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职业迁徙
个人简介
My academic interests lie at the intersection of applied analysis, applied probability, statistics, and machine learning.
When studying a certain data analysis methodology, my approach is to first seek a well posed continuum analogue that can work as an ideal population level counterpart. The population level methodologies that I typically study take the form of variational problems or geometric problems on continuum non-parametric settings. Studying these ideal methodologies requires a combination of tools from PDE theory, geometric measure theory, and ODEs in the space of probability measures taken with respect to optimal transport distances. Through rigorous analysis, a goal of my research is to connect the finite data approaches and their ideal continuum counterparts, with the intention of translating properties of the continuum setting to the discrete one. I have taken this general perspective to provide deep insights into graph-based methodologies for learning such as spectral clustering, graph cut clustering, and supervised learning approaches that rely on the solution of graph differential equations. My work has allowed me and my collaborators to provide strong links between learning problems and geometric problems studied in the mathematics literature, as well as to rigorously motivate the choice of algorithms used for optimization and uncertainty quantification (for example taking a Bayesian perspective and using MCMC algorithms) in learning problems.
When studying a certain data analysis methodology, my approach is to first seek a well posed continuum analogue that can work as an ideal population level counterpart. The population level methodologies that I typically study take the form of variational problems or geometric problems on continuum non-parametric settings. Studying these ideal methodologies requires a combination of tools from PDE theory, geometric measure theory, and ODEs in the space of probability measures taken with respect to optimal transport distances. Through rigorous analysis, a goal of my research is to connect the finite data approaches and their ideal continuum counterparts, with the intention of translating properties of the continuum setting to the discrete one. I have taken this general perspective to provide deep insights into graph-based methodologies for learning such as spectral clustering, graph cut clustering, and supervised learning approaches that rely on the solution of graph differential equations. My work has allowed me and my collaborators to provide strong links between learning problems and geometric problems studied in the mathematics literature, as well as to rigorously motivate the choice of algorithms used for optimization and uncertainty quantification (for example taking a Bayesian perspective and using MCMC algorithms) in learning problems.
研究兴趣
论文共 49 篇作者统计合作学者相似作者
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CoRR (2024)
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arxiv(2023)
CoRR (2023)
CoRR (2023)
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CoRR (2023)
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arxiv(2023)
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