Optimization-based modeling in investment and data science
Abstract/Contents
- Abstract
- Optimization has played a key role in numerous fields including data science, statistics, machine learning, decision science, control and quantitative investment. Optimization offers a way for users to focus on the modeling step. Convex optimization has been a very successful and powerful modeling framework. By formulating a problem as convex optimization, practitioners could focus on the modeling side without worrying about designing problem-specific optimization algorithms during prototyping time. However, there are hurdles in applying this convex modeling framework. First, lots of signal processing and machine learning problems are most naturally formulated as non-convex problems. Second, not all convex problems are tractable. Third, it may be hard to encode the knowledge of data into a simple regularizer or constraint and specify the mathematical form of the optimization problem. In this thesis, we talk about topics in optimization-based modeling, including 1) distributional robust Kelly strategy in investment and gambling; 2) convex sparse blind deconvolution; 3) missing data imputation via a new structure called matrix network; 4) neural proximal method for compressive sensing.In these works. I try to expand the boundary of convex optimization based modeling by conquering several hurdles. In the distributional robust Kelly problem, the original distributional robust optimization formulation isconvex but non-tractable; we transform the problem into a tractable form. In the sparse blind deconvolutionproblem, blind deconvolution has been perceived as a non-convex problem for a long time, we proposea scalable convex formulation, and find a phase transition for the convex algorithm. In the missing dataimputation problem, we study a slice-wise missing pattern on tensorial type data that is beyond the capabilityof typical tensor completion algorithms. We propose a new type of underlying low-dimensional structure thatallows us to impute the missing data. In the first three topics, we solve these problems via convex optimizationformulations. In the last topic, we step out of the safety zone of convexity. On the linear inverse problem, we go beyond the sparsity and1−norm regularizer for compressive sensing. To model complex structure innatural/medical images, we propose a learning-based idea to parameterize the proximal map of an unknownregularizer. This idea is inspired by the convex optimization modeling framework and the learning-basedmethod, although the result need not correspond to convex optimization.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2019; ©2019 |
| Publication date | 2019; 2019 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Sun, Qingyun |
|---|---|
| Degree supervisor | Boyd, Stephen P |
| Degree supervisor | Donoho, David Leigh |
| Thesis advisor | Boyd, Stephen P |
| Thesis advisor | Donoho, David Leigh |
| Thesis advisor | Candès, Emmanuel J. (Emmanuel Jean) |
| Degree committee member | Candès, Emmanuel J. (Emmanuel Jean) |
| Associated with | Stanford University, Department of Mathematics. |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Qingyun Sun. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2019. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2019 by Qingyun Sun
- License
- This work is licensed under a Creative Commons Attribution Non Commercial No Derivatives 3.0 Unported license (CC BY-NC-ND).
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