On the exact minimization of saturated loss functions for robust regression and subspace estimation
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This paper deals with robust regression and subspace estimation and more precisely with the problem of minimizing a saturated loss function. In particular, we focus on computational complexity issues and show that an exact algorithm with polynomial time-complexity with respect to the number of data can be devised for robust regression and subspace estimation. This result is obtained by adopting a classification point of view and relating the problems to the search for a linear model that can approximate the maximal number of points with a given error. Approximate variants of the algorithms based on ramdom sampling are also discussed and experiments show that it offers an accuracy gain over the traditional RANSAC for a similar algorithmic simplicity.
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