Research
Computer science faculty are engaged in research in a multitude of areas within artificial intelligence, theory, and data science. Undergraduate students are involved in many faculty research projects through independent studies or honors projects.听
Theory of Computation
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Most supervised machine learning models "learn" patterns from data by minimizing our error on a set of training data. However, we can only really get a snippet of information describing the true data generating process; which snippet of information we learn is directly tied to the ways we measure error. Jessie Finocchiaro's听work studies the relationship between how we measure this error (and more broadly how we evaluate ML models) and the snippets of information we learn about our data. Importantly, we need to understand this relationship while trying to balance other constraints such as limitations on the design of the error functions (those that must be smooth or convex), limitations on the complexity of the ML model, and how to pick the right "snippet" to learn for a downstream decision problem, like top-k selection or allocating scarce resources.
Carl McTague studies the connection between exotic geometries and chromatic homotopy theory, and what this connection reveals about the surprising relationship between topology and the arithmetic of algebraic curves. Specifically, he is working to uncover higher genus generalizations of elliptic cohomology suggested by the exceptional geometry of the Cayley plane (and categorifying moduli spaces of theta characteristics). He is also working to compute the homotopy type of the string bordism spectrum MO<8> at the prime 3, based on computer-assisted computations of its BP-homology, considered as a Hopf ring. And he is working to formalize (in Coq) and apply machine learning to EHP and Adams spectral sequence calculations. He has also investigated novel uses of curvature in data analysis, pattern formation in cellular automata, as well as computational and geometric aspects of bookbinding and music composition.
Traditional studies on network optimization problems focus on developing algorithms for the sequential setting where computations are done in a single processor. Today, the scales of many real-world networks have grown to be so massive that a single processor cannot handle all the computations efficiently, either due to inefficiency or the infeasibility of global access. This has motivated the study of distributed and parallel algorithms for network optimization problems. For many network optimization problems, we still do not know how to match the same solution quality of sequential algorithms efficiently in those settings.听Hsin-Hao Su is working on developing efficient distributed and parallel algorithms (with provable guarantees on the running times and the solution qualities) for a number of network optimization problems, including matching, clustering, routing, and etc.听
Most of Howard Straubing's research has focused on the connection between finite automata and logic, through the medium of abstract algebra. This has led to effective characterizations of the expressive power of many different logics for expressing properties of words that can be tested by finite automata. Outstanding open problems center around extending this framework to regular languages of trees and forests; and using it to study low-depth circuit complexity.
Ilya Volkovich studies the role of randomness in computation: given an efficient randomized algorithm, can we convert it into a deterministic one of comparable efficiency? He听also studies the fundamental question: what are the necessary and the sufficient assumptions for various cryptographic primitives?听Recently, there has been a flurry of new methods for analysis of algorithms. However, many of these methods require extensive background knowledge. The goal of听Prof.听Volkovich's research is simplification of the analysis, making it more accessible to a wider audience, including undergraduates. Some of his work has already been incorporated into course curricula and included in algorithms textbooks.
Artificial Intelligence & Machine Learning
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Prof. Alvarez's current research focuses on machine learning for human health, usually involving the modeling of physiological time signals such as EEG, ECG, and PPG, or behavioral time signals derived from eye tracking or wearable motion sensors. His group's work has contributed to the understanding and treatment of heart insufficiency, autism, sleep disorders, stroke, and gastrointestinal cancer. He is also pursuing more theoretical directions in machine learning, including the asymptotics of kernel functions and the associated reproducing kernel Hilbert spaces. His earlier research includes widely cited contributions to recommender systems and related topics.