I go through the analytics records for this website from time-to-time just to see how people get to my site or what search terms are popular.  Today, while going through, I found I’m getting hits for:

1- “How Tough is Mas-Colell”. Answer: Tough but feasible.  See my previous post on the standard microeconomics textbook for PhD students.

2- “Fantasy Football Linear Programming”. This one is interesting. I run a mailing list (that has no activity), where people can talk about fantasy football analysis techniques.  However, nobody on the mailing list has used linear programming (to the best of my knowledge). I wonder – are people using linear programming to determine a fantasy football roster? If so – awesome.

For those of you who don’t know – linear programming is a technique in optimization. In words, it is something like this: You have something that you need to maximize (or minimize), like profits for a company or points for your fantasy football team. You have a set of “constraints” – i.e. limitations on this maximization. Things like, for a company, you can only produce a limited quantity of some good or producing one good decreases the production of another good, and so on. I’m not sure how this would go back to fantasy football, though – like what would this constraints look like?

My best simple formulation of a linear program for fantasy football is something like this:

Maximize Potential Points!

Subject to:

• Limited number of positions (i.e. only 2 quarterbacks)
• Players are taken by other teams in the draft.
• Different Bye Weeks. (i.e. you don’t want all players with the same bye week, usually)
• Potential injuries and/or players with chronic injuries (I’m looking at you, Clinton Portis)

Perhaps there might be a way to develop some optimization technique that uses linear programming. The formulation of this program is feasible – but I’m not sure about:

• Computational limitations. The calculations for this optimization may be unreasonable – i.e. this may be an “NP Hard” problem.  I’m not sure about the complexity, yet.
• Points calculations. This is what I’ve been mostly working on the past two years – developing a good prediction algorithm that can account for variation in performance. I’m up to about 50% but this needs to be improved.

This quarter (they’re quarters, not semesters here at Northwestern), I was a TA for EECS310 – Discrete Mathematics. It is a 10 week course, divided into sections: proofs, binary relations, graph theory, counting, combinatorics, and probability. Today is their last quiz, so I’ve compiled a list of my thoughts about TAing and things I will do different next time:

• Be more prepared: I went into this course with not very much discrete math experience. I had encountered most of the material at one time or another through my academic career but I was very new to many of the concepts (especially the formality of writing good proofs). I wish I could have worked through some of the course material, ahead of time, so I could have done a better job answering student questions.
• Don’t be afraid to say “I don’t know”: I felt pressure to give students precise or exact answers to problems.  Mostly, in the classes that I’ve taken, if I’ve asked the TA a question they’ve been able to give me precise answers. So, I felt bad when I couldn’t help them as well as I’d liked to. There were a few times this quarter where I was asked a question and tried to figure it out on the spot but tanked. I learned that sometimes, you have to say “I don’t know” and get back to the student.  It’s okay to defer some questions to other TAs or the professor.
• Be fair when grading problem sets. Don’t be harsh with penalizing for mistakes but reward students who do particularly well.  If I take points off, I try to provide some reasoning to the student, i.e. “You didn’t do this well.”, “You are close but not quite there..”, and so on. If you’re too harsh, students complain and if you’re too easy, they don’t learn from their mistakes.
• Talk to the class about their problem sets. This is something that I didn’t do that I wish I had done, the best TAs that I’ve had have done this.  In the future, after I grade problem sets, I’m going to go in front of the class and talk about what they did: give suggestions for improvement, talk about general proof writing techniques, and make suggestions for future assignments.

That’s all the suggestions that come off of the top of my head.

One of the best things about being in academia: after a long night of studying until 1 or 2am, you can sleep in until 9am the next morning. The value of a decent night’s sleep cannot be beat. The next day, I feel refreshed and ready to pick up where I left off the previous night. Today is going to be a long day of meetings and classes, so I’m glad that I could sleep in and have my sanity together for today’s events. This is a good thing.

I only have a small amount of time before a talk at 11, so I’m going to use this second to talk about a concept in microeconomics that is particularly befuddling to a lot of students (including myself)./

All semester, I’ve been haunted by a concept in my micro-theory course that I just can’t wrap my brain around: convexity and concavity of functions. You learn this stuff in grade school, right? Like the definitions of convex and concave seem obvious. I always think of the grade school example: lenses.  However, take this concept to the world of analysis/economics and it becomes cloudy and confusing, especially after adding in the concepts of *quasi* convexity and *quasi* concavity.  UToronto has one of the best tutorials on quasiconvexity and concavity.  I will have some updates coming soon, attempting to cover this topic as well.

Well, I’m not actually registered for these courses yet, so hopefully I won’t encounter any waitlist issues. Apparently, I need to get some shots first, since they put a “health hold” on my account. Whoops.

• Applied Social Networks Analysis – This course is taught by Nosh Contractor, who is one of the pre-eminent social networks researchers. I have taken a similar course to this before, at Michigan, so hopefully I should be able to do really well in this course. I’m looking for ideas and things I can put into a dissertation (in a few years), so any class like this should help.
• Algorithms – This course is taught by one of the professors in our division (the theory dept). I’ve been told this is a really great course by the undergrads that have taken it. It’s technically an undergrad course (3xx level) but the graduate school lets me take it because of the difficulty.
• Microeconomics Sequence (part 2) – This is just the second part of the PhD Micro Sequence. I’m (hopefully) going to pass the first part, and they’ll let me stick around. I’m pretty sure the topic of this sequence is general equilibrium theory (woo). The goal is to make it through this part, so I can get to the game theory in part 3.

