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Assessment of Case Influence in the Lasso with a Case-Weight Adjusted Solution Path.

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Title: Assessment of Case Influence in the Lasso with a Case-Weight Adjusted Solution Path.
Authors: Jiao, Zhenbang1 (AUTHOR) jiao.180@osu.edu, Lee, Yoonkyung1 (AUTHOR)
Source: Technometrics. Aug2025, Vol. 67 Issue 3, p559-572. 14p.
Subjects: Regularization parameter, Regression analysis, Feature selection
Abstract: We study case influence in the Lasso regression using Cook's distance which measures overall change in the fitted values when one observation is deleted. Unlike in ordinary least squares regression, the estimated coefficients in the Lasso do not have a closed form due to the nondifferentiability of the l 1 penalty, and neither does Cook's distance. To find the case-deleted Lasso solution without refitting the model, we approach it from the full data solution by introducing a weight parameter ranging from 1 to 0 and generating a solution path indexed by this parameter. We show that the solution path is piecewise linear with respect to a simple function of the weight parameter under a fixed penalty. The resulting case influence is a function of the penalty and weight, and it becomes Cook's distance when the weight is 0. As the penalty parameter changes, selected variables change, and the magnitude of Cook's distance for the same data point may vary with the subset of variables selected. In addition, we introduce a case influence graph to visualize how the contribution of each data point changes with the penalty parameter. From the graph, we can identify influential points at different penalty levels and make modeling decisions accordingly. Moreover, we find that case influence graphs exhibit different patterns between underfitting and overfitting phases, which can provide additional information for model selection. [ABSTRACT FROM AUTHOR]
Copyright of Technometrics is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Assessment of Case Influence in the Lasso with a Case-Weight Adjusted Solution Path.
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  Data: <searchLink fieldCode="AR" term="%22Jiao%2C+Zhenbang%22">Jiao, Zhenbang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jiao.180@osu.edu</i><br /><searchLink fieldCode="AR" term="%22Lee%2C+Yoonkyung%22">Lee, Yoonkyung</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Technometrics%22">Technometrics</searchLink>. Aug2025, Vol. 67 Issue 3, p559-572. 14p.
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  Data: We study case influence in the Lasso regression using Cook's distance which measures overall change in the fitted values when one observation is deleted. Unlike in ordinary least squares regression, the estimated coefficients in the Lasso do not have a closed form due to the nondifferentiability of the l 1 penalty, and neither does Cook's distance. To find the case-deleted Lasso solution without refitting the model, we approach it from the full data solution by introducing a weight parameter ranging from 1 to 0 and generating a solution path indexed by this parameter. We show that the solution path is piecewise linear with respect to a simple function of the weight parameter under a fixed penalty. The resulting case influence is a function of the penalty and weight, and it becomes Cook's distance when the weight is 0. As the penalty parameter changes, selected variables change, and the magnitude of Cook's distance for the same data point may vary with the subset of variables selected. In addition, we introduce a case influence graph to visualize how the contribution of each data point changes with the penalty parameter. From the graph, we can identify influential points at different penalty levels and make modeling decisions accordingly. Moreover, we find that case influence graphs exhibit different patterns between underfitting and overfitting phases, which can provide additional information for model selection. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Technometrics is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1080/00401706.2025.2477641
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        Text: English
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        PageCount: 14
        StartPage: 559
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      – SubjectFull: Regularization parameter
        Type: general
      – SubjectFull: Regression analysis
        Type: general
      – SubjectFull: Feature selection
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      – TitleFull: Assessment of Case Influence in the Lasso with a Case-Weight Adjusted Solution Path.
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              Text: Aug2025
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