CS395T/CAM383M Computational Statistics Aayush Sharma Term Project
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#1
04-11-2010, 07:43 PM
 Aayush Sharma Member Join Date: Jan 2010 Posts: 15
Aayush Sharma Term Project

Title - Lecture Sides on Generalized Linear Models and Logistic Regression

I tried to introduce the concept of GLMs using the standard least squares case showing how the Gaussian noise model can be shown as a special case of GLM. Gradually, I introduce exponential family of distributions and show how GLMs arise when the noise term is distributed according to this family of distributions. Finally, I introduced the special case of Logistic regression focussing on how the parameters can be learnt as a maximum leikelihood solution. I also give a simple matlab implementation using the glmfit function.

For the purpose of this project, I will stick to canonical link functions as they cover a sufficiently large class of models and have tractable likelihood maximization via gradient ascent/Newton's methods etc.

The writeup is 5 pages long as I wanted to include all the relevant details.
The final deliverables will include

1. Detailed lecture slides
2. Report on the main concepts
3. Data/Code used in the slides.

I would appreciate suggestions/scope for improvement/extensions etc.

Last edited by Aayush Sharma; 05-04-2010 at 11:51 AM.
#2
04-13-2010, 12:21 PM
 wpress Professor Join Date: Jan 2009 Posts: 222

Looks good. You might consider organizing things to first do a simple example of logistic regression, and then generalize to the GLM.
#3
04-19-2010, 09:26 AM
 TheStig Member Join Date: Jan 2010 Posts: 27

Very thorough, so I don't have much to add; perhaps include a discussion or comparison of general and generalized linear models?
#4
05-04-2010, 11:48 AM
 Aayush Sharma Member Join Date: Jan 2010 Posts: 15
Final Slides

Attached are the final slides on Generalized Linear Models and Logistic Regression. Also learn_theta is a gradient ascent implementation for learning the parameters of a logistic regression model. The rest of the code snippets are included in the relevant slides. E.coli is the dataset from UCI machine learning repository used for evaluating logistic regression in the slides. Fisher iris dataset comes pre-loaded with Matlab.

I have re-organized things to have logistic regression first followed by generalization to GLMs.
Attached Images
 final_slides.pdf (413.6 KB, 2831 views) Report.pdf (171.8 KB, 2435 views)
Attached Files
 learn_theta.txt (1.2 KB, 586 views) ecoli.txt (9.9 KB, 1084 views)

Last edited by Aayush Sharma; 05-04-2010 at 11:58 AM.
#5
05-07-2010, 11:51 AM
 wpress Professor Join Date: Jan 2009 Posts: 222

Nice job!

Slide 6, last bullet, is only nonlinear in a very mild way; general nonlinear fit would be much harder.
Slide 8: Taking sigmas constant is not generally a good model (depending on the application).

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