With the end of the semester coming up soon, I’ve been thinking about my plans for the holidays. Obviously, I’m going to spend some time back in Michigan with my family, around the holidays and especially the week of Christmas. Other than that, I’m going to have a lot of free time around here. I’m looking forward to coming into the office, when campus is empty and doing some work on my pet projects:

• Working on a paper for publication in the Journal of Quantitative Analysis in Sports . I have my fantasy football algorithm, which I’ve been revising over the past few years. The model is pretty simplistic but I’ve been able to isolate more than 50% of the variance in individual player performance (which is pretty good). I think I can formalize the model more, add in some more analysis techniques and submit for publication.
• Working on some research with my adviser, Nicole Immorlica.

In general, I’m starting to feel really good about the direction that I’m going in. For the first couple months, I had a hard time adjusting to the program here. It was dramatically different from my undergraduate and masters programs. I still don’t quite have the math chops to be able to keep up with my colleagues yet but I think after this and next term, I should be caught up. It’s like moving to another country without knowing the language and just picking it up from constant exposure.  It is terrifying at first, but as you adjust things get easier.

On a cool note, it looks like I may be going to KDD2010 this year.  The coolest part of the KDD conference is the annual KDD Cup competition they hold. You are given a dataset and asked to mine it. They’ve done all sorts of cool sets in the past: { website clicks, biomedical data, proteins, particle physics, and netflix }  I’d like to go to EC2010 this year too, it’s in Boston right across the street from the STOC CS convention.  The only problem is that it is during the week of finals here, so I’m not sure if that is going to happen this year.

I finally had a chance to sit down in my office today and configure my desktop. It’s a Lenovo S10, fully loaded and with Windows Vista. After a little bit of effort putting in more RAM and a terabyte drive, I finally got it to boot up into Vista. Holy moly, Vista sucks. It kept freezing up, refused to detect my mouse and keyboard (just stock parts) and took about an hour to download Ubuntu and burn it to DVD.

Installing Ubuntu was easier than I remember (I used to install Debian linux pretty often). It runs quickly, looks good, and the only thing missing is my installation of Mathematica. I’m told that I should be able to transfer my Mac license to a Linux box (but I’m not sure if this is true or not). If not, I’ll just have to get good at using some other software package, like hacking in Python or something.

At Northwestern, every two years, they award a prize in economics and mathematics, the Nemmer Prize. This year’s economics prize winner is Paul Milgrom. Milgrom has done a significant amount of work in auction theory and FCC spectrum auction design. At Michigan, I had to read quite a few of his papers and books. Auction theory is one of my favorite research areas: the theory is pretty straightforward, there is tons data, many real-life applications of the theory, opportunities for simulation, and a lot of activity and current research.

There is a panel discussion today with Al Roth, Susan Athey, Preston McAfee and Paul Milgrom – all really big names in the auction theory field. The research I’ve been doing lately builds on the models developed by all four of these people. I’m consistently amazed by the quality of speakers Northwestern can attract.

At one point, Preston McAfee displayed Yahoo!’s “objective function” for bid ranking on his slides. I wish I had caught a picture of it. I would have liked to run some simulations on his model.

Conclusion of the panel: Computer scientists (me) need to catch up with economists. In other words, I should take more economics courses.

The other day, I needed to make a stochastic matrix in Mathematica. Unfortunately, there didn’t seem to be any existing libraries or anything for this. So, I wrote this function, which is basically a modified function from a Wolfram Demonstrations project.

StochasticMatrix[n_,m_]:=
Flatten[With[{gg=Transpose[Table[
With[{kk=Sort[Flatten[{0,1,Table[RandomReal[],{n-1}]}]]},{Drop[kk,1]-Drop[kk,-1]}]
,{m}]]},{gg}],2]

I hope someone finds this helpful.

Well, this morning was the big Micro-Theory exam.  I overheard that our TA got a 5% on his first Micro Theory exam, which eased my anxiety a little.  So, I lowered my bar a lot. Let’s break the 5% threshold!

Fail.

The two questions on this midterm were easily the most difficult questions I have ever faced on any exam, ever. The first one was an interesting choice theory/binary relations question (I’ll post it here later, if I can) and the second one contained unfamiliar mathematical operators (what’s the exp{} operator do?). So, I immediately had to ignore question #2. It’s impossible to solve an equation when you can’t actually read the equation.  That left question #1. I spent 45 minutes staring at the wall, trying to assess the problem space.  Looking around,  everyone else was doing the same thing (it must have looked funny to the TA).

I came up with what I thought was a decent solution, but with about 10 minutes left realized that my solution was completely wrong and I had approached the problem incorrectly. It was pretty much too late to change anything (that would require another 45 minutes of wall staring), so I sat there trying to think of limericks to write in the empty book for question #2.

My brain was so fried from the previous night’s attempted all-nighter, so all I could think of were “There once was a man from Nantucket…” limericks, so I called it quits without even leaving a poetic verse for the TA. Perhaps I’ll save it for the Final Exam.

* it’s not that unusual for economics PhD students to tank on exams like this. It seems to me like the professors, in general, like to signal to students (study harder!) rather than actually assess the level of learning.