Regularized Least Absolute Deviations Regression and an Efficient Algorithm for Parameter Tuning

Wang, Li; Gordon, Michael D.; Zhu, Ji

doi:10.1109/icdm.2006.134

Cited by 80 publications

(67 citation statements)

References 8 publications

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“…This assumption may be viewed as a regularization [18]. It also reflects the effect of signaldependent noise [9], as it reduces the variability of the neural control signal by preventing its power from becoming too large .…”

Section: Adaptationmentioning

confidence: 99%

A neural model for the adaptive control of saccadic eye movements

Saeb

Weber

Triesch

2009

2009 International Joint Conference on Neural Networks

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Several studies have suggested different cost functions to explain the kinematic characteristics of saccades. However, these studies do not present any neural implementation of the optimization procedure they use. Instead, they are based on optimal control theory approaches that provide a global analytical solution rather than a local adaptation scheme. In this study, we propose a model comprised of an open-loop neural controller and an adaptation unit. The neural controller receives the initial target position as input. The adaptation unit, which is the neural interpretation of a simple cost function, evaluates the optimality of this controller and induces weight changes in the controller via a local learning rule. Realistic saccades are obtained with the proposed model. We speculate that the superior colliculus and the cerebellum behave quite similar to our model's neural controller and adaptation unit.

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Section: Adaptationmentioning

confidence: 99%

A neural model for the adaptive control of saccadic eye movements

Saeb

Weber

Triesch

2009

2009 International Joint Conference on Neural Networks

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“…We therefore utilise here the linear LASSO (Wang et al, 2006) as the LASSO version most suited to model simplification. This permits linear constraints while still giving a single optimal global solution for calibration fitting with specified l. In addition, the linear LASSO can be applied when there are more parameters than data points.…”

Section: The Lasso and Linear Lassomentioning

confidence: 99%

“…We used the open source software lpsolve (Berkelaar et al, 2004). The linear LASSO algorithm described by Wang et al (2006) will be more computationally efficient, which could be a factor for the large LP minimisations created from extended calibration data sets and more complex initial linear models.…”

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confidence: 99%

Toward creating simpler hydrological models: A LASSO subset selection approach

Bardsley

Vetrova

Liu

2015

Environmental Modelling & Software

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a b s t r a c tA formalised means of simplifying hydrological models concurrent with calibration is proposed for use when nonlinear models can be initially formulated as over-parameterised constrained absolute deviation regressions of nonlinear expressions. This provides a flexible modelling framework for approximation of nonlinear situations, while allowing the models to be amenable to algorithmic simplification. The degree of simplification is controlled by a user-specified forcing parameter l. That is, an original overparameterised linear model is reduced to a simpler working model which is no more complex than required for a given application. The degree of simplification is a compromise between two factors. With weak simplification most parameters will remain, risking calibration overfitting. On the other hand, a high degree of simplification generates inflexible models. The linear LASSO (Least Absolute Shrinkage and Selection Operator) is utilised for the simplification process because of its ability to deal with linear constraints in the over-parameterised initial model.

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“…The Huber function is an approximation of the more recent absolute distance based measures (l 1 -norm). Recent studies in robust estimation prefer minimizing the l 1 -norm instead of the Huber function [9]- [11]. The l 1 -norm does not bloat the distance between the estimate and the outliers and hence is robust.…”

Section: Introductionmentioning

confidence: 99%

Robust dictionary learning: Application to signal disaggregation

Majumdar

Ward²

2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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It is well known that the Euclidean norm is sensitive to outliers; yet it is widely used for minimizing it is easy. Dictionary learning is no exception -the l 2 -norm allows for easy update of the basis/dictionary atoms. In this work, we propose a robust dictionary learning method that is based on minimizing the robust l 1 -norm. The ensuing optimization is solved using the Split Bregman approach. We apply the proposed technique to signal (energy and water) disaggregation and show that it excels over existing dictionary learning techniques (based on l 2 -norm).

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Regularized Least Absolute Deviations Regression and an Efficient Algorithm for Parameter Tuning

Cited by 80 publications

References 8 publications

A neural model for the adaptive control of saccadic eye movements

A neural model for the adaptive control of saccadic eye movements

Toward creating simpler hydrological models: A LASSO subset selection approach

Robust dictionary learning: Application to signal disaggregation

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