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Sparse and Robust Linear Regression: An Optimization Algorithm and Its Statistical Properties
Shota Katayama,Hironori Fujisawa +1 more
TL;DR: In this article, a parameter vector for modeling outliers was added to the standard linear regression model and then the sparse estimation problem for both coefficients and outliers is considered, and the algorithm can recover the true support of the coefficients with probability going to one.
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Abstract: This paper studies sparse linear regression analysis with outliers in the responses. A parameter vector for modeling outliers is added to the standard linear regression model and then the sparse estimation problem for both coefficients and outliers is considered. The $\ell_{1}$ penalty is imposed for the coefficients, while various penalties including redescending type penalties are for the outliers. To solve the sparse estimation problem, we introduce an optimization algorithm. Under some conditions, we show the algorithmic and statistical convergence property for the coefficients obtained by the algorithm. Moreover, it is shown that the algorithm can recover the true support of the coefficients with probability going to one.
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Citations
Robust outlier removal using penalized linear regression in multiview geometry
TL;DR: A non-convex penalized regression approach is proposed to effectively remove outliers for robust parameter estimation and validated on three representative estimation problems in multiview geometry, including triangulation, homography estimate and the SFM with known camera orientation.
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•Dissertation
Wavelet Methods and Inverse Problems
Hassan M. Aljohani
- 01 Mar 2017
TL;DR: It is shown that the methodology using a single prior provides good reconstruction, comparable even to several established wavelet methods that use mixture priors.
4
Patent
Robust classification by pre-conditioned lasso and transductive diffusion component analysis
Yanwei Fu,Leonid Sigal +1 more
TL;DR: In this article, techniques for identifying and filtering outliers from a sample set of data prior to training a classifier on an object using the sample set are disclosed. But they do not address the problem of classification.
3
Computational and statistical analyses for robust non-convex sparse regularized regression problem
TL;DR: A two-stage procedure to handle outliers is proposed; at the first stage an initial estimator is calculated and then it is improved at the second stage by iteratively solving a sparse regression problem with reducing outlier effects.
2
•Posted Content
Minimizing Sum of Truncated Convex Functions and Its Applications
Tzu-Ying Liu,Hui Jiang +1 more
TL;DR: This article proposes a general algorithm for the global minimizer in low-dimensional settings and extends the algorithm to high- dimensional settings, where an approximate solution can be found efficiently.
2
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Gideon Schwarz
- 01 Jan 2005
TL;DR: In this paper, the problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion.
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Regularization Paths for Generalized Linear Models via Coordinate Descent
TL;DR: In comparative timings, the new algorithms are considerably faster than competing methods and can handle large problems and can also deal efficiently with sparse features.
Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
Jianqing Fan,Runze Li +1 more
TL;DR: In this article, penalized likelihood approaches are proposed to handle variable selection problems, and it is shown that the newly proposed estimators perform as well as the oracle procedure in variable selection; namely, they work as well if the correct submodel were known.