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Ethan Zhou

Ethan Zhou

Ethan Zhou

2023 Davidson Fellow
$25,000 Scholarship

Age: 18
Hometown: Vienna, VA

Mathematics: “Online Learning of Smooth Functions”

About Ethan

My name is Ethan, and I’m an incoming freshman at MIT. I’ve always been fascinated by the sheer beauty of math, and I’ve been quite involved in math contests for several years. In the past two years, I’ve also gotten to learn a lot about how powerful math can be when applied to real-world problems, which has been truly exciting.

Although I don’t exactly know what I want to do in the future, I hope to use math to solve real-world problems; I plan to use my time in college to explore various fields and their connections to math. Outside of my project, I’ve competed in many math competitions, led my school’s math league, and volunteered as a math teacher at a local Chinese school for several years. I also enjoy playing the piano, studying science and competing in quiz bowl tournaments, and taking walks.

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"I’m honored to be named a Davidson Fellow for my work in math: it gives me confidence in my ability to pursue my interest in applied math, even when I don’t always know where that pursuit will take me."

Project Description

My project is about learning algorithms, or learners, that try to predict how a numerical quantity depends on other numerical parameters – for example, a weather model predicting tomorrow’s temperature based on the time of year and the humidity. Specifically, we care about online learning, in which the learner continuously gets feedback on its predictions and uses that to improve itself: in the above example, the weather model would get feedback each day based on how close its prediction yesterday was. As a learner gets more and more feedback, we’d expect it to make smaller and smaller errors. In my project, we show that this can be guaranteed, as long as our quantity doesn’t behave too erratically. We also show that this happens whether there is a single numerical parameter or several parameters.

Deeper Dive

My project is about online learning, which focuses on making predictions based off of data - specifically, data which appears over time. For example, consider weather algorithms which use past data to predict temperature. They might compare factors, like time of year and the current temperature, to similar days in the past, then use data from those days to guide their prediction. My work looks at how accurately such quantities can be forecasted in worst-case scenarios, proving that usually simple algorithms can quickly make accurate predictions. Although the project considers a rather ideal model of learning, it could potentially give forecasters a useful tool for testing their algorithms, and it also makes progress towards a more general model of learning which could have wider applications.

Through PRIMES-USA, I was also assigned to my mentor, Dr. Jesse Geneson, who gave me invaluable support throughout the project: he proposed the project’s topic, suggested a new direction for research, collaborated with me on proofs, and gave me advice on how to best communicate our results. Dr. Tanya Khovanova and Dr. Felix Gotti, also from the PRIMES-USA program, gave feedback on several drafts of the project as well. Although my school didn’t directly support me in my project, my teachers have been incredibly supportive of me in other ways. Luckily, the pandemic didn’t impact my project at all – the program normally runs virtually anyway.

Because my project looks at a simple model of learning, not accounting for things like noise in the real world, it’s hard to apply the results directly for machine learning purposes. Nevertheless, it does provide tools for forecasters to diagnose machine learning algorithms, which might ultimately make them more accurate. From a purely intellectual standpoint, my project resolves several cases of a very natural mathematical question and introduces a new direction for future research, which could lead to further progress and applications.


What is your favorite food?

I really like soups; my favorite food might be cream of mushroom soup.

What are the top three foreign countries you’d like to visit?

I'd really be open to visiting anywhere, but I suppose I'd like to go to France, Italy, and Japan (partly, I imagine they have good food).

What is your favorite hobby?

My favorite hobby is playing the piano.

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In The News

Washington, D.C. – The Davidson Fellows Scholarship Program has announced the 2023 scholarship winners. Among the honorees is 18-year-old Ethan Zhou of Vienna, Va. Zhou won a $25,000 scholarship for his project, Online Learning of Smooth Functions. He is one of only 21 students across the country to be recognized as a 2023 scholarship winner.

Download the full press release here