Infinitely Imbalanced Logistic Regression

Art Owen had an interesting, if not surprising, paper titled Infinitely Imbalanced Logistic Regression in JMLR 8 (2007). In this paper, Owen investigates logistic regression for binary classification tasks where one of the classes have finite number of samples and the number of samples for the other class approaches infinity, thus creating an infinite imbalance between the two. He shows that although the intercept of the learned logistic regression approaches -infinity, the remaining coefficient vector approaches a non-trivial and useful limit. Furthermore, the minority class affects the coefficient vector ONLY through its empirical mean, thus it suffices (within sampling uncertainty, that is) to replace all the samples of the minority class with a single sample for the mean.

Junction tree notes

I needed a brief and precise refresher for junction tree algorithms to review a paper. I found the following lecture notes from Mark Peshkin very useful:
http://ai.stanford.edu/~paskin/gm-short-course/lec3.pdf

getting cgi to work on Mac

Sorry for this non-vision-ey, non-ML-ey post, but I need to make a note of this to save some time and energy and time in future. Who knows, you might find it useful someday.

Steps to follow:
1) httpd -V (to find out SERVER_CONFIG_FILE)

2) edit this file as following (would need root/super-user access):

(a) insert (somewhere)

<Directory "/Users/*/Sites/cgi-bin">
AllowOverride None
Options ExecCGI
Order allow,deny
Allow from all
</Directory>

(b) Uncomment

AddHandler cgi-script .cgi

You would need to turn Web Sharing OFF and then ON to bring the changes into effect.