December 1, 2022

What led you to your first big project, on error-correcting codes?

My adviser had suggested trying to better understand probabilistically checkable proofs — one of the major developments of theoretical computer science of the time. I had this idea of relating them to expander graphs, and it turned out that was not actually useful — but I realized it was useful for making error-correcting codes. So we were working on one problem and we failed to solve that, but what we developed was useful for something else. Expander codes felt like an accident that we stumbled into.

That’s true with a lot of my research. A lot of the time, the way I’ve done something is not because it was the problem I was setting out to solve. I was setting out to solve something else, and it didn’t work. But I was aware enough of the intellectual landscape to figure out what I could use it for.

Is that what happened with Shang-Hua Teng and smoothed analysis?

That was a really long project; at least, it felt like it then. For some of it Shang-Hua was practically living in our apartment. And it did come out of another research project which Shang-Hua and I had worked on before and failed.

How did you get started on smoothed analysis?

There are a lot of things people do in practice that they find works for them, and we don’t have a good theoretical explanation for why. We were trying to understand one of these algorithms that was used a lot, called the simplex method. Everyone knew that there were examples where it would fail, but it was still used very successfully in practice. And we were trying to figure out how to explain this. The idea that we eventually came up with was that it works because all the cases where it fails seem very, very fragile.

Part of it was that we’d been coding up all these examples. And we noticed if we weren’t really careful with the numerical precision, then suddenly things that were supposed to break the simplex method didn’t. So that’s how we got the idea that if there was a little randomness in the inputs, the method would be fine. And we were able to prove that. It was an influential idea both because it helped people understand why this one algorithm worked, and because people have used the idea and concept to understand why many other algorithms work.

Why do you think your collaborations with Teng were so successful?

When I was starting grad school at MIT, he was an instructor there. We started working on problems then and had a very compatible working style. You’ll notice I have a couch in my office. In my office at MIT I had two couches. That meant Shang-Hua and I could both work — like, literally just spend all day lying down thinking about something, and when you have an idea, get up and talk about it. He was very happy to spend a lot of time thinking about things and talking about problems. Like me, he was happy to work on absurdly hard problems that we probably wouldn’t solve. Failure was the standard result of anything that we worked on, even if we were working on it for years. But that was OK.

At first glance, the topic of controlled trials seems more straightforward than these other problems. What’s so hard about splitting people into groups?

Think of it this way. If I give you a coin and you flip it 10 times and look at those results, even though they were generated randomly, you will see patterns in it, like maybe four heads in a row. If you only give me a few quantities to measure, like just age and gender, and you give me 100 people, if you break it up at random, then there will be a disparity in one of those. Being completely random is almost never the right thing to do.

So you want to walk some kind of tightrope of randomness?

We call it “artfully random.” We describe it as a trade-off between being completely random and balancing the quantities that you care about. If the things you’re measuring [like age or gender] have even a small impact on the outcome, it’s better to balance them a little bit. I initially thought we were going to be balancing the heck out of things, but it turns out you need only a little bit of balancing and a lot of randomness. But this is a recent development. Most of the results just told you there exist divisions that are good, but they didn’t tell you how to find them. It was a breakthrough result from Nikhil Bansal from 2009 that first started getting us efficient algorithms for doing this. In our work we’re leveraging results from theoretical computer science on efficient algorithms for making these balanced divisions. People weren’t thinking about using these before.

Ultimately, why work on such hard problems in the first place, where failure seems to happen so often?

It’s a gamble. I’m most motivated to work on things that if I solve them, I’d be excited to go around and give talks. I don’t work on things otherwise, generally. And usually there’s some of those around. Other problems, I’m not as motivated to spend time on them. I also feel like all research is hard — at least for me. Even problems that might look simple I still think are hard to work on. So if I’m going to be doing something that’s hard, why not work on something that’s high-impact, or that other people think are hard too?

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