Thursday, December 20, 2012

Randomized Bits: Education a Low Rank Problem ?, The JASON Report on Compressive Sensing and more.

Yesterday, I posted the following on the CS/RandNLA/MF Google+ group:

Is Education a Low-Rank Problem ?

You're given a set of grades from students who went several courses in your department. How do you figure out the stuff they *really* have not mastered ? Same problem for pupils in different grades. How do you figure out the ones that really need a concerted effort in one or two subjects, i.e. in subject areas that are so important that by not mastering them, they are in effect failing all others. 

Grading is also not even as different classes from the same grade have different professors and in some educational systems, some students can sail through the whole curriculum without having been engaged in specific subject areas.

All this to say that these problematic seem to be of the low rank approach. In order to check that, one could, provided access to anonymous set of grades, evaluate this approach by removing some grades in classes and see if the low rank reconstruction solvers used in matrix completion ( matrixfactorizations | igorcarron2 ) could in fact recover those "hidden" grades. Do this several times with different mask and see if we get the same results. What would be the flaw of a study like this one ?
José Pablo González responded on the twittter about two papers relevant to this specific question:
  1. Mapping Question Items to Skills with Non-negative Matrix Factorization by Michel C. Desmarais
  2. Dynamic Cognitive Tracing: Towards Unified Discovery of Student and Cognitive Models by Jose P. Gonzalez-Brenes and Jack Mostow

Thanks José, this is quite fascinating. I note that the decomposition in the timeless paper ( the first one) is NMF and not relevant to the issue of rankedness, but this is a good start.

Rodrigo Carvalho and Google alerts let me know of the release of a JASON report on Compressed Sensing that was performed this past summer. I am a little bit surprised at how fast it has been cleared for public release. If you don't know what the JASON group is, then check wikipedia. I think some of the minor issues I have seen with the report may come for the relative non-involvement of DARPA  in the process but this is just speculation. I don't know what I don't know.

If you have not seen the update in Around the blogs in 80 summer hours (NIPS and more), I wondered if "a combination of the faster FREAKs and kernel distance might provide for a speedier way of learning manifold from images and videos ?" Suresh tells me that the answer seems to be Yes.

Join the CompressiveSensing subreddit or the Google+ Community and post there !
Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin.

No comments: