition (SVD): X = UDVT
X is the original data
U (N × N) is the relative
projection of the points
V is project directions
v1 is a unit vector, direction of the first projection
The eigenvector with the largest eigenvalue
Linear combination (relative importance) of each gene (if PCA on samples)

19. PCA D is scaling factor (eigenvalue)
Diagonal matrix, d1  d2  d3  …  0
dm2 measures the variances captures by the mth principal component
u1d1 is distance along v1 from origin (first principal components)
Expression value projected on v1
u1d1 captures the largest variance of original X
v2 is 2nd projection direction, orthogonal to PC1, u2d2 is 2nd principal component and captures the 2nd largest var of X

20. PCA for Classification
Blood transcriptome of healthy individual (HI), cardiovascular risk factor individuals (RF), individuals with asymptomatic left ventricular dysfunction groups (ALVD) and chronic heart failure patients (CHF).
New sample predicted to be CHF.

21. Interpretation of components
See the weights of variables in each component
If Y1= 0.41X X X3+0.03X4+…
X1 and X3 are more important than X2 and X4 in PC1, offers some biological insights
PCA and MDS are both good dimension reduction methods
PCA is a good clustering method, and can be conducted on genes or on samples
PCA is only powerful if the biological question is related to the highest variance in the dataset

22. PCA for Batch Effect Detection
PCA can identify batch effect
Obvious batch effect: early PC’s separate samples by batch
Un-normalized Qnorm COMBAT
Brezina et al, Microarray 2015
Break

23. Supervised Learning

24. Supervised Learning Performance Assessment
If error rate is estimated from whole learning data set, could overfit the data (do well now, but poorly in future observations)
Need cross validation to assess performance
Leave-1 cross validation on n data points
Build classifier on (n-1), test on the one left out
N-fold cross validation
Divide data into N subset (equal size), build classifier on (N-1) subsets, compute error rate on left out subset

25. Logistic Regression Data: (yi, xi), i=1,…, n
Dependent variable is binary: 0, 1
Model
Logit: natural log of odds ratio Pb(1) over Pb(0)
b0+b1X really big, Y =1; b0+b1X really small, Y =0
But change in probability is not linear with changes in X
b0  intercept
b1  regression slope
b0+b1X = 0  decision
boundary Pb(1) = 0.5

26. Example (wiki) Hours study on Pb of passing an exam
Significant association
P-value
Pb (pass) = 1/[1+exp(-b0-b1X)]
= 1/[1+exp( * Hours)]
4.0777/ = 2.71 hours  Pb (pass) = 0.5

27. Logistic Regression Sample classification: Y  Cancer 1, Normal 0
Find subset of p genes whose expression x collectively predict new sample classification
’s are estimated from training data (R)
The decision boundary is determined by the linear regression, i.e., classify yi =1 if:
More later in the semester
x<-c(rnorm(50),rnorm(50)+2)
y<-c(rnorm(50)*0,rnorm(50)*0+1)
plot(x,y)
data1<-data.frame(covariate=x, response=y)
g.test<-glm(response~covariate, family=binomial(), data=data1)
x1<-cbind(c(1:100)*0+1,x) #adding a constant term
g.test<-glm.fit(x1,y,family=binomial())
plot(g.test$fitted.values)

28. Support Vector Machine
SVM
Which hyperplane is the best?

29. Support Vector Machine
SVM finds the hyperplane that maximizes the margin
Margin determined by support vectors (samples lie on the class
edge), others irrelevant

30. Support Vector Machine
SVM finds the hyperplane that maximizes the margin
Margin determined by support vectors others irrelevant
Extensions:
Soft edge, support vectors diff
weight
Non separable: slack var  > 0
Max (margin –   # bad)

31. Nonlinear SVM
Project the data through higher dimensional space with kernel function, so classes can be separated by hyperplane
A few implemented kernel functions available in BioConductor, the choice is usually trial and error and personal experience
K(x,y) = (xy)2

32. Outline GSEA for activities of group of genes
Dimension reduction techniques
MDS, PCA
Unsupervised learning method
Clustering, KNN, MDS
PCA, batch effect
Supervised learning for classification
Logistic regression
SVM
Cross validation