Slides and Registration

I”ve gotten little bit ahead of myself on my seminar slides, so here is a compilation of what I have created so far. For the most part, they should stand on their own, but some degree of familiarity with the Gale–Shapley assignment process wouldn’t hurt (it isn’t hard to grasp).

My DeferredAcceptance package, now at version 0.3.1, was also accepted into the general Julia package registry.

Winter Quarter Update

I have greatly expanded the functionality of DeferredAcceptance, my school-choice code library. New features include the nonatomic form of the DA algorithm, several new tiebreaking mechanisms, and further replications of recent experimental results from the literature on stable assignments. A couple of interesting research results of the past ten years include a tiebreaking mechanism that lets students name a “target school” where they will receive enhanced admissions priority, and a two-round dynamic reassignment mechanism that uses the spaced freed up by students who leave the market (e.g. to attend private school) to compensate for inequality in the primary assignment round.

I also coded a practice implementation of an interior-point method for solving linear programs. During winter break, our lab has been working through Jorge Nocedal and Stephen Wright’s Numerical Optimization textbook, and the section I was responsible for included the predictor-corrector algorithm given above.

During winter quarter, I completed a course in revenue management and pricing. For my final presentation in that class, I reviewed a paper that concerns which products should be presented to a customer in order to maximize revenue (assortment optimization):

One rewarding aspect of this class was the exposure to a wide range of models in choice theory, which allows us to express mathematically the processes consumers use when deciding which product to buy. So far, in my research in school choice, I have focused on the assignment aspect of the problem, which takes place after students’ preferences are revealed. But robust simulation of school-choice markets requires effective modeling of uncertainty and information asymmetry on the demand side.

First Steps in School Choice

Do you know what algorithm your district uses to assign students to public schools? A fair school-choice process is an essential part of a functioning democracy, and determining the “best” algorithm involves carefully weighing tradeoffs between student welfare, equity, and distributional goals like gender equality and racial diversity. Such considerations are the basis for my thesis research in the Management Science/Optimization lab here at SNU.

I coded a few commonly used algorithms in Julia, and this week I've been running computer simulations to reproduce a few well-known results in this area of the literature. Check out my implementation and a brief discussion on Github.

The Optimal Stable Marriage

A one-to-one assignment problem involves a set of two groups, candidates and reviewers, each of whom has ranked the members of the other group on the basis of how much they would like to be paired together. A classic problem in game theory involves finding a stable assignment, or a way of pairing up candidates and reviewers such that no member of either group is incentivized to cheat on their partner. In a large problem, there may be more than one way to do this, but it isn’t necessarily easy to find all of the stable assignments or determine which one represents the best compromise between the candidates’ and reviewers’ interests. I have written some code that solves this latter problem. The algorithm it uses was developed in the 1980s, and I am currently working on improving its performance and extending it to many-to-one assignment problems. My code and further discussion are on Github here.

Three Creations

Python implementations of a two-phase simplex method and sparse LU matrix factorization.

An article about Korean SF in the Emory Journal of Asian Studies.

And an EP:

Day Seven of Fourteen

I’m trying to make everything last. But I already ate the chocolate. I had promised it to myself as a reward for getting halfway through isolation halfway intact, and I kept that promise this afternoon, most of the way between lunch and dinner. Otherwise, I’ve been spending most of my time on math, learning as many math words as I can in Korean and getting comfortable with the concepts I’ll need in my research group. I coded a simplex method.

One of the staff at the quarantine facility gave me his contact info and said we should stay in touch. I have my first friend, then, at SNU, and you could do some Bayesian stuff to argue it won’t be long before I have a couple others. This has me in high spirits. That, and that they are feeding us well.

It occurs to me that there will be a day at the end of this when I look back and say, I can’t believe how fast it went. Certainly it was like that with my time in Naju. I can still recall, if I look far enough inward, the feeling of my bed in my apartment by the river, the way the trees framed the window, the awkward hop between the bedroom and the shower … but I can also feel the memory fading, already, as irretrievable as every other mundane sensation.

Next

They say that we perceive time by the accumulation of novel experiences, so that if you want to have a subjectively long life, you ought to do many spontaneous and hard-to-repeat things, but if you want to have a happy life, you ought to find one or two high pleasures that you can enjoy on a spiritual level and repeat the hell out of them, because they also say that on average, people derive more happiness from repeating a good experience than from trying something new.

You could write a linear program that targets your ideal mix of longevity and happiness and it would tell you exactly how many times to do this or that activity before moving onto something new. But what this calculus leaves out is the feelings of uncertainty that stain the transitions.

I am leaving Naju, after having grown accustomed to this routine, this commute, these faces, and I cannot say with any confidence that I have reached a joy plateau. Every week of teaching here has been better than the last: my skills have improved, my confidence has grown, and the teachers and students have become only more important to me. I could be happy like this for a long time. But.

But too much comfort has a way of smearing all the time together, so that the things that take place in a given day feel less like events and more like footnote references to proto-events hovering in the firmament of the distant past. I have already seen the river clog itself with duckweed; I have already looked down the street from all four of the intersection’s corners, trying to make the buildings line up with the trees. Upon inspection, a more sensitive man might look at these rhododendrons and see something more than last year’s blossoms in a different configuration, but I am a pattern-matcher by nature, too easily bored to remain a recluse. It is time for a new challenge.

As I wrap up my Fulbright grant, I am delighted to share that I have been accepted into the Government of Korea Scholarship program, through which I will be returning to Korea in the fall to pursue a fully funded master’s degree in industrial engineering at Seoul National University.

Thank you to all who have encouraged me.