Multi-Task ElasticNet System

A Multi-Task ElasticNet System is a ElasticNet System that solves multiple ElasticNet Regression Tasks.

• Example(s):
  • sklearn.linear_model.MultiTaskElasticNet [1].
  • …
• Counter-Example(s):
  • ElasticNet System.
  • Multi-Task ElasticNet Cross-Validation System.
  • Multi-Task Lasso System.
• See: Cross-Validation Task, L1-Norm.

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References

2017

• (Scikit Learn, 2017) ⇒ http://scikit-learn.org/stable/modules/linear_model.html#multi-task-elastic-net Retrieved:2017-09-17
  • QUOTE: The MultiTaskElasticNet is an elastic-net model that estimates sparse coefficients for multiple regression problems jointly: Y is a 2D array, of shape (n_samples, n_tasks). The constraint is that the selected features are the same for all the regression problems, also called tasks.

    Mathematically, it consists of a linear model trained with a mixed [math]\displaystyle{ \ell_1 }[/math] [math]\displaystyle{ \ell_2 }[/math] prior and [math]\displaystyle{ \ell_2 }[/math] prior as regularizer. The objective function to minimize is:

    [math]\displaystyle{ \underset{W}{min\,} { \frac{1}{2n_{samples}} ||X W - Y||_{Fro}^2 + \alpha \rho ||W||_{2 1} +\frac{\alpha(1-\rho)}{2} ||W||_{Fro}^2} }[/math]

    The implementation in the class MultiTaskElasticNet uses coordinate descent as the algorithm to fit the coefficients.

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

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