{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/151512"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/151512","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Essays on Algorithmic Learning and Uncertainty Quantification","abstract":"The thesis consists of three essays. The first, titled “Localization, Convexity, and Star Aggregation,” develops new analytical tools based upon the offset Rademacher complexity for studying stochastic optimization in non-convex domains, including statistical prediction and model aggregation problems. Using these tools, I show that a simple procedure called the star algorithm can recover near-optimal convergence rates for non-parametric logistic regression in non-convex models. The second essay, titled “Kernel Ridge Regression Inference,” introduces a new technique for deriving sharp, non-asymptotic, uniform Gaussian approximation for partial sums in a reproducing kernel Hilbert space, which is then applied to construct uniform confidence bands for the widely-used kernel ridge regression algorithm. The third and final essay, titled “Frank-Wolfe Meets Metric Entropy,” uses ideas from asymptotic geometry to derive new dimension-dependent and domain-specific lower bounds for conditional gradient algorithms, a class of optimization procedures including the popular Frank-Wolfe algorithm and many of its variants. Such algorithms have found extensive use in machine learning and high-dimensional statistics, motivating a more thorough analysis of their limitations in high-dimensional problems.","abstract_html":"The thesis consists of three essays. The first, titled “Localization, Convexity, and Star Aggregation,” develops new analytical tools based upon the offset Rademacher complexity for studying stochastic optimization in non-convex domains, including statistical prediction and model aggregation problems. Using these tools, I show that a simple procedure called the star algorithm can recover near-optimal convergence rates for non-parametric logistic regression in non-convex models. The second essay, titled “Kernel Ridge Regression Inference,” introduces a new technique for deriving sharp, non-asymptotic, uniform Gaussian approximation for partial sums in a reproducing kernel Hilbert space, which is then applied to construct uniform confidence bands for the widely-used kernel ridge regression algorithm. The third and final essay, titled “Frank-Wolfe Meets Metric Entropy,” uses ideas from asymptotic geometry to derive new dimension-dependent and domain-specific lower bounds for conditional gradient algorithms, a class of optimization procedures including the popular Frank-Wolfe algorithm and many of its variants. Such algorithms have found extensive use in machine learning and high-dimensional statistics, motivating a more thorough analysis of their limitations in high-dimensional problems.","abstract_has_math":false,"creators":["Vijaykumar, Suhas"],"institution":"Massachusetts Institute of Technology","degree_name":"Doctoral","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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The first, titled “Localization, Convexity, and Star Aggregation,” develops new analytical tools based upon the offset Rademacher complexity for studying stochastic optimization in non-convex domains, including statistical prediction and model aggregation problems. Using these tools, I show that a simple procedure called the star algorithm can recover near-optimal convergence rates for non-parametric logistic regression in non-convex models. The second essay, titled “Kernel Ridge Regression Inference,” introduces a new technique for deriving sharp, non-asymptotic, uniform Gaussian approximation for partial sums in a reproducing kernel Hilbert space, which is then applied to construct uniform confidence bands for the widely-used kernel ridge regression algorithm. The third and final essay, titled “Frank-Wolfe Meets Metric Entropy,” uses ideas from asymptotic geometry to derive new dimension-dependent and domain-specific lower bounds for conditional gradient algorithms, a class of optimization procedures including the popular Frank-Wolfe algorithm and many of its variants. Such algorithms have found extensive use in machine learning and high-dimensional statistics, motivating a more thorough analysis of their limitations in high-dimensional problems."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Essays on Algorithmic Learning and Uncertainty Quantification"]}]}],"canonical_facts":{"dc:contributor.advisor":["Chernozhukov, Victor","Mikusheva, Anna"],"dc:contributor.department":["Massachusetts Institute of Technology. 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The second essay, titled “Kernel Ridge Regression Inference,” introduces a new technique for deriving sharp, non-asymptotic, uniform Gaussian approximation for partial sums in a reproducing kernel Hilbert space, which is then applied to construct uniform confidence bands for the widely-used kernel ridge regression algorithm. The third and final essay, titled “Frank-Wolfe Meets Metric Entropy,” uses ideas from asymptotic geometry to derive new dimension-dependent and domain-specific lower bounds for conditional gradient algorithms, a class of optimization procedures including the popular Frank-Wolfe algorithm and many of its variants. 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