Probabilistic Graphical Models, Fall 2016

[cwyoo]

Class related materials, discussions, Q&A will be posted here.

[cwyoo]

Syllabus of the course.

[cwyoo]

A TV show puts $1 million prize behind one of the three doors (labeled A, B, and C). Only the TV show host knows which door has the $1 million prize. A show contender is asked to pick a door and if the $1 million prize is behind that door, the contender will walk away with the prize. However, to make the show more interesting, once the contender picks a door, the host opens a door that the contender did not pick and has no prize behind it and asks the contender whether she or he want to switch their choice. The contender thinks p(prize behind A) = p(prize behind B) = p(prize behind C) = 1/3 and she picks door A. Now the TV show host opens door C and shows nothing is behind there and gives a chance for the contender to either stay with door A or switch to door B. The contender now thinks p(prize behind A | host open door C) = 1/2 and be amazed by the fact that her chance of winning increased by merely the host opening door C and stays with door A.

(1) Using Bayes theorem, show whether the contender's assessment of p(prize behind A | host open door C) = 1/2 is correct or not.
(2) Discuss whether staying with the initial choice (in this case door A) is a good strategy or not.

[cwyoo]

1. Based on the Sprinkler Bayesian Network attached here, answer the following questions (with explanation):
i) Is Fertilizer d-separated with NBLawnGreen?
ii) Is Fertilizer d-separated with NBLawnGreen given MyLawnGreen?
iii) Is Fertilizer d-separated with NBLawnGreen given Rain?
iv) Is Fertilizer d-separated with NBLawnGreen given Rain and MyLawnGreen?
v) List all sets of variables that makes Fertilizer d-separated with NBLawnGreen if the set of variables are given as an evidence.
vi) Is Sprinkler d-separated with NBLawnGreen?
vii) Is Sprinkler d-separated with NBLawnGreen given MyLawnGreen?
viii) Is Sprinkler d-separated with NBLawnGreen given Rain?
ix) Is Sprinkler d-separated with NBLawnGreen given Rain and MyLawnGreen?
x) List all sets of variables that makes Sprinkler d-separated with NBLawnGreen if the set of variables are given as an evidence.

2. Pick any domain of your interest and identify eight or more binary random variables in that domain. Draw a plausible causal Bayesian networks with the variables you have identified. Select at least five interesting statements of d-separation relationships among the variables and evaluate each statement whether it is true or not.

Please post your submissions here by Tuesday, September 20, 2016. Please discuss the submissions by posting any comments/questions on Wednesday, September 21, 2016 and further discuss in the class on Thursday.

[cwyoo]

Create a class project proposal as a MS word file and include the following sections:

- Abstract: Summarize what you are presenting in the paper.
- Introduction and Background: Briefly identify research questions, discuss how it is important, identify variables that condition the research questions and what the literature tells you about that research questions, sample size selections, relationships between variables (e.g. provide citations from the academic/professional literature) and state what you intend to do in the paper (e.g. objectives, hypotheses,…,etc.).
- Methods (Data Analysis): Briefly present what statistical analysis you are going to use
- Timeline: Present every week what you are going to produce as an outcome.
- References.

Please post your class proposal by Friday, October 7th, 2016. Instructor will make comments directly into your word file for the draft proposals posted here by Monday, October 3, 2016.

[lsand039]

Attached is my draft of the proposal for the class project.

[cwyoo]

Attached is my draft of the proposal for the class project.

Good job!

Here are some comments:
- Read ahead about Model Averaging (section 18.5)
- Read ahead about Causality (chapter 21)
- Read ahead about Learning Graphical Models: Overview (chapter 16)

I suggest you use Model Averaging to evaluate association and causality. Also evaluate the Bayesian Networks model using ROC and/or cross validation.

[cwyoo]

Create a class project proposal as a MS word file and include the following sections:

- Abstract: Summarize what you are presenting in the paper.
- Introduction and Background: Briefly identify research questions, discuss how it is important, identify variables that condition the research questions and what the literature tells you about that research questions, sample size selections, relationships between variables (e.g. provide citations from the academic/professional literature) and state what you intend to do in the paper (e.g. objectives, hypotheses,…,etc.).
- Methods (Data Analysis): Briefly present what statistical analysis you are going to use
- Timeline: Present every week what you are going to produce as an outcome.
- References.

Please post your class proposal by Friday, October 7th, 2016. Instructor will make comments directly into your word file for the draft proposals posted here by Monday, October 3, 2016.

Due to FIU closure on Thursday, Oct. 6th, I will extend the deadline to Friday, October 14th, 2016. Instructor will make comments directly into your word file for the draft proposals posted here by Monday, October 10, 2016.

[igrif005]

Please find the attached draft of my project proposal.

[lsand039]

Attached are the data for my project and descriptive stats.
A few questions I have before I run it through Bene:
How should I descritize age & brain regions?
GSE 44768, 44770, and 44771 were subsets of the same study but each of these subsets are for a particular brain region. I calculated the z-scores of GSE 44768, 44770, and 44771 independently of each other. Other studies have mixed brain regions, but their z-scores were all calculated together. How should I address this?
Some of these samples might be different brain samples from the same subject. Should I try to remove duplicate subjects and choose one brain sample from that subject?