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Special Colloquium (Data Science): Optimization for statistical learning with low dimensional structure: regularity and conditioning

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Speaker: Lijun Ding, University of Wisconsin and the University of Washington
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Location: 1147 MSB
Start time: Mon, Mar 20 2023, 3:10PM

Many statistical machine learning problems, where one aims to recover an underlying low-dimensional signal, are based on optimization. Existing work often either overlooked the computational complexity in solving the optimization problem, or required case-specific algorithm and analysis -- especially for nonconvex problems. This talk addresses the above two issues from a unified perspective of conditioning. In particular, we show that once the sample size exceeds the intrinsic dimension, (1) a broad class of convex and nonsmooth nonconvex problems are well-conditioned, (2) well conditioning, in turn, ensures the efficiency of out-of-box optimization methods and inspires new algorithms. Lastly, we show that a conditioning notion called flatness leads to accurate recovery in overparametrized models.