ElasticNet System

An ElasticNet System is a mixed LASSO Regression System and Ridge Regression System that implements an ElasticNet Algorithm to solve a ElasticNet Regression Task.

• AKA: ElasticNet Regression System.
  • …
• Example(s):
  • sklearn.linear_model.ElasticNet [1]:
    • Lasso and Elastic Net for Sparse Signals
    • Lasso and Elastic Net
• Counter-Example(s):
  • LASSO Regression System.
  • Ridge Regression System.
  • Multi-Task ElasticNet System.
  • ElasticNet Cross-Validation System.
  • Multi-Task ElasticNet Cross-Validation System.
• See: Cross-Validation Task, L1-Norm, L2-norm.

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References

2017

• (Scikit Learn, 2017) ⇒ http://scikit-learn.org/stable/modules/linear_model.html#elastic-net Retrieved:2017-09-17
  • QUOTE: ElasticNet is a linear regression model trained with L1 and L2 prior as regularizer. This combination allows for learning a sparse model where few of the weights are non-zero like Lasso, while still maintaining the regularization properties of Ridge. We control the convex combination of L1 and L2 using the l1_ratio parameter.

     Elastic-net is useful when there are multiple features which are correlated with one another. Lasso is likely to pick one of these at random, while elastic-net is likely to pick both.

    A practical advantage of trading-off between Lasso and Ridge is it allows Elastic-Net to inherit some of Ridge’s stability under rotation.

    The objective function to minimize is in this case

    [math]\displaystyle{ \underset{w}{min\,} { \frac{1}{2n_{samples}} ||X w - y||_2 ^ 2 + \alpha \rho ||w||_1 + \frac{\alpha(1-\rho)}{2} ||w||_2 ^ 2} }[/math]

    The class ElasticNetCV can be used to set the parameters alphaalpha ([math]\displaystyle{ \alpha }[/math]) and l1_ratio ([math]\displaystyle{ \rho }[/math]) by cross-validation.

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