Structured estimation in healthcare and quantized matrix recovery
- We find ourselves in the era of modern data, where new collection technologies provide us with vast amounts of data at an unprecedented speed. While this data provides us with ample opportunities for advancing research efforts in a variety of areas, we must understand how we can use it to achieve our objectives. Structured estimation gives researchers the tools to take advantage of this data, to help overcome the challenges associated with it, and help shape it to be more suitable for our application needs. As a result, we are able to use this data to, for example, enhance patient outcomes, provide recommendations to users of online music or movie streaming services, and predict reliability and identify power tampering of electricity meters. In the first part of this thesis, we use structured estimation to help us design a model for assessing a patients' risk for multiple diseases. While combining models used for individual disease prediction presents one solution, this approach can be improved upon in complexity as well as accuracy. We use methods from machine learning and dimensionality reduction to allow us to select a small set of biomarkers which are accurate predictors of multiple diseases. We validate our methods on real patient data. In the second part of this thesis, we investigate the problem of recovering a matrix from a subset of its entries. We focus on low rank matrices whose entries are from a finite set, especially those whose observations result from quantization of a noisy real-valued matrix. We present a performance guarantee for our approach, which is formulated as a rank-constrained maximum likelihood parameter estimation problem. We develop an algorithm for this approach, based on matrix factorization techniques, for which we provide convergence guarantees. Our proposed method provides a solution to many practical problems, such as collaborative filtering, network localization, and image denoising.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Bhaskar, Sonia A
|Stanford University, Department of Electrical Engineering.
|Statement of responsibility
|Sonia A. Bhaskar.
|Submitted to the Department of Electrical Engineering.
|Thesis (Ph.D.)--Stanford University, 2015.
- © 2015 by Sonia Arti Bhaskar
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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