Essays on Algorithmic Learning and Uncertainty Quantification
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 problem...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2023
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| Online Access: | https://hdl.handle.net/1721.1/151512 https://orcid.org/0000-0001-8383-5617 |
| _version_ | 1826210919946911744 |
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| author | Vijaykumar, Suhas |
| author2 | Chernozhukov, Victor |
| author_facet | Chernozhukov, Victor Vijaykumar, Suhas |
| author_sort | Vijaykumar, Suhas |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T14:57:52Z |
| format | Thesis |
| id | mit-1721.1/151512 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T14:57:52Z |
| publishDate | 2023 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1515122023-08-01T03:17:57Z Essays on Algorithmic Learning and Uncertainty Quantification Vijaykumar, Suhas Chernozhukov, Victor Mikusheva, Anna Massachusetts Institute of Technology. Department of Economics 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. Ph.D. 2023-07-31T19:45:23Z 2023-07-31T19:45:23Z 2023-06 2023-06-01T16:03:39.420Z Thesis https://hdl.handle.net/1721.1/151512 https://orcid.org/0000-0001-8383-5617 Attribution 4.0 International (CC BY 4.0) Copyright retained by author(s) https://creativecommons.org/licenses/by/4.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Vijaykumar, Suhas Essays on Algorithmic Learning and Uncertainty Quantification |
| title | Essays on Algorithmic Learning and Uncertainty Quantification |
| title_full | Essays on Algorithmic Learning and Uncertainty Quantification |
| title_fullStr | Essays on Algorithmic Learning and Uncertainty Quantification |
| title_full_unstemmed | Essays on Algorithmic Learning and Uncertainty Quantification |
| title_short | Essays on Algorithmic Learning and Uncertainty Quantification |
| title_sort | essays on algorithmic learning and uncertainty quantification |
| url | https://hdl.handle.net/1721.1/151512 https://orcid.org/0000-0001-8383-5617 |
| work_keys_str_mv | AT vijaykumarsuhas essaysonalgorithmiclearninganduncertaintyquantification |