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Activity Number: 494
Type: Contributed
Date/Time: Wednesday, August 3, 2016 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Computing
Abstract #318989 View Presentation
Title: Minimizing Sum of Truncated Convex Functions and Its Applications
Author(s): Tzu-Ying Liu* and Hui Jiang
Companies: University of Michigan and University of Michigan
Keywords: non-convex optimization ; polynomial-time algorithm ; robust statistics ; outlier detection ; L0 penalty
Abstract:

We study a class of problems where sum of truncated convex functions is minimized. In statistics it is often encountered when L0-penalized models are fitted. While in general they often leads to NP-hard non-convex optimization problems, we show that there is a polynomial-time algorithm in low-dimensional settings by partitioning the domain of the function. Our algorithm shows superior performance when compared with other global optimization algorithms, especially in cases where the objective function has a complex landscape. We also demonstrate the utility of our algorithm for outlier detection in robust simple linear regression, and we find that it outperforms state-of-the-art methods when a large amount of outliers are present.


Authors who are presenting talks have a * after their name.

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