Meeting Summary for 11/20/2008

We discussed our plans for the upcoming semester and topics that we would like to discuss in Spring.

Meeting Summary for 11/18/2008

We discussed the feature selection techniques outlined in the Hall and Holmes Paper, and looked at comparisons of a few techniques. We also discussed applicability to our research.

Meeting Summary for 11/13/08

We began by discussing the different types of matrices (positive definite etc). Some lectures for this are here:

http://www.youtube.com/watch?v=26lLZZz0KGg (Symmetric Matrices and Positive Definiteness)
http://www.youtube.com/watch?v=0sCLv2EQPg8 (Complex Matrices; Fast Fourier Transform)
http://www.youtube.com/watch?v=ZW8NWVyt4rg (Positive Definite Matrices and Minima)

From Gilbert Strang's lecture on SVD, we identified the most important aspects to be the geometric picture(3:00-4:38) and the equations(7:40-17:00). Here is the lecture:

http://www.youtube.com/watch?v=c9271ZFGKrU

Ina would post the Matlab commands for SVD on the blog. We would all look at the ICA/ NCA papers on our own.

For next week, we decided to look at feature selection. A good paper for this is

http://www.cs.waikato.ac.nz/~mhall/HallHolmesTKDE.pdf

Meeting Summary for 11/6/08

We went over PCA and its applications to microarray data (http://sysbio.soe.ucsc.edu/Pubs/psb00.pdf).

For next week we decided to look SVD with each of us looking at specific aspects

Jang : ICA and NCA

Mike : Excerpts of Strang's lecture;
Application :
Alter O, Brown PO, Botstein D. (2000) Singular value decomposition for genome-wide expression data processing and modeling. Proc Natl Acad Sci U S A, 97, 10101-6.

Ina : Matlab Commands for SVD

Archana : Types of Matrices (Definite, Positive Definite etc)

5 November 2008

We viewed Dr. Gilbert Strang's Linear Algebra lecture (#21) on EigenValue and EigenVectors through MIT OpenCourseware. Ina then ran through a brief tutorial on matlab for functions for calculating eigenvalues and eigenvectors. The tutorials referred to are as under:
1.http://mit.ocw.universia.net/14.452/s02/pdf/MatlabTut.pdf
2.http://amath.colorado.edu/computing/Matlab/Tutorial/LinAlgebra.html

31 October 2008

Today we concluded our introduction to linear algebra with a distribution of Jieping Ye's Basics of Lineal Algebra Matrices handout:

http://www.public.asu.edu/~jye02/CLASSES/Fall-2007/NOTES/Basics-Matrix.pdf

His other class materials are also available here:

http://www.public.asu.edu/~jye02/CLASSES/Fall-2007/index.htm

For next week, we will discuss Eigenvectors and Eigenvalues in the context of Principle Components Analysis with bioinformatics applications. Archana and Jang will locate 2-4 papers including overview information for PCA, ICA and NCA (just a little on independent and network component analysis). Ina will find Matlab tutorial information for eigenvalues, eigenvectors and PCA computation. Mike will find video lecture introductory materials for eigenvectors and eigenvalues.

On Tuesday we will watch and discuss the lecture and Ina will give a Matlab demo for computing eigenvalues and eigenvectors. On Thursday we will discuss the papers we've all been reading all week, and conclude with a tutorial computation of principle components from a biomedical dataset.

28 October 2008

Today we watched much of Gilbert Strang's lecture #10 from his MIT OpenCourseWare linear algebra course: http://www.youtube.com/watch?v=5GmCIoIMlxk We were interested in the 4 fundamental subspaces which are explained therein.

We began to go over the problems from last time and got through the first 2 or 3 of them. We decided that while it's good to work out problems, they often require a deeper degree of study (and time) than we have available. The goal is to understand the concepts, be able to talk about them, and then know WHERE to dig deeper when necessary.

For next time we split the six exercises from chapter 2 up between us. The exercises are the ones with the solutions, unlike the actual problem set. I'm taking 1 and 2, Archana 3 and 4, and Ina 5 and 6. We'll review them on Thursday and set a direction for the weekend and next week.

