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Sparse Least Absolute Deviation Support Vector Machine

The Korean Data Analysis Society, 2023
The support vector machine solves a quadratic programming problem with linear inequality and equality constraints. However, it is not trivial to solve the quadratic problem. The least squares support vector machine(LS-SVM) solves a linear system by equality constraints instead of inequality constraints.
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LEAST ABSOLUTE DEVIATIONS REGRESSION UNDER NONSTANDARD CONDITIONS

Econometric Theory, 2001
Most work on the asymptotic properties of least absolute deviations (LAD) estimators makes use of the assumption that the common distribution of the disturbances has a density that is both positive and finite at zero. We consider the implications of weakening this assumption in a number of regression settings, primarily with a time series ...
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Fuzzy regression using least absolute deviation estimators

Soft Computing, 2007
In fuzzy regression, that was first proposed by Tanaka et al. (Eur J Oper Res 40:389–396, 1989; Int Cong Appl Syst Cybern 4:2933–2938, 1980; IEEE Trans SystMan Cybern 12:903–907, 1982), there is a tendency that the greater the values of independent variables, the wider the width of the estimated dependent variables.
Seung Hoe Choi, James J. Buckley
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Multi-object tracking using least absolute deviation

2014 7th International Congress on Image and Signal Processing, 2014
Recently, attention has been paid to tracking methods using sparse representation. Assuming that the representation residuals follow Gaussian distribution, the multi-object tracking methods based on sparse representation are proposed. However, these methods are sensitive to outliers such as occlusion due to the assumption of Gaussian distribution.
Bing Wang, Fuxiang Wang
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Fuzzy linear regression based on least absolutes deviations

2012
Summary: This study is an investigation of fuzzy linear regression models for crisp/fuzzy input and fuzzy output data. A least absolutes deviations approach to construct such models is developed by introducing and applying a new metric on the space of fuzzy numbers.
Taheri, S. M., Kelkinnama, M.
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Least Absolute Deviation Estimation for Regression with ARMA Errors

Journal of Theoretical Probability, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Davis, Richard A.   +1 more
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A descent method for least absolute deviation lasso problems

Optimization Letters, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yue Shi, Zhiguo Feng, Ka Fai Cedric Yiu
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Least absolute deviation estimates in stable autoregression

1977
We consider an L_1 analogue of the least squares estimator for the parameters of a stationary, finite order autoregressive scheme based on stable random variables. This estimator, the least absolute deviation (LAD), is shown to be strongly consistent via a result that may have independent interest. Finally, the sampling properties are compared to those
Gross, S., Steiger, William L.
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SEQUENTIAL EXTRACTION OF FUZZY REGRESSION MODELS: LEAST SQUARES AND LEAST ABSOLUTE DEVIATIONS

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2011
Fuzzy c-regression models are known to be useful in real applications, but there are two drawbacks: strong dependency on the predefined number of clusters and sensitiveness against outliers or noises. To avoid these drawbacks, we propose sequential fuzzy regression models based on least absolute deviations which we call SFCRMLAD.
Tang, Hengjin, Miyamoto, Sadaaki
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Linear fuzzy clustering based on least absolute deviations

Proceedings of the 41st SICE Annual Conference. SICE 2002., 2003
This paper proposes a technique of linear fuzzy clustering based on least absolute deviations. The least absolute deviations adopted in the method provide robust clustering results that are free from the influence of outliers. The simplicity of the proposed objective function makes it possible to handle missing values by simply ignoring only the ...
K. Honda, N. Togo, H. Ichihashi
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