EE Special Seminar
Nonconvex methods for high-dimensional regression with noisy and missing data
Noisy and missing data are prevalent in many real-world statistical estimation problems. Popular techniques for handling nonidealities in data, such as imputation and expectation-maximization, are often difficult to analyze theoretically and/or terminate in local optima of nonconvex functions -- these problems are only exacerbated in high-dimensional settings. We present new methods for obtaining high-dimensional regression estimators in the presence of corrupted data, and provide theoretical guarantees for the statistical consistency of our methods. Although our estimators also arise as minima of nonconvex functions, we show the rather surprising result that all stationary points are clustered around a global minimum. We demonstrate promising applications of our method within the framework of compressed sensing MRI.
Po-Ling Loh is a 5th year PhD student in the statistics department at UC Berkeley, working under the supervision of Martin Wainwright. She graduated from Caltech in 2009 with a BS in math and a minor in English, and earned an MS in computer science from Berkeley in 2013. Po-Ling's interests lie in the growing intersection between statistics, electrical engineering, and computer science. She received a best paper award at the Neural Information Processing Systems (NIPS) conference in 2012 and is a Hertz fellow.
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