Oct 22 Summary

Discussed orthogonality and orthogonalization process.
Reviewed Gaussian Elimination and well-known types of matrices from
http://math.asu.edu/~bdw/MAT520/Fa98/L2/lect2b.html
http://math.asu.edu/~bdw/MAT520/Fa98/L2/lect2c.html
Will solve following problems next time-
GS: 2.2, 2.4, 2.10, 2.14, 2.15, 2.17, 2.24, 2.27, 2.28, 2.32.

09 October Summary

Continuing on Regression study, we discussed degrees of freedom in different estimators and error sum of squares calculations. We then looked at Coefficient of Determination and discussed its use/application in Regression analysis and its application with respect to gene expression data study. For next week we will be reading the paper by Dougherty et. al on CoD relevant to our work. Archana gave us a brief overview on estimation by maximum likelihood and went through the formulas used to derive the maximum-likelihood estimators.
Next week we will also discuss the first 2 chapters in Linear Algebra by Prof. Gilbert Strang, namely :
1. Matrices and Gaussian Elimination
2. Vector Spaces.

Online lectures of his are available at : http://web.mit.edu/18.06/www/Video/video-fall-99-new.html

Revised Schedule

Revised Schedule

Date	Topic
9/3	Statistical Distributions
9/8	Statistical Distributions
9/10	Normalization
9/15	Normalization
9/17	Hypothesis Testing
9/22	Hypothesis Testing
9/24	Hypothesis Testing
9/30	P-Value Corrections
10/2	Significance Testing
10/7	Regression Analysis
10/9	Regression Analysis
	Matrices, Gaussian Elimination, Vector Spaces (Ch 1&2)
	Matrices, Gaussian Elimination, Vector Spaces (Ch 1&2)
	Orthogonality and Determinants (Ch 3& 4)
	Orthogonality and Determinants (Ch 3& 4)
	Eigenvalue and EigenVectors (Ch5)
	Eigenvalue and EigenVectors (Ch5)
	Positive Definite Matrices (Ch6)
	Computations with Matrices (Ch7) if possible else Ch 6
	Error Estimation
	Error Estimation
	Feature Selection
	Feature Selection
	Kernel Methods (Classification)
	Kernel Methods (Classification)
	EM Optimization (Clustering)
	EM Optimization (Clustering)

07 October Summary

Today we talked mainly about linear regression. Review chapters 1 and 2 in the Montgomery Peck and Vining introduction to linear regression analysis text for next time. Chapter two is posted below.

Also posted are papers relating to GoMiner. We were interested in its use of FDR in reporting significant GO terms from last time.

Finally posted is my ECE 380 capstone project which does a simple linear regression analysis (for an example).

http://www.public.asu.edu/~mverdic/papers

Meeting Summary for 9/30/2008

I spoke about FDR Correction and gave a brief outline of the methods involved in Multiplicity Adjustment and FDR Correction:
Multiplicity/ P Value Adjustment

- Single Step
---Boneferonni
---Sidak

- Step-down
---Holms
---Westfall & Young (min P/ max T)

FDR Correction
---Benjamini & Hochberg

Useful reference for this is : Benjamini & Hochberg 1995, J. Roy. Statist. Soc. Ser. B 57:289-300

Jang went over Hypergeometric tests, Fisher's exact test and its difference with Chi Squared Test.

For the next meeting(Friday instead of Thursday), Mike said he would look at applying Fisher's exact test and FDR Correction(GoMiner).

We also decided we would start off with an introduction to regression.

Meeting Summary for 9/25/08

I gave an overview of T-tests and ANOVA. For further information see their respective wikipedia articles. Linked here are some slides from Philip Stafford's biostatistics class a few years ago: http://www.public.asu.edu/~mverdic/stafford/

Ina gave an overview of the Binomial test Chi-square test, and saved details of KS and DA tests for Tuesday. She'll post any relevant documents in the comments of this post.

