I spent Summer 2021 interning with Prof. Michael Bronstein and the Learning Methods group at Twitter Cortex!

Computing a distance between probability distributions is a fundamental problem in machine learning. In addition to their obvious statistical applications (e.g. deciding whether two samples were drawn from the same distribution), these distances are useful for solving geometric problems involving point clouds or meshes, since we can represent these objects by uniform distributions on their nodes.One popular distance is the so-called Wasserstein distance, which measures the minimum cost of transporting mass from one point cloud to another. (Imagine one point cloud as a set of mines and the other as a set of factories. The Wasserstein distance between these clouds is the cheapest possible cost to transport ore from the mines to the factories.) While this distance has convenient geometric properties, it's very costly to compute and hence impractical to apply to big data problems.Under the supervision of Prof. Prakash Panangaden, I worked on developing highly efficient algorithms for computing approximations to the Wasserstein distance. Such algorithms enable techniques based on this distance measure to be applied to large datasets that have some underlying geometric structure.Funded in part by an IVADO Undergraduate Research Scholarship.

Fairly distributing tasks among a set of agents based on their reported per-task costs is a computationally difficult problem. One common setup, the so-called minimum makespan job scheduling problem, has long been known to be NP-hard. In fact, it's NP-hard to compute a solution to this problem that's always "sufficiently close" to optimal.However, it's often reasonable to assume that each agent ranks the tasks in the same way: They might all agree that one task is the worst, another is second-worst, and so on. In many settings, we'll also give each agent a budget for their costs to prevent them from "cheating" by reporting very high costs for every task.Working under Prof. Adrian Vetta, I designed an efficient approximation scheme (an asymptotic polynomial-time approximation scheme) for an instance of this problem that satisfies the two assumptions I laid out above. This algorithm has potential applications to problems at the nexus of economics and computer science involving the fair division of tasks.Funded in part by an NSERC Undergraduate Student Research Award.

QR codes enable businesses to seamlessly link their physical and digital marketing campaigns by offering audiences the option to quickly access a business' website (or any other digital asset) using their smartphone. Camera blur is a common roadblock in this process, frustrating consumers and making them less likely to follow through with their interaction with a digital campaign. An effective deblurring algorithm mitigates this issue by allowing the QR code reader to receive a usable signal even when the underlying image of the QR code is blurry.In collaboration with Profs. Rustum Choksi and Tim Hoheisel and my colleague Gabriel Rioux, I helped develop the state of the art algorithm for deblurring QR codes. Our method is able to handle far more severe blurs than have previously been considered in the literature. As a bonus, it's easy to implement using well-documented Python packages.We published our algorithm in the paper "Blind Deblurring of Barcodes via Kullback-Leibler Divergence," to appear in IEEE Transactions on Pattern Analysis and Machine Intelligence.Funded in part by an NSERC Undergraduate Student Research Award.

Assisted in grading assignments and invigilating midterms for MATH 151

Published eleven articles synthesizing current research on a wide range of economic policy topics. All articles may be accessed at http://natocouncil.ca/category/ncc-authors/christopher-scarvelis/