Jang will discuss Fisher's exact and Hypergeometric tests on Tuesday. He will post any pre-reading materials here in the comments.

Archana discussed p-value correction. She will discuss FDR and the beginnings of regression analysis on Tuesday. She will post any references to her talking points and pre-reading materials in the comments.

Next meeting is Tuesday at 9ish.

Summary for Tuesday 23 September

Today we reviewed the papers posted from last time and discussed hypothesis testing and p-value usage in papers. Here are the tasks for Thursday's meeting:

Mike: Brief overview and examples for T-test/F-test/ANOVA
Ina: Brief overview and examples for Chi-Square-Test/Binomial Test/KS-Test/DA-Test
Jang: Brief overview and examples for Hypergeometric Test/Fisher's Exact Test
Archana: Overview of FDR/Corrections/P-Value Adjustments for task distribution.

Next time we will also revise the semester schedule. Please post references, links and other resources you encounter in your studies.

Meeting Summary for 9/15/08

Ina discussed how we can apply hypothesis testing to the gene expression data from microarrays. We got to know difference in Z-statistic formula when applied to observations directly versus the mean of observations (which follows the Normal Distribution according to the Central Limit theorem). The rest of the chapter on Hypothesis Testing will be studied individually and an overview of tests will be discussed on Wednesday, when they are applied, how they are applied and differences between tests conducted in same scenarios.

References :
1. X. Cui, G. A. Churchill, "Statistical tests for differential expression in cDNA microarray experiments", (Review), Genome Biology 2003, 4:210.
2. J. A. C. Sterne, G. D. Smith, "Sifting the evidence - what's wrong with significance tests?", (Education and Debate)BMJ, 27 January 2001, Volume 322.

Meeting Summary for 9/10/08

Ina went over a brief summary of Point Estimation and a general overview of Hypothesis Testing. Mike went over a paper he had found on normalization and statistical analysis of microarray experiments. We decided to finish the chapter on Hypothesis Testing, and read some papers on microarray normalization. I've posted the review papers on normalization on Citeulike (tagged by csbstudy and normalization).

Meeting Summary for 9/8/08

Today we talked about data pre-processing for microarrays. We reviewed chapter 12 in Sorin Draghici's "Data Analysis Tools for DNA Microarrays". We also looked at some slides from Dr. Kim's class on the topic. (Archana can you post these as a comment?)

For next time we're going to each look up some review papers on normalization techniques, and hopefully study the pros and cons of each. Archana will look for some information pertaining to chip-chip data. I'm going to review my notes from Stafford's class on M-A plots. Jang is going to summarize the distribution plot he sent in the email last week.

We'll also begin our discussion of hypothesis testing.

Meeting Agenda for 9/8/08

Please add comments to this post to modify the agenda.

1. (Main topic) Discuss data pre-processing for DNA microarray data. Sources include but are not limited to the Knudsen, Draghici and Speed books on my desk.
2. (Archana) Discuss binomial distribution for GO term enrichment.
3. (All) Discuss where the Gamma distribution is used in biology.

Meeting Summary for 9/3/08

We worked through chapter 3 of the Montgomery book and talked about various statistical distributions, i.e. normal, lognormal, gamma, poisson, etc. We also tried to relate them to our area of study, which is elaborated by Archana's post earlier.

For next time we decided to discuss data pre-processing for DNA microarrays. I have a few books on my desk, one by Knudsen, one by Draghici, and one by Speed that could lend some insight. Archana already addressed the other goal of assumption of normal distribution of such data. Next time Archana should also brief us on use of the binomial distribution as it pertains to enrichment of gene ontology terms. We all decided to independently investigate when and where the gamma distribution is used in biology besides the one place we knew already, namely as a step in getting the beta distribution for discrete Bayesian network analysis.

Microarray Data- Normally Distributed ?

I applied the normality tests on the microarray data (expression values for one gene) and it looks like it is NOT normally distributed contrary to our discussion.

The tests are Andersen-Darling & Kolmogorov-Smirnov. Here are the histograms and test results :